{"model_name":"claude-4.5-opus","codes":{"1":{"ahc001":"#include \nusing namespace std;\n\nconst int W = 10000;\nint n;\nvector px, py, rr;\nint a[201], b[201], c[201], d[201];\n\nbool canExpand(int i, int dir) {\n int na = a[i], nb = b[i], nc = c[i], nd = d[i];\n if (dir == 0) na--;\n else if (dir == 1) nc++;\n else if (dir == 2) nb--;\n else nd++;\n \n if (na < 0 || nc > W || nb < 0 || nd > W) return false;\n \n for (int j = 0; j < n; j++) {\n if (i == j) continue;\n if (!(nc <= a[j] || c[j] <= na || nd <= b[j] || d[j] <= nb)) return false;\n }\n return true;\n}\n\nvoid expand(int i, int dir) {\n if (dir == 0) a[i]--;\n else if (dir == 1) c[i]++;\n else if (dir == 2) b[i]--;\n else d[i]++;\n}\n\nlong long area(int i) {\n return (long long)(c[i] - a[i]) * (d[i] - b[i]);\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> n;\n px.resize(n); py.resize(n); rr.resize(n);\n \n for (int i = 0; i < n; i++) {\n cin >> px[i] >> py[i] >> rr[i];\n a[i] = px[i]; b[i] = py[i]; c[i] = px[i]+1; d[i] = py[i]+1;\n }\n \n auto start = chrono::high_resolution_clock::now();\n \n while (true) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > 4.8) break;\n \n bool changed = false;\n \n vector order(n);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int i, int j) {\n return rr[i] - area(i) > rr[j] - area(j);\n });\n \n for (int i : order) {\n for (int dir = 0; dir < 4; dir++) {\n if (canExpand(i, dir)) {\n expand(i, dir);\n changed = true;\n }\n }\n }\n \n if (!changed) break;\n }\n \n // Shrink rectangles that are too big\n for (int iter = 0; iter < 1000; iter++) {\n for (int i = 0; i < n; i++) {\n if (area(i) <= rr[i]) continue;\n for (int dir = 0; dir < 4; dir++) {\n int na = a[i], nb = b[i], nc = c[i], nd = d[i];\n if (dir == 0) na++;\n else if (dir == 1) nc--;\n else if (dir == 2) nb++;\n else nd--;\n \n if (na >= nc || nb >= nd) continue;\n if (!(na <= px[i] && px[i] < nc && nb <= py[i] && py[i] < nd)) continue;\n \n long long newArea = (long long)(nc - na) * (nd - nb);\n if (newArea >= rr[i]) {\n a[i] = na; b[i] = nb; c[i] = nc; d[i] = nd;\n }\n }\n }\n }\n \n for (int i = 0; i < n; i++) {\n cout << a[i] << \" \" << b[i] << \" \" << c[i] << \" \" << d[i] << \"\\n\";\n }\n \n return 0;\n}","ahc002":"#include \nusing namespace std;\n\nconst int N = 50;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nconst char dc[] = {'U', 'D', 'L', 'R'};\n\nint t[N][N], p[N][N];\nint si, sj;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> si >> sj;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n cin >> t[i][j];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n cin >> p[i][j];\n \n struct State {\n int x, y;\n int score;\n bitset<2500> usedTiles;\n string path;\n };\n \n const int BEAM_WIDTH = 400;\n \n vector beam;\n State init;\n init.x = si;\n init.y = sj;\n init.score = p[si][sj];\n init.usedTiles.set(t[si][sj]);\n init.path = \"\";\n beam.push_back(init);\n \n string bestPath = \"\";\n int bestScore = init.score;\n \n auto startTime = chrono::steady_clock::now();\n \n while (!beam.empty()) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration_cast(now - startTime).count() > 1900) {\n for (const auto& state : beam) {\n if (state.score > bestScore) {\n bestScore = state.score;\n bestPath = state.path;\n }\n }\n break;\n }\n \n vector nextBeam;\n nextBeam.reserve(beam.size() * 4);\n \n for (const auto& state : beam) {\n bool canExtend = false;\n for (int d = 0; d < 4; d++) {\n int nx = state.x + dx[d];\n int ny = state.y + dy[d];\n if (nx < 0 || nx >= N || ny < 0 || ny >= N) continue;\n if (state.usedTiles[t[nx][ny]]) continue;\n \n canExtend = true;\n State newState;\n newState.x = nx;\n newState.y = ny;\n newState.score = state.score + p[nx][ny];\n newState.usedTiles = state.usedTiles;\n newState.usedTiles.set(t[nx][ny]);\n newState.path = state.path + dc[d];\n nextBeam.push_back(move(newState));\n }\n \n if (!canExtend && state.score > bestScore) {\n bestScore = state.score;\n bestPath = state.path;\n }\n }\n \n if (nextBeam.size() > BEAM_WIDTH) {\n nth_element(nextBeam.begin(), nextBeam.begin() + BEAM_WIDTH, nextBeam.end(),\n [](const State& a, const State& b) { return a.score > b.score; });\n nextBeam.resize(BEAM_WIDTH);\n }\n \n beam = move(nextBeam);\n }\n \n cout << bestPath << endl;\n \n return 0;\n}","ahc003":"#include \nusing namespace std;\n\nconst int N = 30;\ndouble h[N][N-1], v[N-1][N];\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n fill(&h[0][0], &h[0][0] + N*(N-1), 5000.0);\n fill(&v[0][0], &v[0][0] + (N-1)*N, 5000.0);\n \n for (int q = 0; q < 1000; q++) {\n int si, sj, ti, tj;\n cin >> si >> sj >> ti >> tj;\n \n auto idx = [](int i, int j) { return i * N + j; };\n vector dist(N*N, 1e18);\n vector prv(N*N, -1);\n \n priority_queue, vector>, greater<>> pq;\n dist[idx(si, sj)] = 0;\n pq.push({0, idx(si, sj)});\n \n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > dist[u]) continue;\n int i = u / N, j = u % N;\n \n auto relax = [&](int ni, int nj, double w) {\n int nu = idx(ni, nj);\n if (dist[u] + w < dist[nu]) {\n dist[nu] = dist[u] + w;\n prv[nu] = u;\n pq.push({dist[nu], nu});\n }\n };\n \n if (i > 0) relax(i-1, j, v[i-1][j]);\n if (i < N-1) relax(i+1, j, v[i][j]);\n if (j > 0) relax(i, j-1, h[i][j-1]);\n if (j < N-1) relax(i, j+1, h[i][j]);\n }\n \n string path = \"\";\n vector> edges;\n \n int cur = idx(ti, tj);\n while (prv[cur] != -1) {\n int ci = cur / N, cj = cur % N;\n int pi = prv[cur] / N, pj = prv[cur] % N;\n \n if (ci < pi) { path += 'U'; edges.emplace_back(1, ci, cj); }\n else if (ci > pi) { path += 'D'; edges.emplace_back(1, pi, pj); }\n else if (cj < pj) { path += 'L'; edges.emplace_back(0, ci, cj); }\n else { path += 'R'; edges.emplace_back(0, pi, pj); }\n \n cur = prv[cur];\n }\n \n reverse(path.begin(), path.end());\n cout << path << \"\\n\" << flush;\n \n int feedback;\n cin >> feedback;\n \n double est = 0;\n for (auto& [t, ei, ej] : edges) {\n est += (t == 0) ? h[ei][ej] : v[ei][ej];\n }\n \n double ratio = feedback / est;\n double alpha = 0.2;\n for (auto& [t, ei, ej] : edges) {\n double& w = (t == 0) ? h[ei][ej] : v[ei][ej];\n w *= (1.0 - alpha + alpha * ratio);\n }\n }\n \n return 0;\n}","ahc004":"#include \nusing namespace std;\n\nconst int N = 20;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n, m;\n cin >> n >> m;\n \n vector strs(m);\n for(int i = 0; i < m; i++) cin >> strs[i];\n \n vector order(m);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int a, int b) {\n return strs[a].size() > strs[b].size();\n });\n \n char grid[N][N];\n fill(&grid[0][0], &grid[N][0], '.');\n \n // Greedy placement with max overlap preference\n for(int idx : order) {\n const string& s = strs[idx];\n int bestR = -1, bestC, bestD, bestOv = -1;\n \n for(int r = 0; r < N; r++) {\n for(int c = 0; c < N; c++) {\n for(int d = 0; d < 2; d++) {\n bool can = true;\n int ov = 0;\n for(int p = 0; p < (int)s.size() && can; p++) {\n int ni = d ? (r + p) % N : r;\n int nj = d ? c : (c + p) % N;\n if(grid[ni][nj] != '.' && grid[ni][nj] != s[p]) can = false;\n if(grid[ni][nj] != '.') ov++;\n }\n if(can && ov > bestOv) {\n bestOv = ov;\n bestR = r; bestC = c; bestD = d;\n }\n }\n }\n }\n \n if(bestR >= 0) {\n for(int p = 0; p < (int)s.size(); p++) {\n int ni = bestD ? (bestR + p) % N : bestR;\n int nj = bestD ? bestC : (bestC + p) % N;\n grid[ni][nj] = s[p];\n }\n }\n }\n \n // Fill remaining cells randomly\n mt19937 rng(42);\n for(int i = 0; i < N; i++) {\n for(int j = 0; j < N; j++) {\n if(grid[i][j] == '.') grid[i][j] = 'A' + rng() % 8;\n }\n }\n \n // Count function for SA\n auto countMatched = [&]() {\n int cnt = 0;\n for(const auto& s : strs) {\n bool found = false;\n for(int r = 0; r < N && !found; r++) {\n for(int c = 0; c < N && !found; c++) {\n for(int d = 0; d < 2 && !found; d++) {\n bool ok = true;\n for(int p = 0; p < (int)s.size() && ok; p++) {\n int ni = d ? (r + p) % N : r;\n int nj = d ? c : (c + p) % N;\n if(grid[ni][nj] != s[p]) ok = false;\n }\n if(ok) found = true;\n }\n }\n }\n if(found) cnt++;\n }\n return cnt;\n };\n \n // Simple SA to improve\n char bestGrid[N][N];\n memcpy(bestGrid, grid, sizeof(grid));\n int bestScore = countMatched();\n int curScore = bestScore;\n \n auto start = chrono::high_resolution_clock::now();\n double T = 2.0;\n \n while(true) {\n auto now = chrono::high_resolution_clock::now();\n if(chrono::duration(now - start).count() > 2.7) break;\n \n int i = rng() % N, j = rng() % N;\n char old = grid[i][j];\n char newc = 'A' + rng() % 8;\n if(newc == old) continue;\n \n grid[i][j] = newc;\n int newScore = countMatched();\n \n if(newScore >= curScore || (rng() & 0xFFFF) < 65536.0 * exp((newScore - curScore) / T)) {\n curScore = newScore;\n if(newScore > bestScore) {\n bestScore = newScore;\n memcpy(bestGrid, grid, sizeof(grid));\n }\n } else {\n grid[i][j] = old;\n }\n T *= 0.9999;\n }\n \n for(int i = 0; i < N; i++) {\n cout << string(bestGrid[i], bestGrid[i] + N) << '\\n';\n }\n}","ahc005":"#include \nusing namespace std;\n\nint N, si, sj;\nvector grid;\nvector> visible;\nint visible_count = 0;\n\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nconst char dir_char[] = {'U', 'D', 'L', 'R'};\n\ninline bool is_road(int i, int j) {\n return i >= 0 && i < N && j >= 0 && j < N && grid[i][j] != '#';\n}\n\nvoid mark_visible(int i, int j) {\n if (!visible[i][j]) { visible[i][j] = true; visible_count++; }\n for (int jj = j - 1; jj >= 0 && is_road(i, jj); jj--)\n if (!visible[i][jj]) { visible[i][jj] = true; visible_count++; }\n for (int jj = j + 1; jj < N && is_road(i, jj); jj++)\n if (!visible[i][jj]) { visible[i][jj] = true; visible_count++; }\n for (int ii = i - 1; ii >= 0 && is_road(ii, j); ii--)\n if (!visible[ii][j]) { visible[ii][j] = true; visible_count++; }\n for (int ii = i + 1; ii < N && is_road(ii, j); ii++)\n if (!visible[ii][j]) { visible[ii][j] = true; visible_count++; }\n}\n\nint count_new_visible(int i, int j) {\n int cnt = !visible[i][j];\n for (int jj = j - 1; jj >= 0 && is_road(i, jj); jj--) cnt += !visible[i][jj];\n for (int jj = j + 1; jj < N && is_road(i, jj); jj++) cnt += !visible[i][jj];\n for (int ii = i - 1; ii >= 0 && is_road(ii, j); ii--) cnt += !visible[ii][j];\n for (int ii = i + 1; ii < N && is_road(ii, j); ii++) cnt += !visible[ii][j];\n return cnt;\n}\n\npair>, vector>>> dijkstra(int si, int sj) {\n vector> dist(N, vector(N, INT_MAX));\n vector>> parent(N, vector>(N, {-1,-1}));\n priority_queue, vector>, greater<>> pq;\n dist[si][sj] = 0; pq.push({0, si, sj});\n while (!pq.empty()) {\n auto [d, i, j] = pq.top(); pq.pop();\n if (d > dist[i][j]) continue;\n for (int k = 0; k < 4; k++) {\n int ni = i + dx[k], nj = j + dy[k];\n if (is_road(ni, nj)) {\n int c = grid[ni][nj] - '0';\n if (dist[i][j] + c < dist[ni][nj]) {\n dist[ni][nj] = dist[i][j] + c;\n parent[ni][nj] = {i, j};\n pq.push({dist[ni][nj], ni, nj});\n }\n }\n }\n }\n return {dist, parent};\n}\n\nstring get_path(int i1, int j1, int i2, int j2, vector>>& parent) {\n string path;\n int ci = i2, cj = j2;\n while (ci != i1 || cj != j1) {\n auto [pi, pj] = parent[ci][cj];\n for (int k = 0; k < 4; k++) if (pi + dx[k] == ci && pj + dy[k] == cj) { path += dir_char[k]; break; }\n ci = pi; cj = pj;\n }\n reverse(path.begin(), path.end());\n return path;\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> si >> sj;\n grid.resize(N);\n for (int i = 0; i < N; i++) cin >> grid[i];\n \n int total_roads = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (is_road(i, j)) total_roads++;\n \n visible.assign(N, vector(N, false));\n int cur_i = si, cur_j = sj;\n string result;\n mark_visible(cur_i, cur_j);\n \n while (visible_count < total_roads) {\n auto [dist, parent] = dijkstra(cur_i, cur_j);\n int best_i = -1, best_j = -1; double best_score = -1;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (dist[i][j] == INT_MAX || dist[i][j] == 0) continue;\n int nv = count_new_visible(i, j);\n if (nv == 0) continue;\n double score = (double)nv / dist[i][j];\n if (score > best_score) { best_score = score; best_i = i; best_j = j; }\n }\n if (best_i == -1) break;\n string path = get_path(cur_i, cur_j, best_i, best_j, parent);\n result += path;\n int ti = cur_i, tj = cur_j;\n for (char c : path) {\n if (c == 'U') ti--; else if (c == 'D') ti++; else if (c == 'L') tj--; else tj++;\n mark_visible(ti, tj);\n }\n cur_i = best_i; cur_j = best_j;\n }\n \n if (cur_i != si || cur_j != sj) {\n auto [dist, parent] = dijkstra(cur_i, cur_j);\n result += get_path(cur_i, cur_j, si, sj, parent);\n }\n \n cout << result << endl;\n return 0;\n}","future-contest-2022-qual":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K, R;\n cin >> N >> M >> K >> R;\n \n vector> d(N, vector(K));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < K; j++)\n cin >> d[i][j];\n \n vector> deps(N), rdeps(N);\n for (int i = 0; i < R; i++) {\n int u, v;\n cin >> u >> v;\n u--; v--;\n deps[v].push_back(u);\n rdeps[u].push_back(v);\n }\n \n vector taskStatus(N, -1), memberStatus(M, -1), memberStartDay(M, 0);\n vector> skillEst(M, vector(K, 25.0));\n \n auto estimateTime = [&](int task, int member) -> double {\n double w = 0;\n for (int k = 0; k < K; k++)\n w += max(0.0, (double)d[task][k] - skillEst[member][k]);\n return max(1.0, w);\n };\n \n vector urgency(N, 1);\n for (int i = N - 1; i >= 0; i--)\n for (int v : rdeps[i])\n urgency[i] += urgency[v];\n \n for (int day = 1; ; day++) {\n vector availTasks;\n for (int i = 0; i < N; i++) {\n if (taskStatus[i] != -1) continue;\n bool ok = true;\n for (int dep : deps[i])\n if (taskStatus[dep] != 1) { ok = false; break; }\n if (ok) availTasks.push_back(i);\n }\n \n sort(availTasks.begin(), availTasks.end(), [&](int a, int b) {\n return urgency[a] > urgency[b];\n });\n \n vector freeMembers;\n for (int j = 0; j < M; j++)\n if (memberStatus[j] == -1) freeMembers.push_back(j);\n \n vector> assignments;\n for (int task : availTasks) {\n if (freeMembers.empty()) break;\n int bestIdx = 0;\n double bestTime = estimateTime(task, freeMembers[0]);\n for (int i = 1; i < (int)freeMembers.size(); i++) {\n double t = estimateTime(task, freeMembers[i]);\n if (t < bestTime) { bestTime = t; bestIdx = i; }\n }\n int member = freeMembers[bestIdx];\n assignments.push_back({member + 1, task + 1});\n taskStatus[task] = 0;\n memberStatus[member] = task;\n memberStartDay[member] = day;\n freeMembers.erase(freeMembers.begin() + bestIdx);\n }\n \n cout << assignments.size();\n for (auto& [a, b] : assignments) cout << \" \" << a << \" \" << b;\n cout << \"\\n\";\n cout.flush();\n \n int n; cin >> n;\n if (n == -1) break;\n \n for (int i = 0; i < n; i++) {\n int f; cin >> f; f--;\n int task = memberStatus[f];\n int timeTaken = day - memberStartDay[f] + 1;\n taskStatus[task] = 1;\n memberStatus[f] = -1;\n \n if (timeTaken == 1) {\n for (int k = 0; k < K; k++)\n skillEst[f][k] = max(skillEst[f][k], (double)d[task][k]);\n } else {\n double currW = 0;\n for (int k = 0; k < K; k++)\n currW += max(0.0, (double)d[task][k] - skillEst[f][k]);\n if (currW > 0.5) {\n double ratio = timeTaken / currW;\n for (int k = 0; k < K; k++) {\n double gap = d[task][k] - skillEst[f][k];\n if (gap > 0) skillEst[f][k] = d[task][k] - gap * ratio;\n }\n }\n }\n }\n }\n return 0;\n}","ahc006":"#include \nusing namespace std;\n\nconst int N = 1000, M = 50, CX = 400, CY = 400;\nint ordA[N], ordB[N], ordC[N], ordD[N];\nmt19937 rng(chrono::steady_clock::now().time_since_epoch().count());\n\ninline int manhattan(int x1, int y1, int x2, int y2) {\n return abs(x1 - x2) + abs(y1 - y2);\n}\n\npair>, int> buildGreedyRoute(const vector& selected) {\n vector> events;\n events.reserve(2 * M);\n vector picked(N, false), delivered(N, false);\n int cx = CX, cy = CY, totalCost = 0;\n \n for (int i = 0; i < 2 * M; i++) {\n int best = -1, bestDist = INT_MAX;\n bool isDelivery = false;\n \n for (int idx : selected) {\n if (!picked[idx]) {\n int d = manhattan(cx, cy, ordA[idx], ordB[idx]);\n if (d < bestDist) { bestDist = d; best = idx; isDelivery = false; }\n } else if (!delivered[idx]) {\n int d = manhattan(cx, cy, ordC[idx], ordD[idx]);\n if (d < bestDist) { bestDist = d; best = idx; isDelivery = true; }\n }\n }\n \n totalCost += bestDist;\n if (isDelivery) { cx = ordC[best]; cy = ordD[best]; delivered[best] = true; }\n else { cx = ordA[best]; cy = ordB[best]; picked[best] = true; }\n events.push_back({best, isDelivery});\n }\n totalCost += manhattan(cx, cy, CX, CY);\n return {events, totalCost};\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n auto startTime = chrono::steady_clock::now();\n for (int i = 0; i < N; i++) cin >> ordA[i] >> ordB[i] >> ordC[i] >> ordD[i];\n \n auto elapsed = [&]() {\n return chrono::duration(chrono::steady_clock::now() - startTime).count();\n };\n \n vector> orderedByCenter(N);\n for (int i = 0; i < N; i++) {\n int d = manhattan(CX, CY, ordA[i], ordB[i]) + manhattan(CX, CY, ordC[i], ordD[i]);\n orderedByCenter[i] = {d, i};\n }\n sort(orderedByCenter.begin(), orderedByCenter.end());\n \n vector selected(M), unselected(N - M);\n for (int i = 0; i < M; i++) selected[i] = orderedByCenter[i].second;\n for (int i = 0; i < N - M; i++) unselected[i] = orderedByCenter[M + i].second;\n \n auto [bestEvents, bestCost] = buildGreedyRoute(selected);\n vector bestSelected = selected;\n int currentCost = bestCost;\n double temp = 3000.0;\n \n while (elapsed() < 1.85) {\n int selIdx = rng() % M;\n int unselIdx = rng() % (N - M);\n \n swap(selected[selIdx], unselected[unselIdx]);\n auto [events, cost] = buildGreedyRoute(selected);\n \n int delta = cost - currentCost;\n bool accept = delta < 0 || exp(-delta / temp) > (rng() % 10000) / 10000.0;\n \n if (accept) {\n currentCost = cost;\n if (cost < bestCost) {\n bestCost = cost;\n bestSelected = selected;\n bestEvents = events;\n }\n } else {\n swap(selected[selIdx], unselected[unselIdx]);\n }\n temp *= 0.99995;\n }\n \n cout << M;\n for (int i = 0; i < M; i++) cout << \" \" << (bestSelected[i] + 1);\n cout << \"\\n\" << (2 * M + 2) << \" \" << CX << \" \" << CY;\n for (const auto& [idx, isDel] : bestEvents) {\n if (isDel) cout << \" \" << ordC[idx] << \" \" << ordD[idx];\n else cout << \" \" << ordA[idx] << \" \" << ordB[idx];\n }\n cout << \" \" << CX << \" \" << CY << \"\\n\";\n \n return 0;\n}","ahc007":"#include \nusing namespace std;\n\nclass UnionFind {\n vector parent, rank_;\npublic:\n UnionFind(int n) : parent(n), rank_(n, 0) {\n iota(parent.begin(), parent.end(), 0);\n }\n int find(int x) {\n if (parent[x] != x) parent[x] = find(parent[x]);\n return parent[x];\n }\n bool unite(int x, int y) {\n int px = find(x), py = find(y);\n if (px == py) return false;\n if (rank_[px] < rank_[py]) swap(px, py);\n parent[py] = px;\n if (rank_[px] == rank_[py]) rank_[px]++;\n return true;\n }\n bool same(int x, int y) {\n return find(x) == find(y);\n }\n};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n const int N = 400, M = 1995;\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) {\n cin >> x[i] >> y[i];\n }\n \n vector u(M), v(M), d(M);\n for (int i = 0; i < M; i++) {\n cin >> u[i] >> v[i];\n double dx = x[u[i]] - x[v[i]];\n double dy = y[u[i]] - y[v[i]];\n d[i] = (int)round(sqrt(dx * dx + dy * dy));\n }\n \n UnionFind uf(N);\n int components = N;\n \n for (int i = 0; i < M; i++) {\n int l;\n cin >> l;\n \n int pu = uf.find(u[i]);\n int pv = uf.find(v[i]);\n \n bool already_connected = (pu == pv);\n double ratio = (double)l / d[i];\n \n bool adopt = false;\n \n if (!already_connected) {\n int useful_remaining = 0;\n int same_pair_remaining = 0;\n for (int j = i + 1; j < M; j++) {\n int uj = uf.find(u[j]);\n int vj = uf.find(v[j]);\n if (uj != vj) {\n useful_remaining++;\n if ((uj == pu && vj == pv) || (uj == pv && vj == pu)) {\n same_pair_remaining++;\n }\n }\n }\n \n int needed = components - 1;\n \n if (useful_remaining < needed * 2) {\n adopt = true;\n } else {\n double k = same_pair_remaining;\n double expected_min = 1.0 + 2.0 / (k + 2);\n double threshold = expected_min + 0.2;\n \n if (ratio <= threshold || same_pair_remaining == 0) {\n adopt = true;\n }\n }\n }\n \n if (adopt) {\n uf.unite(u[i], v[i]);\n components--;\n }\n \n cout << (adopt ? 1 : 0) << \"\\n\" << flush;\n }\n \n return 0;\n}","ahc008":"#include \nusing namespace std;\n\nint N, M;\nvector> pets;\nvector> humans;\nbool blocked[32][32];\n\nbool pet_at(int x, int y) {\n for (auto& p : pets) if (p[0] == x && p[1] == y) return true;\n return false;\n}\n\nbool pet_adjacent(int x, int y) {\n int dx[] = {0, -1, 1, 0, 0}, dy[] = {0, 0, 0, -1, 1};\n for (int d = 0; d < 5; d++) if (pet_at(x+dx[d], y+dy[d])) return true;\n return false;\n}\n\nbool can_place(int x, int y) {\n if (x < 1 || x > 30 || y < 1 || y > 30 || blocked[x][y]) return false;\n for (auto& h : humans) if (h[0] == x && h[1] == y) return false;\n return !pet_adjacent(x, y);\n}\n\nbool passable(int x, int y) {\n return x >= 1 && x <= 30 && y >= 1 && y <= 30 && !blocked[x][y];\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N; pets.resize(N);\n for (int i = 0; i < N; i++) cin >> pets[i][0] >> pets[i][1] >> pets[i][2];\n cin >> M; humans.resize(M);\n for (int i = 0; i < M; i++) cin >> humans[i][0] >> humans[i][1];\n \n set> target;\n for (int i = 1; i <= 30; i++) {\n for (int c : {7, 14, 21, 28}) {\n target.insert({i, c});\n target.insert({c, i});\n }\n }\n \n int dx[] = {-1, 1, 0, 0}, dy[] = {0, 0, -1, 1};\n char wc[] = {'u', 'd', 'l', 'r'}, mc[] = {'U', 'D', 'L', 'R'};\n \n for (int turn = 0; turn < 300; turn++) {\n string action(M, '.');\n \n for (int i = 0; i < M; i++) {\n int hx = humans[i][0], hy = humans[i][1];\n int best = -1, bestd = -1;\n \n for (int d = 0; d < 4; d++) {\n int nx = hx + dx[d], ny = hy + dy[d];\n if (can_place(nx, ny)) {\n int sc = target.count({nx, ny}) ? 100 : 1;\n if (sc > best) { best = sc; bestd = d; }\n }\n }\n \n if (bestd >= 0) {\n action[i] = wc[bestd];\n } else {\n int minD = INT_MAX, moveD = -1;\n for (auto& [tx, ty] : target) {\n if (blocked[tx][ty]) continue;\n int dist = abs(hx-tx) + abs(hy-ty);\n if (dist > 0 && dist < minD) minD = dist;\n }\n for (int d = 0; d < 4; d++) {\n int nx = hx + dx[d], ny = hy + dy[d];\n if (!passable(nx, ny) || pet_at(nx, ny)) continue;\n for (auto& [tx, ty] : target) {\n if (blocked[tx][ty]) continue;\n if (abs(nx-tx) + abs(ny-ty) < minD) {\n minD = abs(nx-tx) + abs(ny-ty);\n moveD = d;\n }\n }\n }\n if (moveD >= 0) action[i] = mc[moveD];\n }\n }\n \n cout << action << \"\\n\" << flush;\n \n for (int i = 0; i < M; i++) {\n char a = action[i];\n for (int d = 0; d < 4; d++) {\n if (a == wc[d]) blocked[humans[i][0]+dx[d]][humans[i][1]+dy[d]] = true;\n if (a == mc[d]) { humans[i][0] += dx[d]; humans[i][1] += dy[d]; }\n }\n }\n \n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (char c : s) {\n if (c == 'U') pets[i][0]--;\n else if (c == 'D') pets[i][0]++;\n else if (c == 'L') pets[i][1]--;\n else if (c == 'R') pets[i][1]++;\n }\n }\n }\n return 0;\n}","ahc009":"#include \nusing namespace std;\n\nint N = 20;\nint si, sj, ti, tj;\ndouble p;\nbool hwall[20][19];\nbool vwall[19][20];\n\nbool canMove(int i, int j, char dir) {\n if (dir == 'U') return i > 0 && !vwall[i-1][j];\n if (dir == 'D') return i < 19 && !vwall[i][j];\n if (dir == 'L') return j > 0 && !hwall[i][j-1];\n if (dir == 'R') return j < 19 && !hwall[i][j];\n return false;\n}\n\npair doMove(int i, int j, char dir) {\n if (!canMove(i, j, dir)) return {i, j};\n if (dir == 'U') return {i-1, j};\n if (dir == 'D') return {i+1, j};\n if (dir == 'L') return {i, j-1};\n if (dir == 'R') return {i, j+1};\n return {i, j};\n}\n\ndouble evaluate(const string& s) {\n vector> prob(N, vector(N, 0));\n prob[si][sj] = 1.0;\n double expectedScore = 0;\n for (int t = 1; t <= (int)s.size(); t++) {\n char dir = s[t-1];\n vector> newProb(N, vector(N, 0));\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (prob[i][j] < 1e-15) continue;\n auto [ni, nj] = doMove(i, j, dir);\n if (ni == ti && nj == tj) expectedScore += (1-p) * prob[i][j] * (401 - t);\n else newProb[ni][nj] += (1-p) * prob[i][j];\n newProb[i][j] += p * prob[i][j];\n }\n }\n prob = newProb;\n }\n return expectedScore;\n}\n\nstring bfsWithOrder(vector& order) {\n vector> dist(N, vector(N, -1));\n vector>> parent(N, vector>(N, {-1,-1}));\n vector> fromDir(N, vector(N, ' '));\n queue> q;\n q.push({si, sj});\n dist[si][sj] = 0;\n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (char d : order) {\n auto [ni, nj] = doMove(i, j, d);\n if (ni == i && nj == j) continue;\n if (dist[ni][nj] == -1) {\n dist[ni][nj] = dist[i][j] + 1;\n parent[ni][nj] = {i, j};\n fromDir[ni][nj] = d;\n q.push({ni, nj});\n }\n }\n }\n string path;\n int ci = ti, cj = tj;\n while (ci != si || cj != sj) {\n path += fromDir[ci][cj];\n auto [pi, pj] = parent[ci][cj];\n ci = pi; cj = pj;\n }\n reverse(path.begin(), path.end());\n return path;\n}\n\nmt19937 rng(42);\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n auto startTime = chrono::steady_clock::now();\n cin >> si >> sj >> ti >> tj >> p;\n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < 19; j++) hwall[i][j] = (s[j] == '1');\n }\n for (int i = 0; i < 19; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) vwall[i][j] = (s[j] == '1');\n }\n string best;\n double bestScore = -1;\n vector order = {'U', 'D', 'L', 'R'};\n while (true) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration_cast(now - startTime).count() > 1800) break;\n shuffle(order.begin(), order.end(), rng);\n string path = bfsWithOrder(order);\n int pathLen = path.size();\n for (int rep = 1; rep * pathLen <= 200; rep++) {\n string result;\n for (char c : path) for (int i = 0; i < rep; i++) result += c;\n double score = evaluate(result);\n if (score > bestScore) { bestScore = score; best = result; }\n }\n }\n cout << best << endl;\n return 0;\n}","ahc010":"#include \nusing namespace std;\n\nconst int N = 30;\nint tiles[N][N];\nint rotation[N][N];\n\nconst int di[] = {0, -1, 0, 1};\nconst int dj[] = {-1, 0, 1, 0};\n\nconst int to_arr[8][4] = {\n {1, 0, -1, -1}, {3, -1, -1, 0}, {-1, -1, 3, 2}, {-1, 2, 1, -1},\n {1, 0, 3, 2}, {3, 2, 1, 0}, {2, -1, 0, -1}, {-1, 3, -1, 1},\n};\n\ninline int getState(int i, int j) {\n int t = tiles[i][j], r = rotation[i][j];\n if (t < 4) return (t + r) % 4;\n if (t < 6) return 4 + (t - 4 + r) % 2;\n return 6 + (t - 6 + r) % 2;\n}\n\nint traceLoop(int si, int sj, int sd) {\n int i = si, j = sj, d = sd, length = 0;\n do {\n int state = getState(i, j);\n int d2 = to_arr[state][d];\n if (d2 == -1) return 0;\n length++;\n if (length > 4 * N * N) return 0;\n i += di[d2]; j += dj[d2];\n if ((unsigned)i >= N || (unsigned)j >= N) return 0;\n d = (d2 + 2) % 4;\n } while (i != si || j != sj || d != sd);\n return length;\n}\n\npair computeTopTwoLoops() {\n static bool visited[N][N][4];\n memset(visited, 0, sizeof(visited));\n int top1 = 0, top2 = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n int state = getState(i, j);\n for (int d = 0; d < 4; d++) {\n if (to_arr[state][d] == -1 || visited[i][j][d]) continue;\n int len = traceLoop(i, j, d);\n if (len > 0) {\n if (len > top1) { top2 = top1; top1 = len; }\n else if (len > top2) { top2 = len; }\n int ci = i, cj = j, cd = d;\n do {\n visited[ci][cj][cd] = true;\n int st = getState(ci, cj);\n int d2 = to_arr[st][cd];\n ci += di[d2]; cj += dj[d2];\n cd = (d2 + 2) % 4;\n } while (ci != i || cj != j || cd != d);\n }\n }\n }\n }\n return {top1, top2};\n}\n\nint best_rotation[N][N];\nlong long best_score;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) {\n tiles[i][j] = s[j] - '0';\n rotation[i][j] = 0;\n }\n }\n \n mt19937 rng(42);\n auto start_time = chrono::steady_clock::now();\n \n auto [l1, l2] = computeTopTwoLoops();\n best_score = (long long)l1 * l2;\n memcpy(best_rotation, rotation, sizeof(rotation));\n long long current_score = best_score;\n \n const double TIME_LIMIT = 1.9;\n \n while (true) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start_time).count();\n if (elapsed > TIME_LIMIT) break;\n \n double T = 1000.0 * pow(0.0001, elapsed / TIME_LIMIT);\n \n int i = rng() % N, j = rng() % N;\n int old_rot = rotation[i][j];\n int new_rot = (old_rot + 1 + rng() % 3) % 4;\n \n rotation[i][j] = new_rot;\n auto [nl1, nl2] = computeTopTwoLoops();\n long long new_score = (long long)nl1 * nl2;\n \n double delta = (double)(new_score - current_score);\n if (delta >= 0 || uniform_real_distribution(0, 1)(rng) < exp(delta / T)) {\n current_score = new_score;\n if (new_score > best_score) {\n best_score = new_score;\n memcpy(best_rotation, rotation, sizeof(rotation));\n }\n } else {\n rotation[i][j] = old_rot;\n }\n }\n \n string result;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n result += ('0' + best_rotation[i][j]);\n cout << result << endl;\n \n return 0;\n}","ahc011":"#include \nusing namespace std;\n\nint N, T;\nint dr[] = {-1, 1, 0, 0};\nint dc[] = {0, 0, -1, 1};\nchar dc_char[] = {'U', 'D', 'L', 'R'};\n\nint hexChar(char c) {\n return (c >= '0' && c <= '9') ? c - '0' : c - 'a' + 10;\n}\n\nint calcScore(const vector>& board) {\n vector> adj(N * N);\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (board[i][j] == 0) continue;\n if (i + 1 < N && board[i+1][j] != 0 && (board[i][j] & 8) && (board[i+1][j] & 2)) {\n adj[i*N+j].push_back((i+1)*N+j);\n adj[(i+1)*N+j].push_back(i*N+j);\n }\n if (j + 1 < N && board[i][j+1] != 0 && (board[i][j] & 4) && (board[i][j+1] & 1)) {\n adj[i*N+j].push_back(i*N+j+1);\n adj[i*N+j+1].push_back(i*N+j);\n }\n }\n }\n vector vis(N * N, false);\n int maxTree = 0;\n for (int s = 0; s < N * N; s++) {\n if (vis[s] || board[s/N][s%N] == 0) continue;\n int cnt = 0, edges = 0;\n queue q; q.push(s); vis[s] = true;\n while (!q.empty()) {\n int u = q.front(); q.pop(); cnt++;\n edges += adj[u].size();\n for (int v : adj[u]) if (!vis[v]) { vis[v] = true; q.push(v); }\n }\n if (edges / 2 == cnt - 1) maxTree = max(maxTree, cnt);\n }\n return maxTree;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> T;\n vector> board(N, vector(N));\n int er, ec;\n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) {\n board[i][j] = hexChar(s[j]);\n if (board[i][j] == 0) { er = i; ec = j; }\n }\n }\n \n string best, cur;\n int bestScore = calcScore(board), curScore = bestScore;\n auto bestBoard = board; int bestEr = er, bestEc = ec;\n \n mt19937 rng(42);\n auto start = chrono::steady_clock::now();\n \n while (chrono::duration_cast(chrono::steady_clock::now() - start).count() < 2800) {\n if (cur.size() >= (size_t)T || bestScore >= N * N - 1) break;\n \n vector valid;\n for (int d = 0; d < 4; d++) {\n int nr = er + dr[d], nc = ec + dc[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N) valid.push_back(d);\n }\n int d = valid[rng() % valid.size()];\n int nr = er + dr[d], nc = ec + dc[d];\n \n swap(board[er][ec], board[nr][nc]);\n cur += dc_char[d];\n int newScore = calcScore(board);\n \n double temp = 1.0 - (double)cur.size() / T;\n bool accept = newScore > curScore || (rng() % 1000 < 100 * temp);\n \n if (accept) {\n er = nr; ec = nc; curScore = newScore;\n if (curScore > bestScore || (curScore == bestScore && cur.size() < best.size())) {\n bestScore = curScore; best = cur;\n bestBoard = board; bestEr = er; bestEc = ec;\n }\n } else {\n cur.pop_back();\n swap(board[er][ec], board[nr][nc]);\n }\n \n if (cur.size() > T / 2 && rng() % 100 < 5) {\n board = bestBoard; er = bestEr; ec = bestEc;\n cur = best; curScore = bestScore;\n }\n }\n \n cout << best << endl;\n return 0;\n}","ahc012":"#include \nusing namespace std;\n\ntypedef long long ll;\n\nint N, K;\nvector a(10);\nvector> berries;\nvector> cuts;\n\ninline int side(ll x1, ll y1, ll x2, ll y2, ll px, ll py) {\n __int128 cross = (__int128)(x2 - x1) * (py - y1) - (__int128)(y2 - y1) * (px - x1);\n if (cross > 0) return 1;\n if (cross < 0) return -1;\n return 0;\n}\n\nint calcScore() {\n unordered_map pieceCount;\n int numCuts = cuts.size();\n \n for (int i = 0; i < N; i++) {\n uint64_t sig = 0;\n bool onLine = false;\n for (int j = 0; j < numCuts; j++) {\n int s = side(cuts[j][0], cuts[j][1], cuts[j][2], cuts[j][3], \n berries[i].first, berries[i].second);\n if (s == 0) { onLine = true; break; }\n if (s == 1) sig |= (1ULL << j);\n }\n if (!onLine) pieceCount[sig]++;\n }\n \n vector b(11, 0);\n for (auto& [sig, cnt] : pieceCount) {\n if (cnt >= 1 && cnt <= 10) b[cnt]++;\n }\n \n int total = 0;\n for (int d = 1; d <= 10; d++) total += min(a[d-1], b[d]);\n return total;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> K;\n for (int i = 0; i < 10; i++) cin >> a[i];\n \n berries.resize(N);\n for (int i = 0; i < N; i++) cin >> berries[i].first >> berries[i].second;\n \n mt19937_64 rng(42);\n \n auto randLine = [&]() -> array {\n ll px = (ll)(rng() % 20001) - 10000;\n ll py = (ll)(rng() % 20001) - 10000;\n ll qx = (ll)(rng() % 20001) - 10000;\n ll qy = (ll)(rng() % 20001) - 10000;\n while (px == qx && py == qy) { qx = (ll)(rng() % 20001) - 10000; qy = (ll)(rng() % 20001) - 10000; }\n return {px, py, qx, qy};\n };\n \n auto lineThrough = [&](int i, int j) -> array {\n ll dx = berries[j].first - berries[i].first;\n ll dy = berries[j].second - berries[i].second;\n ll mx = (berries[i].first + berries[j].first) / 2;\n ll my = (berries[i].second + berries[j].second) / 2;\n return {mx - dy, my + dx, mx + dy, my - dx};\n };\n \n int numCuts = min(K, 64);\n for (int i = 0; i < numCuts; i++) cuts.push_back(randLine());\n \n int bestScore = calcScore();\n auto bestCuts = cuts;\n \n auto start = chrono::steady_clock::now();\n \n while (true) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration_cast(now - start).count();\n if (elapsed > 2800) break;\n \n double temp = 50.0 * pow(0.01, elapsed / 2800.0);\n int moveType = rng() % 10;\n \n if (moveType < 7 && !cuts.empty()) {\n int idx = rng() % cuts.size();\n auto oldCut = cuts[idx];\n cuts[idx] = (rng() % 2 == 0) ? randLine() : lineThrough(rng() % N, rng() % N);\n \n int newScore = calcScore();\n if (newScore > bestScore || (double)(rng() % 1000000) / 1000000.0 < exp((newScore - bestScore) / temp)) {\n if (newScore > bestScore) { bestScore = newScore; bestCuts = cuts; }\n } else cuts[idx] = oldCut;\n } else if (moveType < 9 && cuts.size() < (size_t)min(K, 64)) {\n cuts.push_back((rng() % 2 == 0) ? randLine() : lineThrough(rng() % N, rng() % N));\n int newScore = calcScore();\n if (newScore > bestScore || (double)(rng() % 1000000) / 1000000.0 < exp((newScore - bestScore) / temp)) {\n if (newScore > bestScore) { bestScore = newScore; bestCuts = cuts; }\n } else cuts.pop_back();\n } else if (cuts.size() > 10) {\n int idx = rng() % cuts.size();\n auto oldCut = cuts[idx];\n cuts.erase(cuts.begin() + idx);\n int newScore = calcScore();\n if (newScore > bestScore || (double)(rng() % 1000000) / 1000000.0 < exp((newScore - bestScore) / temp)) {\n if (newScore > bestScore) { bestScore = newScore; bestCuts = cuts; }\n } else cuts.insert(cuts.begin() + idx, oldCut);\n }\n }\n \n cuts = bestCuts;\n cout << cuts.size() << \"\\n\";\n for (auto& c : cuts) cout << c[0] << \" \" << c[1] << \" \" << c[2] << \" \" << c[3] << \"\\n\";\n \n return 0;\n}","ahc014":"#include \nusing namespace std;\n\nint N, M, c;\nset> dots;\nset> usedSegs;\nvector> ops;\n\nbool inGrid(int x, int y) { return x >= 0 && x < N && y >= 0 && y < N; }\nlong long wt(int x, int y) { return (long long)(x-c)*(x-c) + (long long)(y-c)*(y-c) + 1; }\n\nvoid addSeg(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g == 0) return;\n dx /= g; dy /= g;\n for (int i = 0; i < g; i++) {\n int a = x1+i*dx, b = y1+i*dy, e = a+dx, f = b+dy;\n if (a > e || (a == e && b > f)) { swap(a,e); swap(b,f); }\n usedSegs.insert({a,b,e,f});\n }\n}\n\nbool segUsed(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g == 0) return false;\n dx /= g; dy /= g;\n for (int i = 0; i < g; i++) {\n int a = x1+i*dx, b = y1+i*dy, e = a+dx, f = b+dy;\n if (a > e || (a == e && b > f)) { swap(a,e); swap(b,f); }\n if (usedSegs.count({a,b,e,f})) return true;\n }\n return false;\n}\n\nbool dotOnSeg(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g <= 1) return false;\n dx /= g; dy /= g;\n for (int i = 1; i < g; i++)\n if (dots.count({x1+i*dx, y1+i*dy})) return true;\n return false;\n}\n\nbool tryAdd(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4) {\n if (!inGrid(x1,y1) || !inGrid(x3,y3) || dots.count({x1,y1})) return false;\n if (!dots.count({x2,y2}) || !dots.count({x3,y3}) || !dots.count({x4,y4})) return false;\n if ((x2==x3&&y2==y3) || (x2==x4&&y2==y4) || (x3==x4&&y3==y4)) return false;\n if (x1==x2&&y1==y2) return false;\n if (dotOnSeg(x1,y1,x2,y2) || dotOnSeg(x2,y2,x3,y3) || dotOnSeg(x3,y3,x4,y4) || dotOnSeg(x4,y4,x1,y1)) return false;\n if (segUsed(x1,y1,x2,y2) || segUsed(x2,y2,x3,y3) || segUsed(x3,y3,x4,y4) || segUsed(x4,y4,x1,y1)) return false;\n \n dots.insert({x1,y1});\n addSeg(x1,y1,x2,y2); addSeg(x2,y2,x3,y3); addSeg(x3,y3,x4,y4); addSeg(x4,y4,x1,y1);\n ops.push_back({x1,y1,x2,y2,x3,y3,x4,y4});\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M;\n c = (N-1) / 2;\n for (int i = 0; i < M; i++) { int x, y; cin >> x >> y; dots.insert({x, y}); }\n \n auto tstart = chrono::steady_clock::now();\n mt19937 rng(42);\n \n while (chrono::duration(chrono::steady_clock::now() - tstart).count() < 4.5) {\n vector> dl(dots.begin(), dots.end());\n shuffle(dl.begin(), dl.end(), rng);\n \n long long bestW = -1; array best;\n for (int i = 0; i < (int)dl.size(); i++) {\n for (int j = 0; j < (int)dl.size(); j++) {\n if (i == j) continue;\n auto [x2, y2] = dl[i]; auto [x4, y4] = dl[j];\n \n auto check = [&](int x1, int y1, int x3, int y3) {\n if (inGrid(x1,y1) && !dots.count({x1,y1}) && wt(x1,y1) > bestW) {\n if (inGrid(x3,y3) && dots.count({x3,y3})) {\n best = {x1,y1,x2,y2,x3,y3,x4,y4}; bestW = wt(x1,y1);\n }\n }\n };\n \n check(x4, y2, x2, y4); // axis-aligned\n \n int s1 = x2-y2, s2 = x4+y4;\n if ((s1+s2)%2==0) check((s1+s2)/2, (s2-s1)/2, x2+x4-(s1+s2)/2, y2+y4-(s2-s1)/2);\n \n s1 = x2+y2; s2 = x4-y4;\n if ((s1+s2)%2==0) check((s1+s2)/2, (s1-s2)/2, x2+x4-(s1+s2)/2, y2+y4-(s1-s2)/2);\n }\n }\n if (bestW < 0 || !tryAdd(best[0],best[1],best[2],best[3],best[4],best[5],best[6],best[7])) break;\n }\n \n cout << ops.size() << \"\\n\";\n for (auto& op : ops) {\n for (int i = 0; i < 8; i++) cout << op[i] << \" \\n\"[i==7];\n }\n return 0;\n}","ahc015":"#include \nusing namespace std;\n\nconst int N = 10;\nint grid[N][N], backup[N][N];\n\nvoid place(int p, int flavor) {\n int cnt = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (grid[i][j] == 0) {\n if (++cnt == p) { grid[i][j] = flavor; return; }\n }\n }\n }\n}\n\nvoid tilt(char dir) {\n if (dir == 'F') {\n for (int j = 0; j < N; j++) {\n int w = 0;\n for (int i = 0; i < N; i++) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[w++][j] = v; }\n }\n } else if (dir == 'B') {\n for (int j = 0; j < N; j++) {\n int w = N - 1;\n for (int i = N - 1; i >= 0; i--) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[w--][j] = v; }\n }\n } else if (dir == 'L') {\n for (int i = 0; i < N; i++) {\n int w = 0;\n for (int j = 0; j < N; j++) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[i][w++] = v; }\n }\n } else {\n for (int i = 0; i < N; i++) {\n int w = N - 1;\n for (int j = N - 1; j >= 0; j--) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[i][w--] = v; }\n }\n }\n}\n\nlong long calcScore() {\n bool vis[N][N] = {};\n long long sum = 0;\n int dx[] = {-1, 1, 0, 0}, dy[] = {0, 0, -1, 1};\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (grid[i][j] && !vis[i][j]) {\n int f = grid[i][j], sz = 0;\n queue> q; q.push({i, j}); vis[i][j] = true;\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop(); sz++;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < N && ny >= 0 && ny < N && !vis[nx][ny] && grid[nx][ny] == f) {\n vis[nx][ny] = true; q.push({nx, ny});\n }\n }\n }\n sum += (long long)sz * sz;\n }\n }\n }\n return sum;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int f[101];\n for (int t = 1; t <= 100; t++) cin >> f[t];\n \n memset(grid, 0, sizeof(grid));\n \n for (int t = 1; t <= 100; t++) {\n int p; cin >> p;\n place(p, f[t]);\n \n char bestDir = 'F';\n long long bestScore = -1;\n memcpy(backup, grid, sizeof(grid));\n \n for (char dir : {'F', 'B', 'L', 'R'}) {\n memcpy(grid, backup, sizeof(grid));\n tilt(dir);\n long long score = calcScore();\n if (score > bestScore) { bestScore = score; bestDir = dir; }\n }\n \n memcpy(grid, backup, sizeof(grid));\n tilt(bestDir);\n cout << bestDir << '\\n' << flush;\n }\n \n return 0;\n}","ahc016":"#include \nusing namespace std;\n\nint N, M;\ndouble eps;\n\nvector get_sorted_degrees(const string& s) {\n vector deg(N, 0);\n int idx = 0;\n for (int i = 0; i < N; i++) {\n for (int j = i + 1; j < N; j++) {\n if (s[idx++] == '1') {\n deg[i]++;\n deg[j]++;\n }\n }\n }\n sort(deg.begin(), deg.end());\n return deg;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(0);\n \n cin >> M >> eps;\n double safe_eps = max(eps, 1e-9);\n \n // Choose N based on M and eps\n // Need enough vertices to distinguish M graphs with noise\n double factor = 1.0 / max(0.1, 1.0 - 2.0 * safe_eps);\n N = (int)ceil(sqrt(2.0 * M * factor * 1.5)) + 5;\n if (eps > 0.25) N += 15;\n if (eps > 0.35) N += 10;\n N = max(N, 10);\n N = min(N, 100);\n \n cout << N << \"\\n\";\n \n int total = N * (N - 1) / 2;\n \n vector G(M);\n vector> expected_deg(M);\n \n for (int i = 0; i < M; i++) {\n string s(total, '0');\n // Spread edge count linearly from 0 to total\n long long edges = (M > 1) ? ((long long)i * total / (M - 1)) : 0;\n for (int e = 0; e < edges; e++) {\n s[e] = '1';\n }\n G[i] = s;\n \n // Compute expected degree sequence after noise transformation\n vector deg = get_sorted_degrees(s);\n expected_deg[i].resize(N);\n for (int j = 0; j < N; j++) {\n // E[d'] = d*(1-2*eps) + (N-1)*eps\n expected_deg[i][j] = deg[j] * (1.0 - 2.0 * safe_eps) + (N - 1) * safe_eps;\n }\n \n cout << s << \"\\n\";\n }\n cout.flush();\n \n for (int q = 0; q < 100; q++) {\n string H;\n cin >> H;\n \n vector deg_h = get_sorted_degrees(H);\n \n int best = 0;\n double best_score = 1e18;\n \n for (int i = 0; i < M; i++) {\n // L2 distance between observed and expected degree sequences\n double score = 0;\n for (int j = 0; j < N; j++) {\n double diff = deg_h[j] - expected_deg[i][j];\n score += diff * diff;\n }\n if (score < best_score) {\n best_score = score;\n best = i;\n }\n }\n \n cout << best << \"\\n\";\n cout.flush();\n }\n \n return 0;\n}","ahc017":"#include \nusing namespace std;\n\nint N, M, D, K;\nvector> edges;\nvector>> adj;\nvector> adjEdge;\nmt19937 rng(42);\nconst long long INF = 1e9;\n\nvector dijkstra(int src, int excludeEdge) {\n vector dist(N, INF);\n priority_queue, vector>, greater<>> pq;\n dist[src] = 0;\n pq.push({0, src});\n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > dist[u]) continue;\n for (size_t i = 0; i < adj[u].size(); i++) {\n if ((int)adjEdge[u][i] == excludeEdge) continue;\n auto [v, w] = adj[u][i];\n if (dist[u] + w < dist[v]) {\n dist[v] = dist[u] + w;\n pq.push({dist[v], v});\n }\n }\n }\n return dist;\n}\n\nvector dijkstraMask(int src, const vector& excl) {\n vector dist(N, INF);\n priority_queue, vector>, greater<>> pq;\n dist[src] = 0;\n pq.push({0, src});\n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > dist[u]) continue;\n for (size_t i = 0; i < adj[u].size(); i++) {\n if (excl[adjEdge[u][i]]) continue;\n auto [v, w] = adj[u][i];\n if (dist[u] + w < dist[v]) {\n dist[v] = dist[u] + w;\n pq.push({dist[v], v});\n }\n }\n }\n return dist;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n auto start = chrono::steady_clock::now();\n \n cin >> N >> M >> D >> K;\n edges.resize(M); adj.resize(N); adjEdge.resize(N);\n \n for (int i = 0; i < M; i++) {\n int u, v, w; cin >> u >> v >> w; u--; v--;\n edges[i] = {u, v, w};\n adj[u].push_back({v, w}); adj[v].push_back({u, w});\n adjEdge[u].push_back(i); adjEdge[v].push_back(i);\n }\n for (int i = 0; i < N; i++) { int x, y; cin >> x >> y; }\n \n vector crit(M);\n for (int e = 0; e < M; e++) {\n auto dist = dijkstra(edges[e][0], e);\n crit[e] = dist[edges[e][1]] - edges[e][2];\n }\n \n vector order(M); iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int a, int b) { return crit[a] > crit[b]; });\n \n vector assign(M);\n vector cnt(D + 1, 0);\n for (int e : order) {\n int best = 1;\n for (int d = 2; d <= D; d++) if (cnt[d] < K && cnt[d] < cnt[best]) best = d;\n assign[e] = best; cnt[best]++;\n }\n \n vector samples(min(40, N));\n iota(samples.begin(), samples.end(), 0);\n shuffle(samples.begin(), samples.end(), rng);\n \n vector> origDist(samples.size());\n for (size_t i = 0; i < samples.size(); i++) origDist[i] = dijkstra(samples[i], -1);\n \n auto eval = [&]() {\n double tot = 0;\n for (int d = 1; d <= D; d++) {\n vector excl(M);\n for (int e = 0; e < M; e++) if (assign[e] == d) excl[e] = true;\n for (size_t i = 0; i < samples.size(); i++) {\n auto dist = dijkstraMask(samples[i], excl);\n for (int v = 0; v < N; v++) if (v != samples[i])\n tot += min(dist[v], INF) - origDist[i][v];\n }\n }\n return tot;\n };\n \n double cur = eval();\n double temp = 1e8;\n \n while (true) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > 5.5) break;\n \n int e1 = rng() % M, e2 = rng() % M;\n if (assign[e1] == assign[e2]) continue;\n \n int d1 = assign[e1], d2 = assign[e2];\n if (cnt[d1] - 1 + 1 > K || cnt[d2] - 1 + 1 > K) continue;\n \n swap(assign[e1], assign[e2]);\n double nv = eval();\n \n if (nv < cur || (rng() % 1000000) < 1000000 * exp((cur - nv) / temp)) {\n cur = nv;\n } else {\n swap(assign[e1], assign[e2]);\n }\n temp *= 0.99999;\n }\n \n for (int i = 0; i < M; i++) cout << assign[i] << \" \\n\"[i == M-1];\n return 0;\n}","ahc019":"#include \nusing namespace std;\n\nint D;\nstring f[2][15], r[2][15];\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> D;\n for (int i = 0; i < 2; i++) {\n for (int k = 0; k < D; k++) cin >> f[i][k];\n for (int k = 0; k < D; k++) cin >> r[i][k];\n }\n \n vector b[2];\n for (int i = 0; i < 2; i++) b[i].assign(D * D * D, 0);\n \n int n = 0;\n int dx[] = {1, -1, 0, 0, 0, 0};\n int dy[] = {0, 0, 1, -1, 0, 0};\n int dz[] = {0, 0, 0, 0, 1, -1};\n \n auto valid = [&](int i, int x, int y, int z) {\n return f[i][z][x] == '1' && r[i][z][y] == '1';\n };\n \n auto idx = [&](int x, int y, int z) { return x * D * D + y * D + z; };\n \n // Step 1: Find shared cells (valid in both) and create shared blocks\n for (int x = 0; x < D; x++) {\n for (int y = 0; y < D; y++) {\n for (int z = 0; z < D; z++) {\n if (valid(0, x, y, z) && valid(1, x, y, z) && b[0][idx(x,y,z)] == 0) {\n n++;\n queue> q;\n q.push({x, y, z});\n b[0][idx(x,y,z)] = b[1][idx(x,y,z)] = n;\n while (!q.empty()) {\n auto [cx, cy, cz] = q.front();\n q.pop();\n for (int d = 0; d < 6; d++) {\n int nx = cx + dx[d], ny = cy + dy[d], nz = cz + dz[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && nz >= 0 && nz < D) {\n if (valid(0, nx, ny, nz) && valid(1, nx, ny, nz) && b[0][idx(nx,ny,nz)] == 0) {\n b[0][idx(nx,ny,nz)] = b[1][idx(nx,ny,nz)] = n;\n q.push({nx, ny, nz});\n }\n }\n }\n }\n }\n }\n }\n }\n \n // Step 2: Handle remaining cells unique to each arrangement\n for (int i = 0; i < 2; i++) {\n for (int x = 0; x < D; x++) {\n for (int y = 0; y < D; y++) {\n for (int z = 0; z < D; z++) {\n if (valid(i, x, y, z) && b[i][idx(x,y,z)] == 0) {\n n++;\n queue> q;\n q.push({x, y, z});\n b[i][idx(x,y,z)] = n;\n while (!q.empty()) {\n auto [cx, cy, cz] = q.front();\n q.pop();\n for (int d = 0; d < 6; d++) {\n int nx = cx + dx[d], ny = cy + dy[d], nz = cz + dz[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && nz >= 0 && nz < D) {\n if (valid(i, nx, ny, nz) && b[i][idx(nx,ny,nz)] == 0) {\n b[i][idx(nx,ny,nz)] = n;\n q.push({nx, ny, nz});\n }\n }\n }\n }\n }\n }\n }\n }\n }\n \n // Output\n cout << n << \"\\n\";\n for (int i = 0; i < 2; i++) {\n for (int j = 0; j < D * D * D; j++) {\n if (j) cout << \" \";\n cout << b[i][j];\n }\n cout << \"\\n\";\n }\n \n return 0;\n}","ahc020":"#include \nusing namespace std;\n\nint N, M, K;\nvector> V, R;\nvector> E;\nvector>> adj;\nvector> distVR;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> K;\n V.resize(N); R.resize(K); E.resize(M); adj.resize(N);\n \n for(int i = 0; i < N; i++) cin >> V[i].first >> V[i].second;\n for(int j = 0; j < M; j++) {\n int u, v; long long w;\n cin >> u >> v >> w; u--; v--;\n E[j] = {u, v, w};\n adj[u].push_back({v, j});\n adj[v].push_back({u, j});\n }\n for(int k = 0; k < K; k++) cin >> R[k].first >> R[k].second;\n \n distVR.resize(N, vector(K));\n for(int i = 0; i < N; i++)\n for(int k = 0; k < K; k++) {\n double dx = V[i].first - R[k].first, dy = V[i].second - R[k].second;\n distVR[i][k] = sqrt(dx*dx + dy*dy);\n }\n \n // Compute shortest paths from vertex 0\n vector dist0(N, LLONG_MAX/2);\n vector parent(N, -1), parentEdge(N, -1);\n priority_queue, vector>, greater<>> pq;\n dist0[0] = 0; pq.push({0, 0});\n while(!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if(d > dist0[u]) continue;\n for(auto [v, eid] : adj[u]) {\n long long w = get<2>(E[eid]);\n if(dist0[u] + w < dist0[v]) {\n dist0[v] = dist0[u] + w;\n parent[v] = u; parentEdge[v] = eid;\n pq.push({dist0[v], v});\n }\n }\n }\n \n // Assign residents considering both broadcast cost and reachability\n vector P(N, 0);\n vector assignment(K);\n \n for(int k = 0; k < K; k++) {\n int best = -1; double bestCost = 1e18;\n for(int i = 0; i < N; i++) {\n if(distVR[i][k] > 5000) continue;\n // Cost: broadcast cost + amortized network cost\n double cost = distVR[i][k] * distVR[i][k] + dist0[i] * 0.01;\n if(cost < bestCost) { bestCost = cost; best = i; }\n }\n assignment[k] = best;\n }\n \n for(int k = 0; k < K; k++) {\n int v = assignment[k];\n P[v] = max(P[v], (int)ceil(distVR[v][k] - 1e-9));\n }\n \n // Build tree\n set active;\n for(int i = 0; i < N; i++) if(P[i] > 0) active.insert(i);\n \n vector B(M, 0);\n for(int v : active) {\n int cur = v;\n while(cur != 0 && parentEdge[cur] != -1) {\n B[parentEdge[cur]] = 1;\n cur = parent[cur];\n }\n }\n \n // Activate intermediate vertices on tree (they're reachable, might help)\n set treeVerts;\n treeVerts.insert(0);\n for(int v : active) {\n int cur = v;\n while(cur != -1) { treeVerts.insert(cur); cur = parent[cur]; }\n }\n \n // Try using tree vertices to reduce costs\n for(int iter = 0; iter < 50; iter++) {\n bool improved = false;\n for(int k = 0; k < K; k++) {\n int curV = assignment[k];\n for(int v : treeVerts) {\n if(v == curV || distVR[v][k] > 5000) continue;\n int newR = (int)ceil(distVR[v][k] - 1e-9);\n int oldR = (int)ceil(distVR[curV][k] - 1e-9);\n if(newR < oldR && newR <= 5000) {\n assignment[k] = v;\n improved = true;\n }\n }\n }\n if(!improved) break;\n \n fill(P.begin(), P.end(), 0);\n for(int k = 0; k < K; k++) {\n int v = assignment[k];\n P[v] = max(P[v], (int)ceil(distVR[v][k] - 1e-9));\n }\n }\n \n // Output\n for(int i = 0; i < N; i++) cout << P[i] << \" \\n\"[i==N-1];\n for(int j = 0; j < M; j++) cout << B[j] << \" \\n\"[j==M-1];\n \n return 0;\n}","ahc021":"#include \nusing namespace std;\n\nconst int N = 30;\nint b[N][N];\nvector> ops;\n\nvoid do_swap(int x1, int y1, int x2, int y2) {\n ops.push_back({x1, y1, x2, y2});\n swap(b[x1][y1], b[x2][y2]);\n}\n\nvoid sift_down(int x, int y) {\n while (x < N - 1) {\n // Find the child with minimum value\n int min_child_y = (b[x + 1][y + 1] < b[x + 1][y]) ? (y + 1) : y;\n // If parent is larger than min child, swap and continue\n if (b[x][y] > b[x + 1][min_child_y]) {\n do_swap(x, y, x + 1, min_child_y);\n x = x + 1;\n y = min_child_y;\n } else {\n break;\n }\n }\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int x = 0; x < N; x++) {\n for (int y = 0; y <= x; y++) {\n cin >> b[x][y];\n }\n }\n \n // Build min-heap by sifting down from second-to-last tier upward\n for (int x = N - 2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) {\n sift_down(x, y);\n }\n }\n \n cout << ops.size() << \"\\n\";\n for (auto& [x1, y1, x2, y2] : ops) {\n cout << x1 << \" \" << y1 << \" \" << x2 << \" \" << y2 << \"\\n\";\n }\n \n return 0;\n}","toyota2023summer-final":"#include \nusing namespace std;\n\nint D, N, ex, ey;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nvector> grid;\n\nvector> getReachable(bool findContainers) {\n vector> result;\n vector> vis(D, vector(D, false));\n queue> q;\n q.push({ex, ey});\n vis[ex][ey] = true;\n \n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n \n if (findContainers && grid[x][y] >= 0) {\n result.push_back({x, y});\n continue;\n }\n if (!findContainers && grid[x][y] == -1 && !(x == ex && y == ey)) {\n result.push_back({x, y});\n }\n if (grid[x][y] >= 0) continue;\n \n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && !vis[nx][ny] && grid[nx][ny] != -2) {\n vis[nx][ny] = true;\n q.push({nx, ny});\n }\n }\n }\n return result;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> D >> N;\n ex = 0; ey = (D - 1) / 2;\n grid.assign(D, vector(D, -1));\n \n for (int i = 0; i < N; i++) {\n int x, y; cin >> x >> y;\n grid[x][y] = -2;\n }\n \n int total = D * D - 1 - N;\n \n vector> bfsOrder;\n map, int> posToIdx;\n {\n vector> vis(D, vector(D, false));\n queue> q;\n q.push({ex, ey});\n vis[ex][ey] = true;\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n if (grid[x][y] == -1 && !(x == ex && y == ey)) {\n posToIdx[{x, y}] = bfsOrder.size();\n bfsOrder.push_back({x, y});\n }\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && !vis[nx][ny] && grid[nx][ny] != -2) {\n vis[nx][ny] = true;\n q.push({nx, ny});\n }\n }\n }\n }\n \n for (int d = 0; d < total; d++) {\n int t; cin >> t;\n auto reach = getReachable(false);\n \n int targetIdx = total - 1 - t;\n pair best = reach[0];\n int bestDist = abs(posToIdx[best] - targetIdx);\n for (auto& pos : reach) {\n int dist = abs(posToIdx[pos] - targetIdx);\n if (dist < bestDist || (dist == bestDist && posToIdx[pos] > posToIdx[best])) {\n bestDist = dist;\n best = pos;\n }\n }\n \n grid[best.first][best.second] = t;\n cout << best.first << \" \" << best.second << \"\\n\";\n cout.flush();\n }\n \n for (int i = 0; i < total; i++) {\n auto reach = getReachable(true);\n pair best = reach[0];\n for (auto& pos : reach) {\n if (grid[pos.first][pos.second] < grid[best.first][best.second]) {\n best = pos;\n }\n }\n cout << best.first << \" \" << best.second << \"\\n\";\n grid[best.first][best.second] = -1;\n }\n \n return 0;\n}","ahc024":"#include \nusing namespace std;\n\nint n, m;\nint dx[] = {0, 0, 1, -1};\nint dy[] = {1, -1, 0, 0};\n\nset> getAdj(vector>& g) {\n set> adj;\n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n int c = g[i][j];\n if (i == 0 || i == n-1 || j == 0 || j == n-1) {\n int a = min(0, c), b = max(0, c);\n if (a != b) adj.insert({a, b});\n }\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n) {\n int nc = g[ni][nj];\n if (c != nc) {\n int a = min(c, nc), b = max(c, nc);\n adj.insert({a, b});\n }\n }\n }\n }\n }\n return adj;\n}\n\nbool isConnected(vector>& g, int c) {\n if (c == 0) return true;\n int si = -1, sj = -1, cnt = 0;\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) {\n if (g[i][j] == c) { if (si < 0) { si = i; sj = j; } cnt++; }\n }\n if (cnt == 0) return true;\n queue> q;\n vector> vis(n, vector(n, false));\n q.push({si, sj}); vis[si][sj] = true;\n int found = 1;\n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n && !vis[ni][nj] && g[ni][nj] == c) {\n vis[ni][nj] = true; found++; q.push({ni, nj});\n }\n }\n }\n return found == cnt;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> n >> m;\n vector> grid(n, vector(n));\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n cin >> grid[i][j];\n \n auto origAdj = getAdj(grid);\n vector> best = grid;\n int bestScore = 0;\n \n // Try greedy shrinking - change cells to 0 when safe\n auto tryGrid = grid;\n for (int iter = 0; iter < 5; iter++) {\n vector> cells;\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++)\n if (tryGrid[i][j] != 0) cells.push_back({i, j});\n \n shuffle(cells.begin(), cells.end(), mt19937(iter * 12345));\n \n for (auto [i, j] : cells) {\n int old = tryGrid[i][j];\n tryGrid[i][j] = 0;\n \n auto newAdj = getAdj(tryGrid);\n bool valid = (newAdj == origAdj);\n if (valid) {\n for (int c = 1; c <= m && valid; c++)\n if (!isConnected(tryGrid, c)) valid = false;\n }\n \n if (!valid) tryGrid[i][j] = old;\n }\n \n int score = 0;\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++)\n if (tryGrid[i][j] == 0) score++;\n \n if (score > bestScore) {\n bestScore = score;\n best = tryGrid;\n }\n }\n \n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n cout << best[i][j];\n if (j < n-1) cout << \" \";\n }\n cout << \"\\n\";\n }\n \n return 0;\n}","ahc025":"#include \nusing namespace std;\n\nint N, D, Q;\nint query_count = 0;\n\nchar query(const vector& L, const vector& R) {\n cout << L.size() << \" \" << R.size();\n for (int x : L) cout << \" \" << x;\n for (int x : R) cout << \" \" << x;\n cout << \"\\n\";\n cout.flush();\n char c;\n cin >> c;\n query_count++;\n return c;\n}\n\nvector items;\n\nvoid merge_sort(int l, int r) {\n if (r - l <= 1) return;\n int m = (l + r) / 2;\n merge_sort(l, m);\n merge_sort(m, r);\n \n vector left(items.begin() + l, items.begin() + m);\n vector right(items.begin() + m, items.begin() + r);\n \n int i = 0, j = 0, k = l;\n while (i < (int)left.size() && j < (int)right.size()) {\n if (query_count >= Q) {\n while (i < (int)left.size()) items[k++] = left[i++];\n while (j < (int)right.size()) items[k++] = right[j++];\n return;\n }\n char c = query({left[i]}, {right[j]});\n if (c != '>') items[k++] = left[i++];\n else items[k++] = right[j++];\n }\n while (i < (int)left.size()) items[k++] = left[i++];\n while (j < (int)right.size()) items[k++] = right[j++];\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> D >> Q;\n \n items.resize(N);\n iota(items.begin(), items.end(), 0);\n merge_sort(0, N);\n \n // Estimate weights using remaining queries\n vector w(N);\n for (int i = 0; i < N; i++) w[i] = i + 1;\n \n for (int j = N - 1; j >= N / 2 && query_count + 10 < Q; j--) {\n int lo = 1, hi = j;\n while (lo < hi && query_count < Q - N) {\n int mid = (lo + hi) / 2;\n vector L, R = {items[j]};\n for (int t = 0; t < mid; t++) L.push_back(items[t]);\n char c = query(L, R);\n if (c == '>' || c == '=') hi = mid;\n else lo = mid + 1;\n }\n double sum = 0;\n for (int t = 0; t < lo; t++) sum += w[t];\n w[j] = sum;\n }\n \n // Greedy assignment\n vector set_weight(D, 0);\n vector assignment(N);\n \n for (int i = N - 1; i >= 0; i--) {\n int best = 0;\n for (int j = 1; j < D; j++)\n if (set_weight[j] < set_weight[best]) best = j;\n assignment[items[i]] = best;\n set_weight[best] += w[i];\n }\n \n while (query_count < Q) query({items[0]}, {items[1]});\n \n for (int i = 0; i < N; i++)\n cout << assignment[i] << \" \\n\"[i == N - 1];\n \n return 0;\n}","ahc026":"#include \nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n, m;\n cin >> n >> m;\n \n vector> stacks(m);\n vector pos(n + 1);\n \n for (int i = 0; i < m; i++) {\n int h = n / m;\n for (int j = 0; j < h; j++) {\n int x;\n cin >> x;\n stacks[i].push_back(x);\n pos[x] = i;\n }\n }\n \n vector> ops;\n \n for (int v = 1; v <= n; v++) {\n int stack_id = pos[v];\n \n int idx = 0;\n while (stacks[stack_id][idx] != v) idx++;\n \n if (idx < (int)stacks[stack_id].size() - 1) {\n int move_start = idx + 1;\n int bottom_box = stacks[stack_id][move_start];\n \n int max_moving = 0;\n for (int j = move_start; j < (int)stacks[stack_id].size(); j++) {\n max_moving = max(max_moving, stacks[stack_id][j]);\n }\n \n int best_dest = -1;\n int best_score = INT_MIN;\n \n for (int i = 0; i < m; i++) {\n if (i == stack_id) continue;\n \n int score = 0;\n \n if (stacks[i].empty()) {\n score = 400;\n } else {\n int top = stacks[i].back();\n score = top;\n if (top > max_moving) {\n score += 300;\n }\n }\n \n score -= (int)stacks[i].size();\n \n if (score > best_score) {\n best_score = score;\n best_dest = i;\n }\n }\n \n ops.push_back({bottom_box, best_dest + 1});\n \n for (int j = move_start; j < (int)stacks[stack_id].size(); j++) {\n int box = stacks[stack_id][j];\n stacks[best_dest].push_back(box);\n pos[box] = best_dest;\n }\n stacks[stack_id].resize(move_start);\n }\n \n ops.push_back({v, 0});\n stacks[stack_id].pop_back();\n }\n \n for (auto& [a, b] : ops) {\n cout << a << \" \" << b << \"\\n\";\n }\n \n return 0;\n}","ahc027":"#include \nusing namespace std;\n\nint N;\nvector h, v;\nvector> d;\n\nint di[] = {0, 1, 0, -1};\nint dj[] = {1, 0, -1, 0};\nchar dirChar[] = {'R', 'D', 'L', 'U'};\n\nbool canMove(int i, int j, int dir) {\n int ni = i + di[dir];\n int nj = j + dj[dir];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) return false;\n \n if (dir == 0) return v[i][j] == '0';\n else if (dir == 1) return h[i][j] == '0';\n else if (dir == 2) return j > 0 && v[i][j-1] == '0';\n else return i > 0 && h[i-1][j] == '0';\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N - 1);\n v.resize(N);\n d.resize(N, vector(N));\n \n for (int i = 0; i < N - 1; i++) {\n cin >> h[i];\n }\n for (int i = 0; i < N; i++) {\n cin >> v[i];\n }\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n cin >> d[i][j];\n }\n }\n \n // Compute subtree sums via BFS from (0,0)\n vector> subtreeSum(N, vector(N, 0));\n vector> parent(N, vector(N, -1));\n vector> depth(N, vector(N, -1));\n \n queue> q;\n q.push({0, 0});\n depth[0][0] = 0;\n vector> order;\n \n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n order.push_back({i, j});\n subtreeSum[i][j] = d[i][j];\n for (int dir = 0; dir < 4; dir++) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (ni >= 0 && ni < N && nj >= 0 && nj < N && depth[ni][nj] == -1 && canMove(i, j, dir)) {\n depth[ni][nj] = depth[i][j] + 1;\n parent[ni][nj] = (dir + 2) % 4;\n q.push({ni, nj});\n }\n }\n }\n \n // Compute subtree sums bottom-up\n for (int idx = order.size() - 1; idx >= 0; idx--) {\n auto [i, j] = order[idx];\n if (parent[i][j] != -1) {\n int pi = i + di[parent[i][j]];\n int pj = j + dj[parent[i][j]];\n subtreeSum[pi][pj] += subtreeSum[i][j];\n }\n }\n \n // DFS with priority based on subtree sums\n vector> visited(N, vector(N, false));\n string path;\n \n function dfs = [&](int i, int j) {\n visited[i][j] = true;\n \n vector> children;\n for (int dir = 0; dir < 4; dir++) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (ni >= 0 && ni < N && nj >= 0 && nj < N && !visited[ni][nj] && canMove(i, j, dir)) {\n children.push_back({subtreeSum[ni][nj], dir});\n }\n }\n // Visit highest subtree sum first (becomes internal node, visited more)\n sort(children.rbegin(), children.rend());\n \n for (auto [sum, dir] : children) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (!visited[ni][nj]) {\n path += dirChar[dir];\n dfs(ni, nj);\n path += dirChar[(dir + 2) % 4];\n }\n }\n };\n \n dfs(0, 0);\n cout << path << endl;\n \n return 0;\n}","ahc028":"#include \nusing namespace std;\n\nint overlap(const string& a, const string& b) {\n int maxOv = min((int)a.length(), (int)b.length());\n for (int ov = maxOv; ov >= 1; ov--) {\n if (a.substr(a.length() - ov) == b.substr(0, ov)) {\n return ov;\n }\n }\n return 0;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, si, sj;\n cin >> N >> M >> si >> sj;\n \n vector A(N);\n map>> charPos;\n for (int i = 0; i < N; i++) {\n cin >> A[i];\n for (int j = 0; j < N; j++) {\n charPos[A[i][j]].push_back({i, j});\n }\n }\n \n vector t(M);\n for (int i = 0; i < M; i++) {\n cin >> t[i];\n }\n \n // Greedy superstring construction\n vector remaining = t;\n \n while (remaining.size() > 1) {\n int bestOv = -1;\n int bestI = -1, bestJ = -1;\n \n for (int i = 0; i < (int)remaining.size(); i++) {\n for (int j = 0; j < (int)remaining.size(); j++) {\n if (i != j) {\n int ov = overlap(remaining[i], remaining[j]);\n if (ov > bestOv) {\n bestOv = ov;\n bestI = i;\n bestJ = j;\n }\n }\n }\n }\n \n string merged = remaining[bestI] + remaining[bestJ].substr(bestOv);\n \n vector newRemaining;\n for (int k = 0; k < (int)remaining.size(); k++) {\n if (k != bestI && k != bestJ) {\n if (merged.find(remaining[k]) == string::npos) {\n newRemaining.push_back(remaining[k]);\n }\n }\n }\n newRemaining.push_back(merged);\n remaining = newRemaining;\n }\n \n string superstring = remaining[0];\n \n // Type the superstring using nearest neighbor\n int curI = si, curJ = sj;\n \n for (char c : superstring) {\n int bestDist = INT_MAX;\n int bI = -1, bJ = -1;\n for (auto [i, j] : charPos[c]) {\n int dist = abs(i - curI) + abs(j - curJ);\n if (dist < bestDist) {\n bestDist = dist;\n bI = i;\n bJ = j;\n }\n }\n cout << bI << \" \" << bJ << \"\\n\";\n curI = bI;\n curJ = bJ;\n }\n \n return 0;\n}","ahc030":"#include \nusing namespace std;\n\nint N, M;\ndouble eps;\nvector>> shapes;\nvector> grid;\n\nint queryDrill(int i, int j) {\n cout << \"q 1 \" << i << \" \" << j << \"\\n\" << flush;\n int v; cin >> v;\n grid[i][j] = v;\n return v;\n}\n\nint queryDivine(const vector>& cells) {\n cout << \"q \" << cells.size();\n for (auto& [i, j] : cells) cout << \" \" << i << \" \" << j;\n cout << \"\\n\" << flush;\n int v; cin >> v;\n return v;\n}\n\nint submit(const set>& oil) {\n cout << \"a \" << oil.size();\n for (auto& [i, j] : oil) cout << \" \" << i << \" \" << j;\n cout << \"\\n\" << flush;\n int r; cin >> r;\n return r;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> eps;\n shapes.resize(M);\n for (int m = 0; m < M; m++) {\n int d; cin >> d;\n shapes[m].resize(d);\n for (int i = 0; i < d; i++) {\n cin >> shapes[m][i].first >> shapes[m][i].second;\n }\n }\n \n grid.assign(N, vector(N, -1));\n set> has_oil;\n \n // When eps is small, use row divination first\n vector rowEstimate(N, -1);\n if (eps <= 0.1) {\n for (int i = 0; i < N; i++) {\n vector> row;\n for (int j = 0; j < N; j++) row.push_back({i, j});\n int est = queryDivine(row);\n rowEstimate[i] = est;\n }\n }\n \n // Drill cells - prioritize rows with higher estimates\n vector order(N);\n iota(order.begin(), order.end(), 0);\n if (eps <= 0.1) {\n sort(order.begin(), order.end(), [&](int a, int b) {\n return rowEstimate[a] > rowEstimate[b];\n });\n }\n \n for (int i : order) {\n for (int j = 0; j < N; j++) {\n int v = queryDrill(i, j);\n if (v > 0) has_oil.insert({i, j});\n }\n }\n \n submit(has_oil);\n return 0;\n}","ahc031":"#include \nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int W, D, N;\n cin >> W >> D >> N;\n \n vector> a(D, vector(N));\n for (int d = 0; d < D; d++) {\n for (int k = 0; k < N; k++) {\n cin >> a[d][k];\n }\n }\n \n for (int d = 0; d < D; d++) {\n long long total = 0;\n for (int k = 0; k < N; k++) {\n total += a[d][k];\n }\n if (total == 0) total = 1;\n \n vector y(N + 1);\n y[0] = 0;\n y[N] = W;\n \n long long cum = 0;\n for (int k = 0; k < N - 1; k++) {\n cum += a[d][k];\n y[k + 1] = (int)(cum * W / total);\n if (y[k + 1] <= y[k]) y[k + 1] = y[k] + 1;\n }\n \n // Ensure validity from the end (each strip must have positive height)\n for (int k = N - 1; k >= 1; k--) {\n if (y[k] >= y[k + 1]) y[k] = y[k + 1] - 1;\n }\n \n for (int k = 0; k < N; k++) {\n cout << y[k] << \" 0 \" << y[k + 1] << \" \" << W << \"\\n\";\n }\n }\n \n return 0;\n}","ahc032":"#include \nusing namespace std;\n\nconst long long P = 998244353;\nint N, M, K;\nvector> a_init;\nvector, 3>> stamps;\n\nlong long eval(const vector>& ops) {\n auto a = a_init;\n for (auto& [m, p, q] : ops) {\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n a[p+i][q+j] = (a[p+i][q+j] + stamps[m][i][j]) % P;\n }\n long long score = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n score += a[i][j];\n return score;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(0);\n \n cin >> N >> M >> K;\n a_init.assign(N, vector(N));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n cin >> a_init[i][j];\n a_init[i][j] %= P;\n }\n \n stamps.resize(M);\n for (int m = 0; m < M; m++)\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n cin >> stamps[m][i][j];\n \n vector> best_ops;\n auto a = a_init;\n for (int op = 0; op < K; op++) {\n long long best_gain = 0;\n int bm = -1, bp = -1, bq = -1;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N-3; p++)\n for (int q = 0; q <= N-3; q++) {\n long long gain = 0;\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n gain += (a[p+i][q+j] + stamps[m][i][j]) % P - a[p+i][q+j];\n if (gain > best_gain) { best_gain = gain; bm = m; bp = p; bq = q; }\n }\n if (bm == -1) break;\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n a[bp+i][bq+j] = (a[bp+i][bq+j] + stamps[bm][i][j]) % P;\n best_ops.push_back({bm, bp, bq});\n }\n \n long long best_score = eval(best_ops);\n mt19937 rng(42);\n auto cur_ops = best_ops;\n long long cur_score = best_score;\n \n auto start = chrono::steady_clock::now();\n while (chrono::duration(chrono::steady_clock::now() - start).count() < 1.9) {\n double t = 1.0 - chrono::duration(chrono::steady_clock::now() - start).count() / 1.9;\n double temp = t * t * 5e7;\n \n auto new_ops = cur_ops;\n int act = rng() % 3;\n if (act == 0 && !new_ops.empty()) {\n new_ops.erase(new_ops.begin() + rng() % new_ops.size());\n } else if (act == 1 && new_ops.size() < (size_t)K) {\n new_ops.push_back({(int)(rng()%M), (int)(rng()%(N-2)), (int)(rng()%(N-2))});\n } else if (!new_ops.empty()) {\n int idx = rng() % new_ops.size();\n new_ops[idx] = {(int)(rng()%M), (int)(rng()%(N-2)), (int)(rng()%(N-2))};\n }\n \n long long new_score = eval(new_ops);\n if (new_score > cur_score || (temp > 0 && exp((new_score-cur_score)/temp) > (rng()%1000000)/1e6)) {\n cur_ops = new_ops;\n cur_score = new_score;\n if (cur_score > best_score) { best_score = cur_score; best_ops = cur_ops; }\n }\n }\n \n cout << best_ops.size() << \"\\n\";\n for (auto& [m,p,q] : best_ops) cout << m << \" \" << p << \" \" << q << \"\\n\";\n}","ahc033":"#include \nusing namespace std;\n\nconst int N = 5;\nint A[N][N];\nint grid[N][N];\nint cr[N], cc[N], hold[N];\nint next_in[N];\nstring ans[N];\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n; cin >> n;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n cin >> A[i][j];\n \n memset(grid, -1, sizeof(grid));\n memset(hold, -1, sizeof(hold));\n memset(next_in, 0, sizeof(next_in));\n for (int i = 0; i < N; i++) { cr[i] = i; cc[i] = 0; }\n \n for (int t = 0; t < 5000; t++) {\n // Step 1: Bring in containers\n for (int i = 0; i < N; i++) {\n if (next_in[i] < N && grid[i][0] == -1) {\n bool blocked = false;\n for (int c = 0; c < N; c++)\n if (cr[c] == i && cc[c] == 0 && hold[c] != -1)\n blocked = true;\n if (!blocked) grid[i][0] = A[i][next_in[i]++];\n }\n }\n \n // Decide moves\n char moves[N];\n for (int c = 0; c < N; c++) moves[c] = '.';\n \n for (int c = 0; c < N; c++) {\n int r = cr[c], col = cc[c];\n \n if (hold[c] == -1) {\n if (grid[r][col] != -1) {\n moves[c] = 'P';\n } else if (col > 0) {\n moves[c] = 'L';\n }\n } else {\n int target_row = hold[c] / N;\n if (col < N-1) {\n bool can_move = (c == 0 || grid[r][col+1] == -1);\n if (can_move) moves[c] = 'R';\n } else {\n moves[c] = 'Q';\n }\n }\n }\n \n // Step 2: Execute moves\n for (int c = 0; c < N; c++) {\n char m = moves[c];\n if (m == 'P') {\n hold[c] = grid[cr[c]][cc[c]];\n grid[cr[c]][cc[c]] = -1;\n } else if (m == 'Q') {\n grid[cr[c]][cc[c]] = hold[c];\n hold[c] = -1;\n } else if (m == 'R') cc[c]++;\n else if (m == 'L') cc[c]--;\n else if (m == 'U') cr[c]--;\n else if (m == 'D') cr[c]++;\n }\n \n // Step 3: Dispatch\n for (int i = 0; i < N; i++) grid[i][N-1] = -1;\n \n for (int c = 0; c < N; c++) ans[c] += moves[c];\n \n // Check if done\n bool done = true;\n for (int i = 0; i < N; i++) if (next_in[i] < N) done = false;\n for (int c = 0; c < N; c++) if (hold[c] != -1) done = false;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (grid[i][j] != -1) done = false;\n if (done) break;\n }\n \n // Trim trailing dots\n size_t maxlen = 0;\n for (int i = 0; i < N; i++) maxlen = max(maxlen, ans[i].size());\n \n while (maxlen > 1) {\n bool all_dot = true;\n for (int i = 0; i < N; i++) {\n if (ans[i].size() >= maxlen && ans[i][maxlen-1] != '.') all_dot = false;\n }\n if (!all_dot) break;\n maxlen--;\n for (int i = 0; i < N; i++)\n if (ans[i].size() > maxlen) ans[i].resize(maxlen);\n }\n \n for (int i = 0; i < N; i++) cout << ans[i] << \"\\n\";\n return 0;\n}","ahc034":"#include \nusing namespace std;\n\nint N;\nvector> h;\nvector ops;\nint cx = 0, cy = 0;\nint load = 0;\n\nvoid move_one(char dir) {\n ops.push_back(string(1, dir));\n if (dir == 'U') cx--;\n else if (dir == 'D') cx++;\n else if (dir == 'L') cy--;\n else if (dir == 'R') cy++;\n}\n\nvoid move_to(int tx, int ty) {\n while (cx < tx) move_one('D');\n while (cx > tx) move_one('U');\n while (cy < ty) move_one('R');\n while (cy > ty) move_one('L');\n}\n\nvoid do_load(int d) {\n if (d <= 0) return;\n ops.push_back(\"+\" + to_string(d));\n load += d;\n h[cx][cy] -= d;\n}\n\nvoid do_unload(int d) {\n if (d <= 0) return;\n ops.push_back(\"-\" + to_string(d));\n load -= d;\n h[cx][cy] += d;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N, vector(N));\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n cin >> h[i][j];\n }\n }\n \n while (true) {\n int si = -1, sj = -1, best_dist = INT_MAX;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (h[i][j] > 0) {\n int dist = abs(i - cx) + abs(j - cy);\n if (dist < best_dist) {\n best_dist = dist;\n si = i;\n sj = j;\n }\n }\n }\n }\n \n if (si == -1) break;\n \n move_to(si, sj);\n do_load(h[cx][cy]);\n \n while (load > 0) {\n int ti = -1, tj = -1;\n best_dist = INT_MAX;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (h[i][j] < 0) {\n int dist = abs(i - cx) + abs(j - cy);\n if (dist < best_dist) {\n best_dist = dist;\n ti = i;\n tj = j;\n }\n }\n }\n }\n \n if (ti == -1) break;\n \n move_to(ti, tj);\n do_unload(min(load, -h[cx][cy]));\n }\n }\n \n for (const auto& op : ops) {\n cout << op << \"\\n\";\n }\n \n return 0;\n}","ahc035":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, T;\n cin >> N >> M >> T;\n\n int seed_count = 2 * N * (N - 1);\n vector> X(seed_count, vector(M, 0));\n\n for (int i = 0; i < seed_count; i++) {\n for (int j = 0; j < M; j++) {\n cin >> X[i][j];\n }\n }\n\n for (int t = 0; t < T; t++) {\n // Find max value for each criterion\n vector maxVal(M, -1);\n for (int l = 0; l < M; l++) {\n for (int i = 0; i < seed_count; i++) {\n maxVal[l] = max(maxVal[l], X[i][l]);\n }\n }\n \n // Calculate score for each seed (bonus for having max values)\n vector> seed_scores(seed_count);\n for (int i = 0; i < seed_count; i++) {\n double score = 0;\n for (int l = 0; l < M; l++) {\n if (X[i][l] == maxVal[l]) {\n score += 1000;\n }\n score += X[i][l];\n }\n seed_scores[i] = {score, i};\n }\n \n sort(seed_scores.begin(), seed_scores.end(), greater>());\n \n vector selected(N * N);\n for (int i = 0; i < N * N; i++) {\n selected[i] = seed_scores[i].second;\n }\n \n auto getValue = [&](int idx) {\n int total = 0;\n for (int l = 0; l < M; l++) total += X[idx][l];\n return total;\n };\n \n sort(selected.begin(), selected.end(), [&](int a, int b) {\n return getValue(a) > getValue(b);\n });\n \n vector> pos_order;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n pos_order.push_back({i, j});\n }\n }\n \n double cx = (N - 1) / 2.0;\n double cy = (N - 1) / 2.0;\n sort(pos_order.begin(), pos_order.end(), [&](auto& a, auto& b) {\n double da = abs(a.first - cx) + abs(a.second - cy);\n double db = abs(b.first - cx) + abs(b.second - cy);\n if (da != db) return da < db;\n if (a.first != b.first) return a.first < b.first;\n return a.second < b.second;\n });\n \n vector> A(N, vector(N, -1));\n for (int i = 0; i < N * N; i++) {\n A[pos_order[i].first][pos_order[i].second] = selected[i];\n }\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n cout << A[i][j];\n if (j < N - 1) cout << \" \";\n else cout << \"\\n\";\n }\n }\n cout.flush();\n\n for (int i = 0; i < seed_count; i++) {\n for (int j = 0; j < M; j++) {\n cin >> X[i][j];\n }\n }\n }\n\n return 0;\n}","ahc038":"#include \nusing namespace std;\n\nint N, M, V;\nint rx, ry, dir; // root pos and fingertip direction (0=R,1=D,2=L,3=U)\nconst int DX[] = {0, 1, 0, -1};\nconst int DY[] = {1, 0, -1, 0};\n\npair fingertip() { return {rx + DX[dir], ry + DY[dir]}; }\nbool valid(int x, int y) { return x >= 0 && x < N && y >= 0 && y < N; }\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> V;\n vector grid(N), target(N);\n for (int i = 0; i < N; i++) cin >> grid[i];\n for (int i = 0; i < N; i++) cin >> target[i];\n \n cout << \"2\\n0 1\\n0 0\\n\";\n rx = ry = dir = 0;\n \n set> pickup, drop;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n if (grid[i][j] == '1' && target[i][j] == '0') pickup.insert({i, j});\n if (target[i][j] == '1' && grid[i][j] == '0') drop.insert({i, j});\n }\n \n vector ops;\n bool holding = false;\n \n auto output = [&](char m, char r, char a) {\n string s; s += m; s += r; s += '.'; s += a;\n ops.push_back(s);\n };\n \n auto navigate = [&](set>& targets, bool is_pickup) {\n while (!targets.empty() && ops.size() < 95000) {\n auto [fx, fy] = fingertip();\n if (valid(fx, fy) && targets.count({fx, fy})) {\n output('.', '.', 'P');\n targets.erase({fx, fy});\n return true;\n }\n \n pair best; int best_d = INT_MAX;\n for (auto& p : targets) {\n int d = abs(p.first - fx) + abs(p.second - fy);\n if (d < best_d) { best_d = d; best = p; }\n }\n \n int tx = best.first, ty = best.second;\n int dx = tx - rx, dy = ty - ry;\n char m = '.', r = '.';\n \n if (abs(dx) + abs(dy) == 1) {\n int want = (dx == 0 && dy == 1) ? 0 : (dx == 1 && dy == 0) ? 1 : \n (dx == 0 && dy == -1) ? 2 : 3;\n if (want != dir) {\n r = ((dir + 1) % 4 == want) ? 'R' : 'L';\n dir = (r == 'R') ? (dir + 1) % 4 : (dir + 3) % 4;\n }\n } else {\n auto [fx2, fy2] = fingertip();\n if (fx2 < tx && valid(rx + 1, ry)) { m = 'D'; rx++; }\n else if (fx2 > tx && valid(rx - 1, ry)) { m = 'U'; rx--; }\n else if (fy2 < ty && valid(rx, ry + 1)) { m = 'R'; ry++; }\n else if (fy2 > ty && valid(rx, ry - 1)) { m = 'L'; ry--; }\n else {\n // Need to reposition - just try any valid move\n if (valid(rx + 1, ry)) { m = 'D'; rx++; }\n else if (valid(rx - 1, ry)) { m = 'U'; rx--; }\n else if (valid(rx, ry + 1)) { m = 'R'; ry++; }\n else if (valid(rx, ry - 1)) { m = 'L'; ry--; }\n }\n }\n output(m, r, '.');\n }\n return false;\n };\n \n while (ops.size() < 95000) {\n if (!holding) {\n if (pickup.empty()) break;\n if (navigate(pickup, true)) holding = true;\n else break;\n } else {\n if (drop.empty()) break;\n if (navigate(drop, false)) holding = false;\n else break;\n }\n }\n \n for (auto& op : ops) cout << op << \"\\n\";\n return 0;\n}","ahc039":"#include \nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N;\n cin >> N;\n \n vector> mackerel(N), sardine(N);\n \n for (int i = 0; i < N; i++)\n cin >> mackerel[i].first >> mackerel[i].second;\n for (int i = 0; i < N; i++)\n cin >> sardine[i].first >> sardine[i].second;\n \n vector xs, ys;\n for (auto& p : mackerel) { xs.push_back(p.first); ys.push_back(p.second); }\n for (auto& p : sardine) { xs.push_back(p.first); ys.push_back(p.second); }\n \n sort(xs.begin(), xs.end()); xs.erase(unique(xs.begin(), xs.end()), xs.end());\n sort(ys.begin(), ys.end()); ys.erase(unique(ys.begin(), ys.end()), ys.end());\n \n int nx = xs.size(), ny = ys.size();\n map x_idx, y_idx;\n for (int i = 0; i < nx; i++) x_idx[xs[i]] = i;\n for (int i = 0; i < ny; i++) y_idx[ys[i]] = i;\n \n vector>> points_by_y(ny);\n for (auto& p : mackerel)\n points_by_y[y_idx[p.second]].emplace_back(x_idx[p.first], 1);\n for (auto& p : sardine)\n points_by_y[y_idx[p.second]].emplace_back(x_idx[p.first], -1);\n \n int best_score = 0;\n int best_x1i = 0, best_y1i = 0, best_x2i = 0, best_y2i = 0;\n \n int y_step = max(1, ny / 80);\n \n for (int y1 = 0; y1 < ny; y1 += y_step) {\n vector col_sum(nx, 0);\n \n for (int y2 = y1; y2 < ny; y2++) {\n for (auto& [xi, val] : points_by_y[y2])\n col_sum[xi] += val;\n \n int cur_sum = 0, max_sum = 0;\n int cur_start = 0, best_start = 0, best_end = 0;\n for (int x = 0; x < nx; x++) {\n cur_sum += col_sum[x];\n if (cur_sum > max_sum) {\n max_sum = cur_sum;\n best_start = cur_start;\n best_end = x;\n }\n if (cur_sum < 0) {\n cur_sum = 0;\n cur_start = x + 1;\n }\n }\n \n if (max_sum > best_score) {\n best_score = max_sum;\n best_x1i = best_start;\n best_x2i = best_end;\n best_y1i = y1;\n best_y2i = y2;\n }\n }\n }\n \n int best_x1 = best_x1i < nx ? xs[best_x1i] : 0;\n int best_x2 = best_x2i < nx ? xs[best_x2i] : 1;\n int best_y1 = best_y1i < ny ? ys[best_y1i] : 0;\n int best_y2 = best_y2i < ny ? ys[best_y2i] : 1;\n \n if (best_score == 0) {\n best_x1 = 0; best_y1 = 0;\n best_x2 = 1; best_y2 = 1;\n }\n \n cout << 4 << \"\\n\";\n cout << best_x1 << \" \" << best_y1 << \"\\n\";\n cout << best_x2 << \" \" << best_y1 << \"\\n\";\n cout << best_x2 << \" \" << best_y2 << \"\\n\";\n cout << best_x1 << \" \" << best_y2 << \"\\n\";\n \n return 0;\n}","ahc040":"#include \nusing namespace std;\n\nint N, T;\nlong long sigma;\nvector w, h;\n\nstruct PlacedRect { long long x1, y1, x2, y2; int id; };\n\ntuple simulate(const vector>& ops) {\n vector placed;\n long long W = 0, H = 0;\n for (auto& [p, r, d, b] : ops) {\n long long rw = w[p], rh = h[p];\n if (r) swap(rw, rh);\n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n placed.push_back({x, y, x + rw, y + rh, p});\n W = max(W, x + rw); H = max(H, y + rh);\n }\n return {W, H};\n}\n\nmt19937 rng(42);\n\nvector> genGreedy() {\n vector> ops;\n vector placed;\n long long curW = 0, curH = 0;\n for (int i = 0; i < N; i++) {\n long long best = LLONG_MAX; tuple bc = {0,'U',-1};\n for (int r = 0; r < 2; r++) for (char d : {'U','L'}) for (int b = -1; b < i; b++) {\n long long rw = w[i], rh = h[i]; if (r) swap(rw, rh);\n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n long long sc = max(curW, x+rw) + max(curH, y+rh);\n if (sc < best) { best = sc; bc = {r, d, b}; }\n }\n auto [r, d, b] = bc;\n long long rw = w[i], rh = h[i]; if (r) swap(rw, rh);\n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n placed.push_back({x, y, x+rw, y+rh, i}); curW = max(curW, x+rw); curH = max(curH, y+rh);\n ops.push_back({i, r, d, b});\n }\n return ops;\n}\n\nvector> mutate(vector> ops) {\n for (int i = 0; i < N; i++) if (rng() % 4 == 0) {\n auto& [p, r, d, b] = ops[i];\n int choice = rng() % 3;\n if (choice == 0) r = 1 - r;\n else if (choice == 1) d = (d == 'U') ? 'L' : 'U';\n else if (i > 0) b = (int)(rng() % (i + 1)) - 1;\n }\n return ops;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> T >> sigma;\n w.resize(N); h.resize(N);\n for (int i = 0; i < N; i++) cin >> w[i] >> h[i];\n \n auto bestOps = genGreedy();\n auto [bw, bh] = simulate(bestOps);\n long long bestSim = bw + bh;\n \n vector>> candidates;\n candidates.push_back(bestOps);\n \n for (int iter = 0; iter < 5000 && (int)candidates.size() < T; iter++) {\n auto ops = mutate(bestOps);\n auto [sw, sh] = simulate(ops);\n if (sw + sh < bestSim * 1.1) {\n candidates.push_back(ops);\n if (sw + sh < bestSim) { bestSim = sw + sh; bestOps = ops; }\n }\n }\n \n while ((int)candidates.size() < T) candidates.push_back(mutate(bestOps));\n \n for (int t = 0; t < T; t++) {\n auto& ops = candidates[t % candidates.size()];\n cout << ops.size() << \"\\n\";\n for (auto& [p, r, d, b] : ops) cout << p << \" \" << r << \" \" << d << \" \" << b << \"\\n\";\n cout.flush();\n long long W, H; cin >> W >> H;\n }\n \n return 0;\n}","ahc041":"#include \nusing namespace std;\n\nint N, M, H;\nvector A;\nvector> adj;\nvector parent_arr;\nvector depth_arr;\n\nvoid dfs(int u) {\n // Sort neighbors by descending beauty - visit high beauty first to place them deep\n vector> neighbors;\n for (int v : adj[u]) {\n if (depth_arr[v] == -1) {\n neighbors.push_back({-A[v], v}); // negative for descending sort\n }\n }\n sort(neighbors.begin(), neighbors.end());\n \n for (auto& [neg_beauty, v] : neighbors) {\n if (depth_arr[v] == -1 && depth_arr[u] < H) {\n parent_arr[v] = u;\n depth_arr[v] = depth_arr[u] + 1;\n dfs(v);\n }\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> H;\n \n A.resize(N);\n for (int i = 0; i < N; i++) {\n cin >> A[i];\n }\n \n adj.resize(N);\n for (int i = 0; i < M; i++) {\n int u, v;\n cin >> u >> v;\n adj[u].push_back(v);\n adj[v].push_back(u);\n }\n \n for (int i = 0; i < N; i++) {\n int x, y;\n cin >> x >> y;\n }\n \n parent_arr.resize(N, -1);\n depth_arr.resize(N, -1);\n \n // Sort vertices by ascending beauty - low beauty vertices become roots first\n vector order(N);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int a, int b) {\n return A[a] < A[b];\n });\n \n // Build trees using DFS from low-beauty roots\n for (int start : order) {\n if (depth_arr[start] != -1) continue;\n \n depth_arr[start] = 0;\n parent_arr[start] = -1;\n dfs(start);\n }\n \n // Output\n for (int i = 0; i < N; i++) {\n cout << parent_arr[i];\n if (i < N - 1) cout << \" \";\n }\n cout << \"\\n\";\n \n return 0;\n}","ahc042":"#include \nusing namespace std;\n\nint N;\nvector board;\nvector> ops;\n\nvoid L(int r) { ops.push_back({'L', r}); for (int j = 0; j < N-1; j++) board[r][j] = board[r][j+1]; board[r][N-1] = '.'; }\nvoid R(int r) { ops.push_back({'R', r}); for (int j = N-1; j > 0; j--) board[r][j] = board[r][j-1]; board[r][0] = '.'; }\nvoid U(int c) { ops.push_back({'U', c}); for (int i = 0; i < N-1; i++) board[i][c] = board[i+1][c]; board[N-1][c] = '.'; }\nvoid D(int c) { ops.push_back({'D', c}); for (int i = N-1; i > 0; i--) board[i][c] = board[i-1][c]; board[0][c] = '.'; }\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n board.resize(N);\n for (int i = 0; i < N; i++) cin >> board[i];\n \n auto count_oni = [&]() {\n int c = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (board[i][j] == 'x') c++;\n return c;\n };\n \n while (count_oni() > 0) {\n double best_ratio = 1e18;\n int best_type = -1, best_idx = -1, best_dist = -1;\n \n auto consider = [&](int type, int idx, int dist, int cnt) {\n if (cnt == 0) return;\n double ratio = (double)(2 * dist) / cnt;\n if (ratio < best_ratio) { best_ratio = ratio; best_type = type; best_idx = idx; best_dist = dist; }\n };\n \n for (int j = 0; j < N; j++) {\n int first_fuku = N;\n for (int i = 0; i < N; i++) if (board[i][j] == 'o') { first_fuku = i; break; }\n int last_oni = -1, cnt = 0;\n for (int i = 0; i < first_fuku; i++) if (board[i][j] == 'x') { last_oni = i; cnt++; }\n if (cnt > 0) consider(0, j, last_oni + 1, cnt);\n }\n \n for (int j = 0; j < N; j++) {\n int last_fuku = -1;\n for (int i = N-1; i >= 0; i--) if (board[i][j] == 'o') { last_fuku = i; break; }\n int first_oni = N, cnt = 0;\n for (int i = N-1; i > last_fuku; i--) if (board[i][j] == 'x') { first_oni = i; cnt++; }\n if (cnt > 0) consider(1, j, N - first_oni, cnt);\n }\n \n for (int i = 0; i < N; i++) {\n int first_fuku = N;\n for (int j = 0; j < N; j++) if (board[i][j] == 'o') { first_fuku = j; break; }\n int last_oni = -1, cnt = 0;\n for (int j = 0; j < first_fuku; j++) if (board[i][j] == 'x') { last_oni = j; cnt++; }\n if (cnt > 0) consider(2, i, last_oni + 1, cnt);\n }\n \n for (int i = 0; i < N; i++) {\n int last_fuku = -1;\n for (int j = N-1; j >= 0; j--) if (board[i][j] == 'o') { last_fuku = j; break; }\n int first_oni = N, cnt = 0;\n for (int j = N-1; j > last_fuku; j--) if (board[i][j] == 'x') { first_oni = j; cnt++; }\n if (cnt > 0) consider(3, i, N - first_oni, cnt);\n }\n \n if (best_type == 0) { for (int t = 0; t < best_dist; t++) U(best_idx); for (int t = 0; t < best_dist; t++) D(best_idx); }\n else if (best_type == 1) { for (int t = 0; t < best_dist; t++) D(best_idx); for (int t = 0; t < best_dist; t++) U(best_idx); }\n else if (best_type == 2) { for (int t = 0; t < best_dist; t++) L(best_idx); for (int t = 0; t < best_dist; t++) R(best_idx); }\n else { for (int t = 0; t < best_dist; t++) R(best_idx); for (int t = 0; t < best_dist; t++) L(best_idx); }\n }\n \n for (auto& [d, p] : ops) cout << d << \" \" << p << \"\\n\";\n \n return 0;\n}","ahc044":"#include \nusing namespace std;\n\nint N, L;\nvector T;\n\nlong long simulate(const vector& a, const vector& b, vector& t) {\n fill(t.begin(), t.end(), 0);\n int x = 0;\n for (int week = 0; week < L; week++) {\n t[x]++;\n x = (t[x] & 1) ? a[x] : b[x];\n }\n long long error = 0;\n for (int i = 0; i < N; i++) {\n error += abs(t[i] - T[i]);\n }\n return error;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> L;\n T.resize(N);\n for (int i = 0; i < N; i++) {\n cin >> T[i];\n }\n \n vector a(N), b(N);\n mt19937 rng(42);\n \n // Build weighted list for biased sampling\n vector weighted;\n for (int i = 0; i < N; i++) {\n int cnt = max(1, T[i] / 500);\n for (int j = 0; j < cnt; j++) weighted.push_back(i);\n }\n \n // Initialize: circular\n for (int i = 0; i < N; i++) {\n a[i] = (i + 1) % N;\n b[i] = (i + 1) % N;\n }\n \n vector t(N);\n long long best_error = simulate(a, b, t);\n vector best_a = a, best_b = b;\n long long cur_error = best_error;\n \n auto start = chrono::steady_clock::now();\n double time_limit = 1.85;\n \n while (true) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > time_limit) break;\n \n double progress = elapsed / time_limit;\n double temp = 5000.0 * pow(0.0001, progress);\n \n int i = rng() % N;\n int choice = rng() % 2;\n int old_val = (choice == 0) ? a[i] : b[i];\n int new_val;\n if (rng() % 3 == 0) {\n new_val = rng() % N;\n } else {\n new_val = weighted[rng() % weighted.size()];\n }\n \n if (choice == 0) a[i] = new_val;\n else b[i] = new_val;\n \n long long new_error = simulate(a, b, t);\n \n double delta = (double)(new_error - cur_error);\n if (delta <= 0 || (temp > 0 && exp(-delta / temp) > (double)(rng() % 100000) / 100000.0)) {\n cur_error = new_error;\n if (new_error < best_error) {\n best_error = new_error;\n best_a = a;\n best_b = b;\n }\n } else {\n if (choice == 0) a[i] = old_val;\n else b[i] = old_val;\n }\n }\n \n for (int i = 0; i < N; i++) {\n cout << best_a[i] << \" \" << best_b[i] << \"\\n\";\n }\n \n return 0;\n}","ahc045":"#include \nusing namespace std;\n\nint queries_used = 0;\n\nvector> query(vector cities) {\n cout << \"? \" << cities.size();\n for (int c : cities) cout << \" \" << c;\n cout << endl;\n \n vector> edges;\n for (size_t i = 0; i + 1 < cities.size(); i++) {\n int a, b;\n cin >> a >> b;\n edges.emplace_back(a, b);\n }\n queries_used++;\n return edges;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, Q, L, W;\n cin >> N >> M >> Q >> L >> W;\n \n vector G(M);\n for (int i = 0; i < M; i++) cin >> G[i];\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) {\n int lx, rx, ly, ry;\n cin >> lx >> rx >> ly >> ry;\n x[i] = (lx + rx) / 2.0;\n y[i] = (ly + ry) / 2.0;\n }\n \n vector order(N);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int a, int b) {\n return x[a] + y[a] < x[b] + y[b];\n });\n \n vector> groups(M);\n int idx = 0;\n for (int i = 0; i < M; i++) {\n for (int j = 0; j < G[i]; j++) {\n groups[i].push_back(order[idx++]);\n }\n }\n \n vector>> edges(M);\n \n for (int k = 0; k < M; k++) {\n int g = groups[k].size();\n if (g == 1) continue;\n \n vector> all_edges;\n \n for (int i = 0; i < g - 1 && queries_used < Q; ) {\n int end = min(i + L, g);\n if (end - i >= 2) {\n vector subset(groups[k].begin() + i, groups[k].begin() + end);\n auto e = query(subset);\n all_edges.insert(all_edges.end(), e.begin(), e.end());\n i += max(1, end - i - 1);\n } else break;\n }\n \n map city_to_local;\n for (int i = 0; i < g; i++) city_to_local[groups[k][i]] = i;\n \n vector parent(g);\n iota(parent.begin(), parent.end(), 0);\n function find = [&](int x) -> int {\n return parent[x] == x ? x : parent[x] = find(parent[x]);\n };\n \n for (auto& e : all_edges) {\n int u = city_to_local[e.first];\n int v = city_to_local[e.second];\n if (find(u) != find(v)) {\n parent[find(u)] = find(v);\n edges[k].push_back(e);\n }\n }\n \n for (int i = 0; i + 1 < g && (int)edges[k].size() < g - 1; i++) {\n int u = i, v = i + 1;\n if (find(u) != find(v)) {\n parent[find(u)] = find(v);\n edges[k].push_back({groups[k][u], groups[k][v]});\n }\n }\n }\n \n cout << \"!\" << endl;\n for (int k = 0; k < M; k++) {\n for (int c : groups[k]) cout << c << \" \";\n cout << \"\\n\";\n for (auto& e : edges[k]) {\n cout << e.first << \" \" << e.second << \"\\n\";\n }\n }\n \n return 0;\n}","ahc046":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M;\n cin >> N >> M;\n \n vector> targets(M);\n for (int i = 0; i < M; i++) {\n cin >> targets[i].first >> targets[i].second;\n }\n \n vector actions;\n int curR = targets[0].first, curC = targets[0].second;\n \n for (int i = 1; i < M; i++) {\n int tR = targets[i].first, tC = targets[i].second;\n \n int moveCost = abs(tR - curR) + abs(tC - curC);\n int bestCost = moveCost;\n int bestStrategy = 0;\n \n // Strategy 1: Move to column, slide up (target at row 0)\n if (tR == 0 && curR > 0) {\n int cost = abs(tC - curC) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 1; }\n }\n \n // Strategy 2: Move to column, slide down (target at row N-1)\n if (tR == N - 1 && curR < N - 1) {\n int cost = abs(tC - curC) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 2; }\n }\n \n // Strategy 3: Move to row, slide left (target at col 0)\n if (tC == 0 && curC > 0) {\n int cost = abs(tR - curR) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 3; }\n }\n \n // Strategy 4: Move to row, slide right (target at col N-1)\n if (tC == N - 1 && curC < N - 1) {\n int cost = abs(tR - curR) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 4; }\n }\n \n switch (bestStrategy) {\n case 0:\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n break;\n case 1:\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n actions.push_back(\"S U\");\n curR = 0;\n break;\n case 2:\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n actions.push_back(\"S D\");\n curR = N - 1;\n break;\n case 3:\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n actions.push_back(\"S L\");\n curC = 0;\n break;\n case 4:\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n actions.push_back(\"S R\");\n curC = N - 1;\n break;\n }\n }\n \n for (const string& action : actions) {\n cout << action << \"\\n\";\n }\n \n return 0;\n}"},"2":{"ahc001":"#include \nusing namespace std;\n\nconst int W = 10000;\nint n;\nvector px, py, rr;\nint a[201], b[201], c[201], d[201];\n\nbool canExpand(int i, int dir) {\n int na = a[i], nb = b[i], nc = c[i], nd = d[i];\n if (dir == 0) na--;\n else if (dir == 1) nc++;\n else if (dir == 2) nb--;\n else nd++;\n \n if (na < 0 || nc > W || nb < 0 || nd > W) return false;\n \n for (int j = 0; j < n; j++) {\n if (i == j) continue;\n if (!(nc <= a[j] || c[j] <= na || nd <= b[j] || d[j] <= nb)) return false;\n }\n return true;\n}\n\nvoid expand(int i, int dir) {\n if (dir == 0) a[i]--;\n else if (dir == 1) c[i]++;\n else if (dir == 2) b[i]--;\n else d[i]++;\n}\n\nlong long area(int i) {\n return (long long)(c[i] - a[i]) * (d[i] - b[i]);\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> n;\n px.resize(n); py.resize(n); rr.resize(n);\n \n for (int i = 0; i < n; i++) {\n cin >> px[i] >> py[i] >> rr[i];\n a[i] = px[i]; b[i] = py[i]; c[i] = px[i]+1; d[i] = py[i]+1;\n }\n \n auto start = chrono::high_resolution_clock::now();\n \n while (true) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > 4.8) break;\n \n bool changed = false;\n \n vector order(n);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int i, int j) {\n return rr[i] - area(i) > rr[j] - area(j);\n });\n \n for (int i : order) {\n for (int dir = 0; dir < 4; dir++) {\n if (canExpand(i, dir)) {\n expand(i, dir);\n changed = true;\n }\n }\n }\n \n if (!changed) break;\n }\n \n // Shrink rectangles that are too big\n for (int iter = 0; iter < 1000; iter++) {\n for (int i = 0; i < n; i++) {\n if (area(i) <= rr[i]) continue;\n for (int dir = 0; dir < 4; dir++) {\n int na = a[i], nb = b[i], nc = c[i], nd = d[i];\n if (dir == 0) na++;\n else if (dir == 1) nc--;\n else if (dir == 2) nb++;\n else nd--;\n \n if (na >= nc || nb >= nd) continue;\n if (!(na <= px[i] && px[i] < nc && nb <= py[i] && py[i] < nd)) continue;\n \n long long newArea = (long long)(nc - na) * (nd - nb);\n if (newArea >= rr[i]) {\n a[i] = na; b[i] = nb; c[i] = nc; d[i] = nd;\n }\n }\n }\n }\n \n for (int i = 0; i < n; i++) {\n cout << a[i] << \" \" << b[i] << \" \" << c[i] << \" \" << d[i] << \"\\n\";\n }\n \n return 0;\n}","ahc002":"#include \nusing namespace std;\n\nconst int N = 50;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nconst char dc[] = {'U', 'D', 'L', 'R'};\n\nint t[N][N], p[N][N];\nint si, sj;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> si >> sj;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n cin >> t[i][j];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n cin >> p[i][j];\n \n struct State {\n int x, y;\n int score;\n bitset<2500> usedTiles;\n string path;\n };\n \n const int BEAM_WIDTH = 400;\n \n vector beam;\n State init;\n init.x = si;\n init.y = sj;\n init.score = p[si][sj];\n init.usedTiles.set(t[si][sj]);\n init.path = \"\";\n beam.push_back(init);\n \n string bestPath = \"\";\n int bestScore = init.score;\n \n auto startTime = chrono::steady_clock::now();\n \n while (!beam.empty()) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration_cast(now - startTime).count() > 1900) {\n for (const auto& state : beam) {\n if (state.score > bestScore) {\n bestScore = state.score;\n bestPath = state.path;\n }\n }\n break;\n }\n \n vector nextBeam;\n nextBeam.reserve(beam.size() * 4);\n \n for (const auto& state : beam) {\n bool canExtend = false;\n for (int d = 0; d < 4; d++) {\n int nx = state.x + dx[d];\n int ny = state.y + dy[d];\n if (nx < 0 || nx >= N || ny < 0 || ny >= N) continue;\n if (state.usedTiles[t[nx][ny]]) continue;\n \n canExtend = true;\n State newState;\n newState.x = nx;\n newState.y = ny;\n newState.score = state.score + p[nx][ny];\n newState.usedTiles = state.usedTiles;\n newState.usedTiles.set(t[nx][ny]);\n newState.path = state.path + dc[d];\n nextBeam.push_back(move(newState));\n }\n \n if (!canExtend && state.score > bestScore) {\n bestScore = state.score;\n bestPath = state.path;\n }\n }\n \n if (nextBeam.size() > BEAM_WIDTH) {\n nth_element(nextBeam.begin(), nextBeam.begin() + BEAM_WIDTH, nextBeam.end(),\n [](const State& a, const State& b) { return a.score > b.score; });\n nextBeam.resize(BEAM_WIDTH);\n }\n \n beam = move(nextBeam);\n }\n \n cout << bestPath << endl;\n \n return 0;\n}","ahc003":"#include \nusing namespace std;\n\nconst int N = 30;\ndouble h[N][N-1], v[N-1][N];\nint h_cnt[N][N-1], v_cnt[N-1][N];\ndouble h_row[N], v_col[N];\nint h_row_cnt[N], v_col_cnt[N];\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n fill(&h[0][0], &h[0][0] + N*(N-1), 5000.0);\n fill(&v[0][0], &v[0][0] + (N-1)*N, 5000.0);\n fill(&h_cnt[0][0], &h_cnt[0][0] + N*(N-1), 0);\n fill(&v_cnt[0][0], &v_cnt[0][0] + (N-1)*N, 0);\n fill(h_row, h_row + N, 5000.0);\n fill(v_col, v_col + N, 5000.0);\n fill(h_row_cnt, h_row_cnt + N, 0);\n fill(v_col_cnt, v_col_cnt + N, 0);\n \n auto getH = [&](int i, int j) {\n if (h_cnt[i][j] > 0) return h[i][j];\n if (h_row_cnt[i] > 0) return h_row[i];\n return 5000.0;\n };\n \n auto getV = [&](int i, int j) {\n if (v_cnt[i][j] > 0) return v[i][j];\n if (v_col_cnt[j] > 0) return v_col[j];\n return 5000.0;\n };\n \n for (int q = 0; q < 1000; q++) {\n int si, sj, ti, tj;\n cin >> si >> sj >> ti >> tj;\n \n auto idx = [](int i, int j) { return i * N + j; };\n vector dist(N*N, 1e18);\n vector prv(N*N, -1);\n \n priority_queue, vector>, greater<>> pq;\n dist[idx(si, sj)] = 0;\n pq.push({0, idx(si, sj)});\n \n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > dist[u]) continue;\n int i = u / N, j = u % N;\n \n auto relax = [&](int ni, int nj, double w) {\n int nu = idx(ni, nj);\n if (dist[u] + w < dist[nu]) {\n dist[nu] = dist[u] + w;\n prv[nu] = u;\n pq.push({dist[nu], nu});\n }\n };\n \n if (i > 0) relax(i-1, j, getV(i-1, j));\n if (i < N-1) relax(i+1, j, getV(i, j));\n if (j > 0) relax(i, j-1, getH(i, j-1));\n if (j < N-1) relax(i, j+1, getH(i, j));\n }\n \n string path = \"\";\n vector> edges;\n \n int cur = idx(ti, tj);\n while (prv[cur] != -1) {\n int ci = cur / N, cj = cur % N;\n int pi = prv[cur] / N, pj = prv[cur] % N;\n \n if (ci < pi) { path += 'U'; edges.emplace_back(1, ci, cj); }\n else if (ci > pi) { path += 'D'; edges.emplace_back(1, pi, pj); }\n else if (cj < pj) { path += 'L'; edges.emplace_back(0, ci, cj); }\n else { path += 'R'; edges.emplace_back(0, pi, pj); }\n \n cur = prv[cur];\n }\n \n reverse(path.begin(), path.end());\n cout << path << \"\\n\" << flush;\n \n int feedback;\n cin >> feedback;\n \n double est = 0;\n for (auto& [t, ei, ej] : edges) {\n est += (t == 0) ? getH(ei, ej) : getV(ei, ej);\n }\n \n double ratio = feedback / est;\n \n for (auto& [t, ei, ej] : edges) {\n double implied = (t == 0) ? getH(ei, ej) * ratio : getV(ei, ej) * ratio;\n \n if (t == 0) {\n int cnt = ++h_cnt[ei][ej];\n double alpha = 1.0 / (1.0 + cnt);\n h[ei][ej] = h[ei][ej] * (1 - alpha) + implied * alpha;\n } else {\n int cnt = ++v_cnt[ei][ej];\n double alpha = 1.0 / (1.0 + cnt);\n v[ei][ej] = v[ei][ej] * (1 - alpha) + implied * alpha;\n }\n }\n \n // Update row/column averages\n for (int i = 0; i < N; i++) {\n double sum = 0; int cnt = 0;\n for (int j = 0; j < N-1; j++) {\n if (h_cnt[i][j] > 0) { sum += h[i][j]; cnt++; }\n }\n if (cnt > 0) { h_row[i] = sum / cnt; h_row_cnt[i] = cnt; }\n }\n \n for (int j = 0; j < N; j++) {\n double sum = 0; int cnt = 0;\n for (int i = 0; i < N-1; i++) {\n if (v_cnt[i][j] > 0) { sum += v[i][j]; cnt++; }\n }\n if (cnt > 0) { v_col[j] = sum / cnt; v_col_cnt[j] = cnt; }\n }\n }\n \n return 0;\n}","ahc004":"#include \nusing namespace std;\n\nconst int N = 20;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n, m;\n cin >> n >> m;\n \n vector strs(m);\n for(int i = 0; i < m; i++) cin >> strs[i];\n \n vector order(m);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int a, int b) {\n return strs[a].size() > strs[b].size();\n });\n \n char grid[N][N];\n fill(&grid[0][0], &grid[N][0], '.');\n \n // Greedy placement with max overlap preference\n for(int idx : order) {\n const string& s = strs[idx];\n int bestR = -1, bestC, bestD, bestOv = -1;\n \n for(int r = 0; r < N; r++) {\n for(int c = 0; c < N; c++) {\n for(int d = 0; d < 2; d++) {\n bool can = true;\n int ov = 0;\n for(int p = 0; p < (int)s.size() && can; p++) {\n int ni = d ? (r + p) % N : r;\n int nj = d ? c : (c + p) % N;\n if(grid[ni][nj] != '.' && grid[ni][nj] != s[p]) can = false;\n if(grid[ni][nj] != '.') ov++;\n }\n if(can && ov > bestOv) {\n bestOv = ov;\n bestR = r; bestC = c; bestD = d;\n }\n }\n }\n }\n \n if(bestR >= 0) {\n for(int p = 0; p < (int)s.size(); p++) {\n int ni = bestD ? (bestR + p) % N : bestR;\n int nj = bestD ? bestC : (bestC + p) % N;\n grid[ni][nj] = s[p];\n }\n }\n }\n \n // Fill remaining cells randomly\n mt19937 rng(42);\n for(int i = 0; i < N; i++) {\n for(int j = 0; j < N; j++) {\n if(grid[i][j] == '.') grid[i][j] = 'A' + rng() % 8;\n }\n }\n \n // Count function for SA\n auto countMatched = [&]() {\n int cnt = 0;\n for(const auto& s : strs) {\n bool found = false;\n for(int r = 0; r < N && !found; r++) {\n for(int c = 0; c < N && !found; c++) {\n for(int d = 0; d < 2 && !found; d++) {\n bool ok = true;\n for(int p = 0; p < (int)s.size() && ok; p++) {\n int ni = d ? (r + p) % N : r;\n int nj = d ? c : (c + p) % N;\n if(grid[ni][nj] != s[p]) ok = false;\n }\n if(ok) found = true;\n }\n }\n }\n if(found) cnt++;\n }\n return cnt;\n };\n \n // Simple SA to improve\n char bestGrid[N][N];\n memcpy(bestGrid, grid, sizeof(grid));\n int bestScore = countMatched();\n int curScore = bestScore;\n \n auto start = chrono::high_resolution_clock::now();\n double T = 2.0;\n \n while(true) {\n auto now = chrono::high_resolution_clock::now();\n if(chrono::duration(now - start).count() > 2.7) break;\n \n int i = rng() % N, j = rng() % N;\n char old = grid[i][j];\n char newc = 'A' + rng() % 8;\n if(newc == old) continue;\n \n grid[i][j] = newc;\n int newScore = countMatched();\n \n if(newScore >= curScore || (rng() & 0xFFFF) < 65536.0 * exp((newScore - curScore) / T)) {\n curScore = newScore;\n if(newScore > bestScore) {\n bestScore = newScore;\n memcpy(bestGrid, grid, sizeof(grid));\n }\n } else {\n grid[i][j] = old;\n }\n T *= 0.9999;\n }\n \n for(int i = 0; i < N; i++) {\n cout << string(bestGrid[i], bestGrid[i] + N) << '\\n';\n }\n}","ahc005":"#include \nusing namespace std;\n\nint N, si, sj;\nvector grid;\nvector> visible;\nint visible_count = 0;\n\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nconst char dir_char[] = {'U', 'D', 'L', 'R'};\n\ninline bool is_road(int i, int j) {\n return i >= 0 && i < N && j >= 0 && j < N && grid[i][j] != '#';\n}\n\nvoid mark_visible(int i, int j) {\n if (!visible[i][j]) { visible[i][j] = true; visible_count++; }\n for (int jj = j - 1; jj >= 0 && is_road(i, jj); jj--)\n if (!visible[i][jj]) { visible[i][jj] = true; visible_count++; }\n for (int jj = j + 1; jj < N && is_road(i, jj); jj++)\n if (!visible[i][jj]) { visible[i][jj] = true; visible_count++; }\n for (int ii = i - 1; ii >= 0 && is_road(ii, j); ii--)\n if (!visible[ii][j]) { visible[ii][j] = true; visible_count++; }\n for (int ii = i + 1; ii < N && is_road(ii, j); ii++)\n if (!visible[ii][j]) { visible[ii][j] = true; visible_count++; }\n}\n\nint count_new_visible(int i, int j) {\n int cnt = !visible[i][j];\n for (int jj = j - 1; jj >= 0 && is_road(i, jj); jj--) cnt += !visible[i][jj];\n for (int jj = j + 1; jj < N && is_road(i, jj); jj++) cnt += !visible[i][jj];\n for (int ii = i - 1; ii >= 0 && is_road(ii, j); ii--) cnt += !visible[ii][j];\n for (int ii = i + 1; ii < N && is_road(ii, j); ii++) cnt += !visible[ii][j];\n return cnt;\n}\n\npair>, vector>>> dijkstra(int si, int sj) {\n vector> dist(N, vector(N, INT_MAX));\n vector>> parent(N, vector>(N, {-1,-1}));\n priority_queue, vector>, greater<>> pq;\n dist[si][sj] = 0; pq.push({0, si, sj});\n while (!pq.empty()) {\n auto [d, i, j] = pq.top(); pq.pop();\n if (d > dist[i][j]) continue;\n for (int k = 0; k < 4; k++) {\n int ni = i + dx[k], nj = j + dy[k];\n if (is_road(ni, nj)) {\n int c = grid[ni][nj] - '0';\n if (dist[i][j] + c < dist[ni][nj]) {\n dist[ni][nj] = dist[i][j] + c;\n parent[ni][nj] = {i, j};\n pq.push({dist[ni][nj], ni, nj});\n }\n }\n }\n }\n return {dist, parent};\n}\n\nstring get_path(int i1, int j1, int i2, int j2, vector>>& parent) {\n string path;\n int ci = i2, cj = j2;\n while (ci != i1 || cj != j1) {\n auto [pi, pj] = parent[ci][cj];\n for (int k = 0; k < 4; k++) if (pi + dx[k] == ci && pj + dy[k] == cj) { path += dir_char[k]; break; }\n ci = pi; cj = pj;\n }\n reverse(path.begin(), path.end());\n return path;\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> si >> sj;\n grid.resize(N);\n for (int i = 0; i < N; i++) cin >> grid[i];\n \n int total_roads = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (is_road(i, j)) total_roads++;\n \n visible.assign(N, vector(N, false));\n int cur_i = si, cur_j = sj;\n string result;\n mark_visible(cur_i, cur_j);\n \n while (visible_count < total_roads) {\n auto [dist, parent] = dijkstra(cur_i, cur_j);\n int best_i = -1, best_j = -1; double best_score = -1;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (dist[i][j] == INT_MAX || dist[i][j] == 0) continue;\n int nv = count_new_visible(i, j);\n if (nv == 0) continue;\n double score = (double)nv / dist[i][j];\n if (score > best_score) { best_score = score; best_i = i; best_j = j; }\n }\n if (best_i == -1) break;\n string path = get_path(cur_i, cur_j, best_i, best_j, parent);\n result += path;\n int ti = cur_i, tj = cur_j;\n for (char c : path) {\n if (c == 'U') ti--; else if (c == 'D') ti++; else if (c == 'L') tj--; else tj++;\n mark_visible(ti, tj);\n }\n cur_i = best_i; cur_j = best_j;\n }\n \n if (cur_i != si || cur_j != sj) {\n auto [dist, parent] = dijkstra(cur_i, cur_j);\n result += get_path(cur_i, cur_j, si, sj, parent);\n }\n \n cout << result << endl;\n return 0;\n}","future-contest-2022-qual":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K, R;\n cin >> N >> M >> K >> R;\n \n vector> d(N, vector(K));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < K; j++)\n cin >> d[i][j];\n \n vector> deps(N), rdeps(N);\n for (int i = 0; i < R; i++) {\n int u, v;\n cin >> u >> v;\n u--; v--;\n deps[v].push_back(u);\n rdeps[u].push_back(v);\n }\n \n vector taskStatus(N, -1);\n vector memberTask(M, -1), memberStartDay(M, 0);\n \n // Better initial skill estimate based on generation (L2 norm 20-60, avg ~40)\n double initSkill = 40.0 / sqrt(K);\n vector> skillEst(M, vector(K, initSkill));\n vector> skillLo(M, vector(K, 0.0));\n \n auto estimateTime = [&](int task, int member) -> double {\n double w = 0;\n for (int k = 0; k < K; k++)\n w += max(0.0, (double)d[task][k] - skillEst[member][k]);\n return max(1.0, w);\n };\n \n // Critical path depth\n vector depth(N, 1);\n for (int i = N - 1; i >= 0; i--)\n for (int v : rdeps[i])\n depth[i] = max(depth[i], depth[v] + 1);\n \n // Downstream task count\n vector downstream(N, 0);\n for (int i = N - 1; i >= 0; i--) {\n downstream[i] = (int)rdeps[i].size();\n for (int v : rdeps[i])\n downstream[i] += downstream[v];\n }\n \n for (int day = 1; ; day++) {\n vector availTasks;\n for (int i = 0; i < N; i++) {\n if (taskStatus[i] != -1) continue;\n bool ok = true;\n for (int dep : deps[i])\n if (taskStatus[dep] != 1) { ok = false; break; }\n if (ok) availTasks.push_back(i);\n }\n \n // Priority: depth first, then downstream count\n sort(availTasks.begin(), availTasks.end(), [&](int a, int b) {\n if (depth[a] != depth[b]) return depth[a] > depth[b];\n return downstream[a] > downstream[b];\n });\n \n vector freeMembers;\n for (int j = 0; j < M; j++)\n if (memberTask[j] == -1) freeMembers.push_back(j);\n \n vector> assignments;\n vector usedMember(M, false);\n \n for (int task : availTasks) {\n int bestMember = -1;\n double bestTime = 1e18;\n for (int member : freeMembers) {\n if (usedMember[member]) continue;\n double t = estimateTime(task, member);\n if (t < bestTime) {\n bestTime = t;\n bestMember = member;\n }\n }\n if (bestMember == -1) break;\n \n usedMember[bestMember] = true;\n assignments.push_back({bestMember + 1, task + 1});\n taskStatus[task] = 0;\n memberTask[bestMember] = task;\n memberStartDay[bestMember] = day;\n }\n \n cout << assignments.size();\n for (auto& [a, b] : assignments) cout << \" \" << a << \" \" << b;\n cout << \"\\n\";\n cout.flush();\n \n int n; cin >> n;\n if (n == -1) break;\n \n for (int i = 0; i < n; i++) {\n int f; cin >> f; f--;\n int task = memberTask[f];\n int timeTaken = day - memberStartDay[f] + 1;\n taskStatus[task] = 1;\n memberTask[f] = -1;\n \n if (timeTaken == 1) {\n // High confidence: member skills >= task requirements\n for (int k = 0; k < K; k++) {\n skillLo[f][k] = max(skillLo[f][k], (double)d[task][k]);\n skillEst[f][k] = max(skillEst[f][k], (double)d[task][k]);\n }\n } else {\n // w \u2248 timeTaken (noise \u00b13), adjust estimates\n double wEst = (double)timeTaken;\n double currW = 0;\n for (int k = 0; k < K; k++)\n currW += max(0.0, (double)d[task][k] - skillEst[f][k]);\n \n if (currW > 0.5) {\n // Blend factor: if we overestimated skills, reduce them\n double factor = wEst / currW;\n factor = 0.7 * factor + 0.3; // Smooth adjustment\n factor = max(0.5, min(1.8, factor));\n \n for (int k = 0; k < K; k++) {\n double gap = d[task][k] - skillEst[f][k];\n if (gap > 0) {\n double newSkill = d[task][k] - gap * factor;\n skillEst[f][k] = max(skillLo[f][k], newSkill);\n }\n }\n } else if (wEst > 3) {\n // We thought w\u22480, but time > 3, so skills are overestimated\n for (int k = 0; k < K; k++) {\n if (d[task][k] > skillLo[f][k]) {\n skillEst[f][k] = max(skillLo[f][k], \n skillEst[f][k] - wEst / K);\n }\n }\n }\n }\n }\n }\n return 0;\n}","ahc006":"#include \nusing namespace std;\n\nconst int N = 1000, M = 50, CX = 400, CY = 400;\nint ordA[N], ordB[N], ordC[N], ordD[N];\nmt19937 rng(chrono::steady_clock::now().time_since_epoch().count());\n\ninline int manhattan(int x1, int y1, int x2, int y2) {\n return abs(x1 - x2) + abs(y1 - y2);\n}\n\npair>, int> buildGreedyRoute(const vector& selected) {\n vector> events;\n events.reserve(2 * M);\n vector picked(N, false), delivered(N, false);\n int cx = CX, cy = CY, totalCost = 0;\n \n for (int i = 0; i < 2 * M; i++) {\n int best = -1, bestDist = INT_MAX;\n bool isDelivery = false;\n \n for (int idx : selected) {\n if (!picked[idx]) {\n int d = manhattan(cx, cy, ordA[idx], ordB[idx]);\n if (d < bestDist) { bestDist = d; best = idx; isDelivery = false; }\n } else if (!delivered[idx]) {\n int d = manhattan(cx, cy, ordC[idx], ordD[idx]);\n if (d < bestDist) { bestDist = d; best = idx; isDelivery = true; }\n }\n }\n \n totalCost += bestDist;\n if (isDelivery) { cx = ordC[best]; cy = ordD[best]; delivered[best] = true; }\n else { cx = ordA[best]; cy = ordB[best]; picked[best] = true; }\n events.push_back({best, isDelivery});\n }\n totalCost += manhattan(cx, cy, CX, CY);\n return {events, totalCost};\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n auto startTime = chrono::steady_clock::now();\n for (int i = 0; i < N; i++) cin >> ordA[i] >> ordB[i] >> ordC[i] >> ordD[i];\n \n auto elapsed = [&]() {\n return chrono::duration(chrono::steady_clock::now() - startTime).count();\n };\n \n vector> orderedByCenter(N);\n for (int i = 0; i < N; i++) {\n int d = manhattan(CX, CY, ordA[i], ordB[i]) + manhattan(CX, CY, ordC[i], ordD[i]);\n orderedByCenter[i] = {d, i};\n }\n sort(orderedByCenter.begin(), orderedByCenter.end());\n \n vector selected(M), unselected(N - M);\n for (int i = 0; i < M; i++) selected[i] = orderedByCenter[i].second;\n for (int i = 0; i < N - M; i++) unselected[i] = orderedByCenter[M + i].second;\n \n auto [bestEvents, bestCost] = buildGreedyRoute(selected);\n vector bestSelected = selected;\n int currentCost = bestCost;\n double temp = 3000.0;\n \n while (elapsed() < 1.85) {\n int selIdx = rng() % M;\n int unselIdx = rng() % (N - M);\n \n swap(selected[selIdx], unselected[unselIdx]);\n auto [events, cost] = buildGreedyRoute(selected);\n \n int delta = cost - currentCost;\n bool accept = delta < 0 || exp(-delta / temp) > (rng() % 10000) / 10000.0;\n \n if (accept) {\n currentCost = cost;\n if (cost < bestCost) {\n bestCost = cost;\n bestSelected = selected;\n bestEvents = events;\n }\n } else {\n swap(selected[selIdx], unselected[unselIdx]);\n }\n temp *= 0.99995;\n }\n \n cout << M;\n for (int i = 0; i < M; i++) cout << \" \" << (bestSelected[i] + 1);\n cout << \"\\n\" << (2 * M + 2) << \" \" << CX << \" \" << CY;\n for (const auto& [idx, isDel] : bestEvents) {\n if (isDel) cout << \" \" << ordC[idx] << \" \" << ordD[idx];\n else cout << \" \" << ordA[idx] << \" \" << ordB[idx];\n }\n cout << \" \" << CX << \" \" << CY << \"\\n\";\n \n return 0;\n}","ahc007":"#include \nusing namespace std;\n\nclass UnionFind {\n vector parent, rank_;\npublic:\n UnionFind(int n) : parent(n), rank_(n, 0) {\n iota(parent.begin(), parent.end(), 0);\n }\n int find(int x) {\n if (parent[x] != x) parent[x] = find(parent[x]);\n return parent[x];\n }\n bool unite(int x, int y) {\n int px = find(x), py = find(y);\n if (px == py) return false;\n if (rank_[px] < rank_[py]) swap(px, py);\n parent[py] = px;\n if (rank_[px] == rank_[py]) rank_[px]++;\n return true;\n }\n bool same(int x, int y) {\n return find(x) == find(y);\n }\n};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n const int N = 400, M = 1995;\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) {\n cin >> x[i] >> y[i];\n }\n \n vector u(M), v(M), d(M);\n for (int i = 0; i < M; i++) {\n cin >> u[i] >> v[i];\n double dx = x[u[i]] - x[v[i]];\n double dy = y[u[i]] - y[v[i]];\n d[i] = (int)round(sqrt(dx * dx + dy * dy));\n }\n \n UnionFind uf(N);\n int components = N;\n \n for (int i = 0; i < M; i++) {\n int l;\n cin >> l;\n \n int pu = uf.find(u[i]);\n int pv = uf.find(v[i]);\n \n bool already_connected = (pu == pv);\n double ratio = (double)l / d[i];\n \n bool adopt = false;\n \n if (!already_connected) {\n int useful_remaining = 0;\n int same_pair_remaining = 0;\n for (int j = i + 1; j < M; j++) {\n int uj = uf.find(u[j]);\n int vj = uf.find(v[j]);\n if (uj != vj) {\n useful_remaining++;\n if ((uj == pu && vj == pv) || (uj == pv && vj == pu)) {\n same_pair_remaining++;\n }\n }\n }\n \n int needed = components - 1;\n \n if (useful_remaining < needed * 2) {\n adopt = true;\n } else {\n double k = same_pair_remaining;\n double expected_min = 1.0 + 2.0 / (k + 2);\n double threshold = expected_min + 0.2;\n \n if (ratio <= threshold || same_pair_remaining == 0) {\n adopt = true;\n }\n }\n }\n \n if (adopt) {\n uf.unite(u[i], v[i]);\n components--;\n }\n \n cout << (adopt ? 1 : 0) << \"\\n\" << flush;\n }\n \n return 0;\n}","ahc008":"#include \nusing namespace std;\n\nint N, M;\nvector> pets;\nvector> humans;\nbool blocked[32][32];\n\nbool pet_at(int x, int y) {\n for (auto& p : pets) if (p[0] == x && p[1] == y) return true;\n return false;\n}\n\nbool pet_adjacent(int x, int y) {\n int dx[] = {0, -1, 1, 0, 0}, dy[] = {0, 0, 0, -1, 1};\n for (int d = 0; d < 5; d++) if (pet_at(x+dx[d], y+dy[d])) return true;\n return false;\n}\n\nbool can_place(int x, int y) {\n if (x < 1 || x > 30 || y < 1 || y > 30 || blocked[x][y]) return false;\n for (auto& h : humans) if (h[0] == x && h[1] == y) return false;\n return !pet_adjacent(x, y);\n}\n\nbool passable(int x, int y) {\n return x >= 1 && x <= 30 && y >= 1 && y <= 30 && !blocked[x][y];\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N; pets.resize(N);\n for (int i = 0; i < N; i++) cin >> pets[i][0] >> pets[i][1] >> pets[i][2];\n cin >> M; humans.resize(M);\n for (int i = 0; i < M; i++) cin >> humans[i][0] >> humans[i][1];\n \n set> target;\n for (int i = 1; i <= 30; i++) {\n for (int c : {7, 14, 21, 28}) {\n target.insert({i, c});\n target.insert({c, i});\n }\n }\n \n int dx[] = {-1, 1, 0, 0}, dy[] = {0, 0, -1, 1};\n char wc[] = {'u', 'd', 'l', 'r'}, mc[] = {'U', 'D', 'L', 'R'};\n \n for (int turn = 0; turn < 300; turn++) {\n string action(M, '.');\n \n for (int i = 0; i < M; i++) {\n int hx = humans[i][0], hy = humans[i][1];\n int best = -1, bestd = -1;\n \n for (int d = 0; d < 4; d++) {\n int nx = hx + dx[d], ny = hy + dy[d];\n if (can_place(nx, ny)) {\n int sc = target.count({nx, ny}) ? 100 : 1;\n if (sc > best) { best = sc; bestd = d; }\n }\n }\n \n if (bestd >= 0) {\n action[i] = wc[bestd];\n } else {\n int minD = INT_MAX, moveD = -1;\n for (auto& [tx, ty] : target) {\n if (blocked[tx][ty]) continue;\n int dist = abs(hx-tx) + abs(hy-ty);\n if (dist > 0 && dist < minD) minD = dist;\n }\n for (int d = 0; d < 4; d++) {\n int nx = hx + dx[d], ny = hy + dy[d];\n if (!passable(nx, ny) || pet_at(nx, ny)) continue;\n for (auto& [tx, ty] : target) {\n if (blocked[tx][ty]) continue;\n if (abs(nx-tx) + abs(ny-ty) < minD) {\n minD = abs(nx-tx) + abs(ny-ty);\n moveD = d;\n }\n }\n }\n if (moveD >= 0) action[i] = mc[moveD];\n }\n }\n \n cout << action << \"\\n\" << flush;\n \n for (int i = 0; i < M; i++) {\n char a = action[i];\n for (int d = 0; d < 4; d++) {\n if (a == wc[d]) blocked[humans[i][0]+dx[d]][humans[i][1]+dy[d]] = true;\n if (a == mc[d]) { humans[i][0] += dx[d]; humans[i][1] += dy[d]; }\n }\n }\n \n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (char c : s) {\n if (c == 'U') pets[i][0]--;\n else if (c == 'D') pets[i][0]++;\n else if (c == 'L') pets[i][1]--;\n else if (c == 'R') pets[i][1]++;\n }\n }\n }\n return 0;\n}","ahc009":"#include \nusing namespace std;\n\nint N = 20;\nint si, sj, ti, tj;\ndouble p;\nbool hwall[20][19];\nbool vwall[19][20];\n\nbool canMove(int i, int j, char dir) {\n if (dir == 'U') return i > 0 && !vwall[i-1][j];\n if (dir == 'D') return i < 19 && !vwall[i][j];\n if (dir == 'L') return j > 0 && !hwall[i][j-1];\n if (dir == 'R') return j < 19 && !hwall[i][j];\n return false;\n}\n\npair doMove(int i, int j, char dir) {\n if (!canMove(i, j, dir)) return {i, j};\n if (dir == 'U') return {i-1, j};\n if (dir == 'D') return {i+1, j};\n if (dir == 'L') return {i, j-1};\n if (dir == 'R') return {i, j+1};\n return {i, j};\n}\n\ndouble evaluate(const string& s) {\n if (s.empty() || s.size() > 200) return -1;\n vector> prob(N, vector(N, 0));\n prob[si][sj] = 1.0;\n double expectedScore = 0;\n for (int t = 1; t <= (int)s.size(); t++) {\n char dir = s[t-1];\n vector> newProb(N, vector(N, 0));\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (prob[i][j] < 1e-18) continue;\n auto [ni, nj] = doMove(i, j, dir);\n if (ni == ti && nj == tj) {\n expectedScore += (1-p) * prob[i][j] * (401 - t);\n } else {\n newProb[ni][nj] += (1-p) * prob[i][j];\n }\n newProb[i][j] += p * prob[i][j];\n }\n }\n prob = newProb;\n }\n return expectedScore;\n}\n\nstring bfsWithOrder(vector& order) {\n vector> dist(N, vector(N, -1));\n vector>> parent(N, vector>(N, {-1,-1}));\n vector> fromDir(N, vector(N, ' '));\n queue> q;\n q.push({si, sj});\n dist[si][sj] = 0;\n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (char d : order) {\n auto [ni, nj] = doMove(i, j, d);\n if (ni == i && nj == j) continue;\n if (dist[ni][nj] == -1) {\n dist[ni][nj] = dist[i][j] + 1;\n parent[ni][nj] = {i, j};\n fromDir[ni][nj] = d;\n q.push({ni, nj});\n }\n }\n }\n string path;\n int ci = ti, cj = tj;\n while (ci != si || cj != sj) {\n path += fromDir[ci][cj];\n auto [pi, pj] = parent[ci][cj];\n ci = pi; cj = pj;\n }\n reverse(path.begin(), path.end());\n return path;\n}\n\nmt19937 rng(12345);\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n auto startTime = chrono::steady_clock::now();\n \n cin >> si >> sj >> ti >> tj >> p;\n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < 19; j++) hwall[i][j] = (s[j] == '1');\n }\n for (int i = 0; i < 19; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) vwall[i][j] = (s[j] == '1');\n }\n \n string best;\n double bestScore = -1;\n vector order = {'U', 'D', 'L', 'R'};\n \n auto updateBest = [&](const string& s) {\n if (s.size() > 200) return;\n double score = evaluate(s);\n if (score > bestScore) {\n bestScore = score;\n best = s;\n }\n };\n \n while (true) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration_cast(now - startTime).count() > 1850) break;\n \n shuffle(order.begin(), order.end(), rng);\n string path = bfsWithOrder(order);\n int pathLen = path.size();\n \n // Strategy 1: Uniform repetition of each move\n for (int rep = 1; rep * pathLen <= 200; rep++) {\n string result;\n for (char c : path) {\n for (int i = 0; i < rep; i++) result += c;\n }\n updateBest(result);\n }\n \n // Strategy 2: Repeat entire path multiple times\n for (int rep = 1; rep * pathLen <= 200; rep++) {\n string result;\n for (int i = 0; i < rep; i++) result += path;\n updateBest(result);\n }\n \n // Strategy 3: Wall-aware repetition\n int ci = si, cj = sj;\n for (int baseRep = 1; baseRep <= 10; baseRep++) {\n string result;\n ci = si; cj = sj;\n for (char c : path) {\n auto [ni, nj] = doMove(ci, cj, c);\n bool safeAfter = !canMove(ni, nj, c);\n int reps = safeAfter ? baseRep + 2 : baseRep;\n for (int i = 0; i < reps && result.size() < 200; i++) result += c;\n ci = ni; cj = nj;\n }\n updateBest(result);\n }\n \n // Strategy 4: Combine path and move repetition\n for (int pathRep = 1; pathRep <= 5; pathRep++) {\n for (int moveRep = 1; moveRep * pathLen * pathRep <= 200 && moveRep <= 5; moveRep++) {\n string result;\n for (int pr = 0; pr < pathRep; pr++) {\n for (char c : path) {\n for (int mr = 0; mr < moveRep; mr++) result += c;\n }\n }\n updateBest(result);\n }\n }\n }\n \n cout << best << endl;\n return 0;\n}","ahc010":"#include \nusing namespace std;\n\nconst int N = 30;\nint tiles[N][N];\nint rotation[N][N];\n\nconst int di[] = {0, -1, 0, 1};\nconst int dj[] = {-1, 0, 1, 0};\n\nconst int to_arr[8][4] = {\n {1, 0, -1, -1}, {3, -1, -1, 0}, {-1, -1, 3, 2}, {-1, 2, 1, -1},\n {1, 0, 3, 2}, {3, 2, 1, 0}, {2, -1, 0, -1}, {-1, 3, -1, 1},\n};\n\ninline int getState(int i, int j) {\n int t = tiles[i][j], r = rotation[i][j];\n if (t < 4) return (t + r) % 4;\n if (t < 6) return 4 + (t - 4 + r) % 2;\n return 6 + (t - 6 + r) % 2;\n}\n\nint traceLoop(int si, int sj, int sd) {\n int i = si, j = sj, d = sd, length = 0;\n do {\n int state = getState(i, j);\n int d2 = to_arr[state][d];\n if (d2 == -1) return 0;\n length++;\n if (length > 4 * N * N) return 0;\n i += di[d2]; j += dj[d2];\n if ((unsigned)i >= N || (unsigned)j >= N) return 0;\n d = (d2 + 2) % 4;\n } while (i != si || j != sj || d != sd);\n return length;\n}\n\npair computeTopTwoLoops() {\n static bool visited[N][N][4];\n memset(visited, 0, sizeof(visited));\n int top1 = 0, top2 = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n int state = getState(i, j);\n for (int d = 0; d < 4; d++) {\n if (to_arr[state][d] == -1 || visited[i][j][d]) continue;\n int len = traceLoop(i, j, d);\n if (len > 0) {\n if (len > top1) { top2 = top1; top1 = len; }\n else if (len > top2) { top2 = len; }\n int ci = i, cj = j, cd = d;\n do {\n visited[ci][cj][cd] = true;\n int st = getState(ci, cj);\n int d2 = to_arr[st][cd];\n ci += di[d2]; cj += dj[d2];\n cd = (d2 + 2) % 4;\n } while (ci != i || cj != j || cd != d);\n }\n }\n }\n }\n return {top1, top2};\n}\n\nint best_rotation[N][N];\nlong long best_score;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) {\n tiles[i][j] = s[j] - '0';\n rotation[i][j] = 0;\n }\n }\n \n mt19937 rng(42);\n auto start_time = chrono::steady_clock::now();\n \n auto [l1, l2] = computeTopTwoLoops();\n best_score = (long long)l1 * l2;\n memcpy(best_rotation, rotation, sizeof(rotation));\n long long current_score = best_score;\n \n const double TIME_LIMIT = 1.9;\n \n while (true) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start_time).count();\n if (elapsed > TIME_LIMIT) break;\n \n double T = 1000.0 * pow(0.0001, elapsed / TIME_LIMIT);\n \n int i = rng() % N, j = rng() % N;\n int old_rot = rotation[i][j];\n int new_rot = (old_rot + 1 + rng() % 3) % 4;\n \n rotation[i][j] = new_rot;\n auto [nl1, nl2] = computeTopTwoLoops();\n long long new_score = (long long)nl1 * nl2;\n \n double delta = (double)(new_score - current_score);\n if (delta >= 0 || uniform_real_distribution(0, 1)(rng) < exp(delta / T)) {\n current_score = new_score;\n if (new_score > best_score) {\n best_score = new_score;\n memcpy(best_rotation, rotation, sizeof(rotation));\n }\n } else {\n rotation[i][j] = old_rot;\n }\n }\n \n string result;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n result += ('0' + best_rotation[i][j]);\n cout << result << endl;\n \n return 0;\n}","ahc011":"#include \nusing namespace std;\n\nint N, T;\nint dr[] = {-1, 1, 0, 0};\nint dc[] = {0, 0, -1, 1};\nchar dc_char[] = {'U', 'D', 'L', 'R'};\n\nint hexChar(char c) {\n return (c >= '0' && c <= '9') ? c - '0' : c - 'a' + 10;\n}\n\nint calcScore(const vector>& board) {\n vector> adj(N * N);\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (board[i][j] == 0) continue;\n if (i + 1 < N && board[i+1][j] != 0 && (board[i][j] & 8) && (board[i+1][j] & 2)) {\n adj[i*N+j].push_back((i+1)*N+j);\n adj[(i+1)*N+j].push_back(i*N+j);\n }\n if (j + 1 < N && board[i][j+1] != 0 && (board[i][j] & 4) && (board[i][j+1] & 1)) {\n adj[i*N+j].push_back(i*N+j+1);\n adj[i*N+j+1].push_back(i*N+j);\n }\n }\n }\n vector vis(N * N, false);\n int maxTree = 0;\n for (int s = 0; s < N * N; s++) {\n if (vis[s] || board[s/N][s%N] == 0) continue;\n int cnt = 0, edges = 0;\n queue q; q.push(s); vis[s] = true;\n while (!q.empty()) {\n int u = q.front(); q.pop(); cnt++;\n edges += adj[u].size();\n for (int v : adj[u]) if (!vis[v]) { vis[v] = true; q.push(v); }\n }\n if (edges / 2 == cnt - 1) maxTree = max(maxTree, cnt);\n }\n return maxTree;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> T;\n vector> board(N, vector(N));\n int er, ec;\n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) {\n board[i][j] = hexChar(s[j]);\n if (board[i][j] == 0) { er = i; ec = j; }\n }\n }\n \n string best, cur;\n int bestScore = calcScore(board), curScore = bestScore;\n auto bestBoard = board; int bestEr = er, bestEc = ec;\n \n mt19937 rng(42);\n auto start = chrono::steady_clock::now();\n \n while (chrono::duration_cast(chrono::steady_clock::now() - start).count() < 2800) {\n if (cur.size() >= (size_t)T || bestScore >= N * N - 1) break;\n \n vector valid;\n for (int d = 0; d < 4; d++) {\n int nr = er + dr[d], nc = ec + dc[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N) valid.push_back(d);\n }\n int d = valid[rng() % valid.size()];\n int nr = er + dr[d], nc = ec + dc[d];\n \n swap(board[er][ec], board[nr][nc]);\n cur += dc_char[d];\n int newScore = calcScore(board);\n \n double temp = 1.0 - (double)cur.size() / T;\n bool accept = newScore > curScore || (rng() % 1000 < 100 * temp);\n \n if (accept) {\n er = nr; ec = nc; curScore = newScore;\n if (curScore > bestScore || (curScore == bestScore && cur.size() < best.size())) {\n bestScore = curScore; best = cur;\n bestBoard = board; bestEr = er; bestEc = ec;\n }\n } else {\n cur.pop_back();\n swap(board[er][ec], board[nr][nc]);\n }\n \n if (cur.size() > T / 2 && rng() % 100 < 5) {\n board = bestBoard; er = bestEr; ec = bestEc;\n cur = best; curScore = bestScore;\n }\n }\n \n cout << best << endl;\n return 0;\n}","ahc012":"#include \nusing namespace std;\n\ntypedef long long ll;\n\nint N, K;\nvector a(10);\nvector> berries;\nvector> cuts;\n\ninline int side(ll x1, ll y1, ll x2, ll y2, ll px, ll py) {\n __int128 cross = (__int128)(x2 - x1) * (py - y1) - (__int128)(y2 - y1) * (px - x1);\n if (cross > 0) return 1;\n if (cross < 0) return -1;\n return 0;\n}\n\nint calcScore() {\n int numCuts = cuts.size();\n map, int> pieceCount;\n \n for (int i = 0; i < N; i++) {\n vector sig(numCuts);\n bool onLine = false;\n for (int j = 0; j < numCuts; j++) {\n int s = side(cuts[j][0], cuts[j][1], cuts[j][2], cuts[j][3], \n berries[i].first, berries[i].second);\n if (s == 0) { onLine = true; break; }\n sig[j] = s;\n }\n if (!onLine) pieceCount[sig]++;\n }\n \n vector b(11, 0);\n for (auto& [sig, cnt] : pieceCount) {\n if (cnt >= 1 && cnt <= 10) b[cnt]++;\n }\n \n int total = 0;\n for (int d = 1; d <= 10; d++) total += min(a[d-1], b[d]);\n return total;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> K;\n for (int i = 0; i < 10; i++) cin >> a[i];\n \n berries.resize(N);\n for (int i = 0; i < N; i++) cin >> berries[i].first >> berries[i].second;\n \n mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());\n \n auto randLine = [&]() -> array {\n ll px = (ll)(rng() % 20001) - 10000;\n ll py = (ll)(rng() % 20001) - 10000;\n ll qx = (ll)(rng() % 20001) - 10000;\n ll qy = (ll)(rng() % 20001) - 10000;\n while (px == qx && py == qy) { qx = (ll)(rng() % 20001) - 10000; qy = (ll)(rng() % 20001) - 10000; }\n return {px, py, qx, qy};\n };\n \n auto perpBisector = [&](int i, int j) -> array {\n if (i == j) return randLine();\n ll dx = berries[j].first - berries[i].first;\n ll dy = berries[j].second - berries[i].second;\n ll mx = berries[i].first + berries[j].first;\n ll my = berries[i].second + berries[j].second;\n ll px = mx - dy * 1000, py = my + dx * 1000;\n ll qx = mx + dy * 1000, qy = my - dx * 1000;\n if (px == qx && py == qy) return randLine();\n return {px, py, qx, qy};\n };\n \n auto radialLine = [&](double angle) -> array {\n ll px = (ll)(cos(angle) * 15000);\n ll py = (ll)(sin(angle) * 15000);\n ll qx = -px, qy = -py;\n if (px == 0) px = 1;\n if (qx == 0) qx = -1;\n return {px, py, qx, qy};\n };\n \n int bestScore = 0;\n vector> bestCuts;\n \n auto start = chrono::steady_clock::now();\n \n for (int restart = 0; ; restart++) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration_cast(now - start).count();\n if (elapsed > 2850) break;\n \n cuts.clear();\n int numCuts = 20 + rng() % 30;\n \n // Initialize with mix of strategies\n for (int i = 0; i < numCuts; i++) {\n int strategy = rng() % 3;\n if (strategy == 0) cuts.push_back(randLine());\n else if (strategy == 1) cuts.push_back(perpBisector(rng() % N, rng() % N));\n else cuts.push_back(radialLine((double)(rng() % 1000) / 1000.0 * M_PI * 2));\n }\n \n int curScore = calcScore();\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n \n // Local search\n for (int iter = 0; iter < 500; iter++) {\n now = chrono::steady_clock::now();\n elapsed = chrono::duration_cast(now - start).count();\n if (elapsed > 2850) break;\n \n double temp = 5.0 * (1.0 - elapsed / 2850.0);\n int moveType = rng() % 10;\n \n if (moveType < 7 && !cuts.empty()) {\n int idx = rng() % cuts.size();\n auto oldCut = cuts[idx];\n int strat = rng() % 3;\n if (strat == 0) cuts[idx] = randLine();\n else if (strat == 1) cuts[idx] = perpBisector(rng() % N, rng() % N);\n else cuts[idx] = radialLine((double)(rng() % 1000) / 1000.0 * M_PI * 2);\n \n int newScore = calcScore();\n if (newScore >= curScore || (double)(rng() % 1000000) / 1000000.0 < exp((newScore - curScore) / max(temp, 0.1))) {\n curScore = newScore;\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n } else cuts[idx] = oldCut;\n } else if (moveType < 9 && cuts.size() < (size_t)K) {\n int strat = rng() % 3;\n if (strat == 0) cuts.push_back(randLine());\n else if (strat == 1) cuts.push_back(perpBisector(rng() % N, rng() % N));\n else cuts.push_back(radialLine((double)(rng() % 1000) / 1000.0 * M_PI * 2));\n \n int newScore = calcScore();\n if (newScore >= curScore || (double)(rng() % 1000000) / 1000000.0 < exp((newScore - curScore) / max(temp, 0.1))) {\n curScore = newScore;\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n } else cuts.pop_back();\n } else if (cuts.size() > 5) {\n int idx = rng() % cuts.size();\n auto oldCut = cuts[idx];\n cuts.erase(cuts.begin() + idx);\n int newScore = calcScore();\n if (newScore >= curScore || (double)(rng() % 1000000) / 1000000.0 < exp((newScore - curScore) / max(temp, 0.1))) {\n curScore = newScore;\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n } else cuts.insert(cuts.begin() + idx, oldCut);\n }\n }\n }\n \n cout << bestCuts.size() << \"\\n\";\n for (auto& c : bestCuts) cout << c[0] << \" \" << c[1] << \" \" << c[2] << \" \" << c[3] << \"\\n\";\n \n return 0;\n}","ahc014":"#include \nusing namespace std;\n\nint N, M, c;\nset> dots;\nset> usedSegs;\nvector> ops;\n\nbool inGrid(int x, int y) { return x >= 0 && x < N && y >= 0 && y < N; }\nlong long wt(int x, int y) { return (long long)(x-c)*(x-c) + (long long)(y-c)*(y-c) + 1; }\n\nvoid addSeg(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g == 0) return;\n dx /= g; dy /= g;\n for (int i = 0; i < g; i++) {\n int a = x1+i*dx, b = y1+i*dy, e = a+dx, f = b+dy;\n if (a > e || (a == e && b > f)) { swap(a,e); swap(b,f); }\n usedSegs.insert({a,b,e,f});\n }\n}\n\nbool segUsed(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g == 0) return false;\n dx /= g; dy /= g;\n for (int i = 0; i < g; i++) {\n int a = x1+i*dx, b = y1+i*dy, e = a+dx, f = b+dy;\n if (a > e || (a == e && b > f)) { swap(a,e); swap(b,f); }\n if (usedSegs.count({a,b,e,f})) return true;\n }\n return false;\n}\n\nbool dotOnSeg(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g <= 1) return false;\n dx /= g; dy /= g;\n for (int i = 1; i < g; i++)\n if (dots.count({x1+i*dx, y1+i*dy})) return true;\n return false;\n}\n\nbool isValidSide(int dx, int dy) {\n return (dx == 0 || dy == 0 || abs(dx) == abs(dy));\n}\n\nbool tryAdd(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4) {\n if (!inGrid(x1,y1) || dots.count({x1,y1})) return false;\n if (!dots.count({x2,y2}) || !dots.count({x3,y3}) || !dots.count({x4,y4})) return false;\n \n set> corners = {{x1,y1},{x2,y2},{x3,y3},{x4,y4}};\n if (corners.size() != 4) return false;\n \n int v1x = x2-x1, v1y = y2-y1, v2x = x3-x2, v2y = y3-y2;\n if (v1x*v2x + v1y*v2y != 0) return false;\n if (!isValidSide(v1x, v1y) || !isValidSide(v2x, v2y)) return false;\n if (x4 != x1+v2x || y4 != y1+v2y) return false;\n if (v1x == 0 && v1y == 0) return false;\n \n if (dotOnSeg(x1,y1,x2,y2) || dotOnSeg(x2,y2,x3,y3) || \n dotOnSeg(x3,y3,x4,y4) || dotOnSeg(x4,y4,x1,y1)) return false;\n if (segUsed(x1,y1,x2,y2) || segUsed(x2,y2,x3,y3) || \n segUsed(x3,y3,x4,y4) || segUsed(x4,y4,x1,y1)) return false;\n \n dots.insert({x1,y1});\n addSeg(x1,y1,x2,y2); addSeg(x2,y2,x3,y3); \n addSeg(x3,y3,x4,y4); addSeg(x4,y4,x1,y1);\n ops.push_back({x1,y1,x2,y2,x3,y3,x4,y4});\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M;\n c = (N-1) / 2;\n for (int i = 0; i < M; i++) { int x, y; cin >> x >> y; dots.insert({x, y}); }\n \n auto tstart = chrono::steady_clock::now();\n mt19937 rng(42);\n \n int failCount = 0;\n while (chrono::duration(chrono::steady_clock::now() - tstart).count() < 4.5) {\n vector> dl(dots.begin(), dots.end());\n shuffle(dl.begin(), dl.end(), rng);\n \n long long bestW = -1;\n array best;\n int sz = min((int)dl.size(), 150);\n \n for (int i = 0; i < sz && bestW < 0; i++) {\n for (int j = 0; j < sz; j++) {\n if (i == j) continue;\n auto [x2, y2] = dl[i];\n auto [x3, y3] = dl[j];\n int vx = x3-x2, vy = y3-y2;\n \n // Try perpendicular vectors for p1-p2\n vector> perps;\n if (vx == 0 || vy == 0) { perps = {{vy, -vx}, {-vy, vx}}; }\n else if (abs(vx) == abs(vy)) { perps = {{vy, -vx}, {-vy, vx}}; }\n \n for (auto [px, py] : perps) {\n for (int len = 1; len <= max(N, 61); len++) {\n int dx = (px > 0 ? len : (px < 0 ? -len : 0));\n int dy = (py > 0 ? len : (py < 0 ? -len : 0));\n if (px != 0 && py != 0) { if (abs(px) != abs(py)) continue; }\n else if (px == 0) dx = 0;\n else dy = 0;\n \n int x1 = x2 - dx, y1 = y2 - dy;\n int x4 = x3 - dx, y4 = y3 - dy;\n \n if (!inGrid(x1,y1) || !inGrid(x4,y4)) continue;\n if (dots.count({x1,y1}) || !dots.count({x4,y4})) continue;\n \n long long w = wt(x1, y1);\n if (w > bestW) { best = {x1,y1,x2,y2,x3,y3,x4,y4}; bestW = w; }\n }\n for (int len = 1; len <= max(N, 61); len++) {\n int dx = (px > 0 ? len : (px < 0 ? -len : 0));\n int dy = (py > 0 ? len : (py < 0 ? -len : 0));\n if (px != 0 && py != 0) { if (abs(px) != abs(py)) continue; }\n else if (px == 0) dx = 0;\n else dy = 0;\n \n int x4 = x3 + dx, y4 = y3 + dy;\n int x1 = x2 + dx, y1 = y2 + dy;\n \n if (!inGrid(x1,y1) || !inGrid(x4,y4)) continue;\n if (dots.count({x1,y1}) || !dots.count({x4,y4})) continue;\n \n long long w = wt(x1, y1);\n if (w > bestW) { best = {x1,y1,x2,y2,x3,y3,x4,y4}; bestW = w; }\n }\n }\n }\n }\n \n if (bestW < 0) { if (++failCount > 50) break; continue; }\n if (!tryAdd(best[0],best[1],best[2],best[3],best[4],best[5],best[6],best[7])) {\n if (++failCount > 100) break;\n continue;\n }\n failCount = 0;\n }\n \n cout << ops.size() << \"\\n\";\n for (auto& op : ops) {\n for (int i = 0; i < 8; i++) cout << op[i] << \" \\n\"[i==7];\n }\n return 0;\n}","ahc015":"#include \nusing namespace std;\n\nconst int N = 10;\n\nstruct State {\n int grid[N][N];\n \n State() { memset(grid, 0, sizeof(grid)); }\n \n int countEmpty() const {\n int cnt = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (grid[i][j] == 0) cnt++;\n return cnt;\n }\n \n void place(int p, int flavor) {\n int cnt = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (grid[i][j] == 0 && ++cnt == p) { grid[i][j] = flavor; return; }\n }\n \n void tilt(char dir) {\n if (dir == 'F') {\n for (int j = 0; j < N; j++) {\n int w = 0;\n for (int i = 0; i < N; i++) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[w++][j] = v; }\n }\n } else if (dir == 'B') {\n for (int j = 0; j < N; j++) {\n int w = N - 1;\n for (int i = N - 1; i >= 0; i--) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[w--][j] = v; }\n }\n } else if (dir == 'L') {\n for (int i = 0; i < N; i++) {\n int w = 0;\n for (int j = 0; j < N; j++) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[i][w++] = v; }\n }\n } else {\n for (int i = 0; i < N; i++) {\n int w = N - 1;\n for (int j = N - 1; j >= 0; j--) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[i][w--] = v; }\n }\n }\n }\n \n long long calcScore() const {\n bool vis[N][N] = {};\n long long sum = 0;\n int dx[] = {-1, 1, 0, 0}, dy[] = {0, 0, -1, 1};\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (grid[i][j] && !vis[i][j]) {\n int f = grid[i][j], sz = 0;\n queue> q; q.push({i, j}); vis[i][j] = true;\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop(); sz++;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < N && ny >= 0 && ny < N && !vis[nx][ny] && grid[nx][ny] == f) {\n vis[nx][ny] = true; q.push({nx, ny});\n }\n }\n }\n sum += (long long)sz * sz;\n }\n }\n }\n return sum;\n }\n};\n\nmt19937 rng(12345);\nconst char dirs[] = {'F', 'B', 'L', 'R'};\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int f[101];\n for (int t = 1; t <= 100; t++) cin >> f[t];\n \n State state;\n \n for (int t = 1; t <= 100; t++) {\n int p; cin >> p;\n state.place(p, f[t]);\n \n int depth = min(12, 100 - t);\n int numSims = 25;\n \n char bestDir = 'F';\n long long bestScore = -1;\n \n for (char dir : dirs) {\n long long totalScore = 0;\n \n for (int sim = 0; sim < numSims; sim++) {\n State s = state;\n s.tilt(dir);\n \n for (int step = 1; step <= depth && t + step <= 100; step++) {\n int empty = s.countEmpty();\n if (empty == 0) break;\n int randPos = (rng() % empty) + 1;\n s.place(randPos, f[t + step]);\n \n // Greedy tilt\n char simBest = 'F';\n long long simBestScore = -1;\n for (char d : dirs) {\n State tmp = s;\n tmp.tilt(d);\n long long sc = tmp.calcScore();\n if (sc > simBestScore) { simBestScore = sc; simBest = d; }\n }\n s.tilt(simBest);\n }\n totalScore += s.calcScore();\n }\n \n if (totalScore > bestScore) {\n bestScore = totalScore;\n bestDir = dir;\n }\n }\n \n state.tilt(bestDir);\n cout << bestDir << '\\n' << flush;\n }\n \n return 0;\n}","ahc016":"#include \nusing namespace std;\n\nint N, M;\ndouble eps;\n\nvector get_sorted_degrees(const string& s) {\n vector deg(N, 0);\n int idx = 0;\n for (int i = 0; i < N; i++) {\n for (int j = i + 1; j < N; j++) {\n if (s[idx++] == '1') {\n deg[i]++;\n deg[j]++;\n }\n }\n }\n sort(deg.begin(), deg.end());\n return deg;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(0);\n \n cin >> M >> eps;\n \n // Better N selection based on theoretical analysis\n // Need larger N for higher noise to maintain distinguishability\n double noise_factor = (eps < 0.001) ? 1.0 : 1.0 / max(0.2, 1.0 - 2.0 * eps);\n \n // Base N on M and noise\n if (eps < 0.01) {\n N = (int)ceil(sqrt(2.0 * M)) + 2;\n } else if (eps < 0.05) {\n N = (int)ceil(sqrt(2.5 * M)) + 4;\n } else if (eps < 0.15) {\n N = (int)ceil(sqrt(3.0 * M * noise_factor)) + 8;\n } else if (eps < 0.25) {\n N = (int)ceil(sqrt(4.0 * M * noise_factor)) + 15;\n } else if (eps < 0.35) {\n N = (int)ceil(sqrt(5.0 * M * noise_factor)) + 25;\n } else {\n N = (int)ceil(sqrt(6.0 * M * noise_factor)) + 35;\n }\n \n N = max(N, (int)(2.0 * sqrt(M)));\n N = max(N, 8);\n N = min(N, 100);\n \n cout << N << \"\\n\";\n \n int total = N * (N - 1) / 2;\n \n vector G(M);\n vector> expected_deg(M);\n \n // Create M graphs with linearly spaced edge counts\n for (int i = 0; i < M; i++) {\n string s(total, '0');\n long long edges = (M > 1) ? ((long long)i * total / (M - 1)) : 0;\n \n // Fill edges in a pattern that creates varied degree distribution\n int idx = 0;\n int filled = 0;\n for (int a = 0; a < N && filled < edges; a++) {\n for (int b = a + 1; b < N && filled < edges; b++) {\n int pos = a * (2 * N - a - 1) / 2 + (b - a - 1);\n s[pos] = '1';\n filled++;\n }\n }\n \n G[i] = s;\n \n // Compute expected degree sequence after noise\n vector deg = get_sorted_degrees(s);\n expected_deg[i].resize(N);\n double transform = 1.0 - 2.0 * eps;\n double base = (N - 1) * eps;\n for (int j = 0; j < N; j++) {\n expected_deg[i][j] = deg[j] * transform + base;\n }\n \n cout << s << \"\\n\";\n }\n cout.flush();\n \n for (int q = 0; q < 100; q++) {\n string H;\n cin >> H;\n \n vector deg_h = get_sorted_degrees(H);\n \n int best = 0;\n double best_score = 1e18;\n \n for (int i = 0; i < M; i++) {\n // Weighted L2 distance - weight more heavily at extremes\n double score = 0;\n for (int j = 0; j < N; j++) {\n double diff = deg_h[j] - expected_deg[i][j];\n // Weight endpoints more (more informative)\n double weight = 1.0 + 0.5 * (abs(j - N/2.0) / (N/2.0));\n score += weight * diff * diff;\n }\n \n if (score < best_score) {\n best_score = score;\n best = i;\n }\n }\n \n cout << best << \"\\n\";\n cout.flush();\n }\n \n return 0;\n}","ahc017":"#include \nusing namespace std;\n\nint N, M, D, K;\nvector> edges;\nvector>> adj;\nvector> adjEdge;\nmt19937 rng(42);\nconst long long INF = 1e9;\n\nvector dijkstraMask(int src, const vector& excl) {\n vector dist(N, INF);\n priority_queue, vector>, greater<>> pq;\n dist[src] = 0;\n pq.push({0, src});\n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > dist[u]) continue;\n for (size_t i = 0; i < adj[u].size(); i++) {\n if (excl[adjEdge[u][i]]) continue;\n auto [v, w] = adj[u][i];\n if (dist[u] + w < dist[v]) {\n dist[v] = dist[u] + w;\n pq.push({dist[v], v});\n }\n }\n }\n return dist;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n auto start = chrono::steady_clock::now();\n \n cin >> N >> M >> D >> K;\n edges.resize(M); adj.resize(N); adjEdge.resize(N);\n \n for (int i = 0; i < M; i++) {\n int u, v, w; cin >> u >> v >> w; u--; v--;\n edges[i] = {u, v, w};\n adj[u].push_back({v, w}); adj[v].push_back({u, w});\n adjEdge[u].push_back(i); adjEdge[v].push_back(i);\n }\n for (int i = 0; i < N; i++) { int x, y; cin >> x >> y; }\n \n vector noEdge(M, false);\n vector crit(M);\n for (int e = 0; e < M; e++) {\n noEdge[e] = true;\n auto dist = dijkstraMask(edges[e][0], noEdge);\n crit[e] = dist[edges[e][1]] - edges[e][2];\n noEdge[e] = false;\n }\n \n vector order(M); iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int a, int b) { return crit[a] > crit[b]; });\n \n vector assign(M, 0);\n vector cnt(D + 1, 0);\n vector> dayVertices(D + 1);\n \n for (int e : order) {\n int u = edges[e][0], v = edges[e][1];\n int best = 1, bestScore = INT_MAX;\n for (int d = 1; d <= D; d++) {\n if (cnt[d] >= K) continue;\n int conflict = (dayVertices[d].count(u) ? 1 : 0) + (dayVertices[d].count(v) ? 1 : 0);\n int score = conflict * 10000 + cnt[d];\n if (score < bestScore) { bestScore = score; best = d; }\n }\n assign[e] = best; cnt[best]++;\n dayVertices[best].insert(u); dayVertices[best].insert(v);\n }\n \n int numSamples = min(60, N);\n vector samples(N); iota(samples.begin(), samples.end(), 0);\n shuffle(samples.begin(), samples.end(), rng);\n samples.resize(numSamples);\n \n vector> origDist(numSamples);\n for (int i = 0; i < numSamples; i++) origDist[i] = dijkstraMask(samples[i], noEdge);\n \n auto evalDay = [&](int d) -> double {\n vector excl(M);\n for (int e = 0; e < M; e++) if (assign[e] == d) excl[e] = true;\n double tot = 0;\n for (int i = 0; i < numSamples; i++) {\n auto dist = dijkstraMask(samples[i], excl);\n for (int v = 0; v < N; v++) if (v != samples[i])\n tot += min(dist[v], INF) - origDist[i][v];\n }\n return tot;\n };\n \n vector dayCost(D + 1);\n double cur = 0;\n for (int d = 1; d <= D; d++) { dayCost[d] = evalDay(d); cur += dayCost[d]; }\n \n double bestScore = cur;\n vector bestAssign = assign;\n double temp = cur / D / 10;\n \n while (true) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > 5.5) break;\n \n int moveType = rng() % 3;\n \n if (moveType < 2) {\n int e1 = rng() % M, e2 = rng() % M;\n if (assign[e1] == assign[e2]) continue;\n int d1 = assign[e1], d2 = assign[e2];\n \n swap(assign[e1], assign[e2]);\n double nc1 = evalDay(d1), nc2 = evalDay(d2);\n double delta = (nc1 + nc2) - (dayCost[d1] + dayCost[d2]);\n \n if (delta < 0 || (double)(rng() % 1000000) / 1000000 < exp(-delta / temp)) {\n dayCost[d1] = nc1; dayCost[d2] = nc2; cur += delta;\n if (cur < bestScore) { bestScore = cur; bestAssign = assign; }\n } else { swap(assign[e1], assign[e2]); }\n } else {\n int e = rng() % M;\n int oldD = assign[e], newD = rng() % D + 1;\n if (newD == oldD || cnt[newD] >= K) continue;\n \n assign[e] = newD; cnt[oldD]--; cnt[newD]++;\n double nc1 = evalDay(oldD), nc2 = evalDay(newD);\n double delta = (nc1 + nc2) - (dayCost[oldD] + dayCost[newD]);\n \n if (delta < 0 || (double)(rng() % 1000000) / 1000000 < exp(-delta / temp)) {\n dayCost[oldD] = nc1; dayCost[newD] = nc2; cur += delta;\n if (cur < bestScore) { bestScore = cur; bestAssign = assign; }\n } else { assign[e] = oldD; cnt[oldD]++; cnt[newD]--; }\n }\n temp *= 0.999995;\n }\n \n for (int i = 0; i < M; i++) cout << bestAssign[i] << \" \\n\"[i == M-1];\n return 0;\n}","ahc019":"#include \nusing namespace std;\n\nint D;\nstring f[2][15], r[2][15];\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> D;\n for (int i = 0; i < 2; i++) {\n for (int k = 0; k < D; k++) cin >> f[i][k];\n for (int k = 0; k < D; k++) cin >> r[i][k];\n }\n \n vector b[2];\n for (int i = 0; i < 2; i++) b[i].assign(D * D * D, 0);\n \n auto idx = [&](int x, int y, int z) { return x * D * D + y * D + z; };\n \n // For each arrangement, find minimal cells to cover silhouettes\n vector> cells[2];\n \n for (int arr = 0; arr < 2; arr++) {\n set needFront, needRight;\n for (int z = 0; z < D; z++) {\n for (int x = 0; x < D; x++) {\n if (f[arr][z][x] == '1') needFront.insert(z * D + x);\n }\n for (int y = 0; y < D; y++) {\n if (r[arr][z][y] == '1') needRight.insert(z * D + y);\n }\n }\n \n // Greedily pick cells that cover the most uncovered constraints\n while (!needFront.empty() || !needRight.empty()) {\n int bestX = -1, bestY = -1, bestZ = -1, bestScore = -1;\n \n for (int z = 0; z < D; z++) {\n for (int x = 0; x < D; x++) {\n if (f[arr][z][x] != '1') continue;\n for (int y = 0; y < D; y++) {\n if (r[arr][z][y] != '1') continue;\n \n int score = 0;\n if (needFront.count(z * D + x)) score++;\n if (needRight.count(z * D + y)) score++;\n \n if (score > bestScore) {\n bestScore = score;\n bestX = x; bestY = y; bestZ = z;\n }\n }\n }\n }\n \n if (bestScore <= 0) break;\n \n cells[arr].push_back({bestX, bestY, bestZ});\n needFront.erase(bestZ * D + bestX);\n needRight.erase(bestZ * D + bestY);\n }\n }\n \n int n1 = cells[0].size(), n2 = cells[1].size();\n int n = max(n1, n2);\n \n // Assign block numbers - shared unit blocks (1x1x1 all same shape)\n // Blocks 1..min(n1,n2) are shared, rest are unique\n for (int i = 0; i < n1; i++) {\n auto [x, y, z] = cells[0][i];\n b[0][idx(x, y, z)] = i + 1;\n }\n for (int i = 0; i < n2; i++) {\n auto [x, y, z] = cells[1][i];\n b[1][idx(x, y, z)] = i + 1;\n }\n \n cout << n << \"\\n\";\n for (int i = 0; i < 2; i++) {\n for (int j = 0; j < D * D * D; j++) {\n if (j) cout << \" \";\n cout << b[i][j];\n }\n cout << \"\\n\";\n }\n \n return 0;\n}","ahc020":"#include \nusing namespace std;\n\nint N, M, K;\nvector> V, R;\nvector> E;\nvector>> adj;\nvector> distVR;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> K;\n V.resize(N); R.resize(K); E.resize(M); adj.resize(N);\n \n for(int i = 0; i < N; i++) cin >> V[i].first >> V[i].second;\n for(int j = 0; j < M; j++) {\n int u, v; long long w;\n cin >> u >> v >> w; u--; v--;\n E[j] = {u, v, w};\n adj[u].push_back({v, j});\n adj[v].push_back({u, j});\n }\n for(int k = 0; k < K; k++) cin >> R[k].first >> R[k].second;\n \n distVR.resize(N, vector(K));\n for(int i = 0; i < N; i++)\n for(int k = 0; k < K; k++) {\n double dx = V[i].first - R[k].first, dy = V[i].second - R[k].second;\n distVR[i][k] = sqrt(dx*dx + dy*dy);\n }\n \n // Compute shortest paths from vertex 0\n vector dist0(N, LLONG_MAX/2);\n vector parent(N, -1), parentEdge(N, -1);\n priority_queue, vector>, greater<>> pq;\n dist0[0] = 0; pq.push({0, 0});\n while(!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if(d > dist0[u]) continue;\n for(auto [v, eid] : adj[u]) {\n long long w = get<2>(E[eid]);\n if(dist0[u] + w < dist0[v]) {\n dist0[v] = dist0[u] + w;\n parent[v] = u; parentEdge[v] = eid;\n pq.push({dist0[v], v});\n }\n }\n }\n \n // Assign residents considering both broadcast cost and reachability\n vector P(N, 0);\n vector assignment(K);\n \n for(int k = 0; k < K; k++) {\n int best = -1; double bestCost = 1e18;\n for(int i = 0; i < N; i++) {\n if(distVR[i][k] > 5000) continue;\n // Cost: broadcast cost + amortized network cost\n double cost = distVR[i][k] * distVR[i][k] + dist0[i] * 0.01;\n if(cost < bestCost) { bestCost = cost; best = i; }\n }\n assignment[k] = best;\n }\n \n for(int k = 0; k < K; k++) {\n int v = assignment[k];\n P[v] = max(P[v], (int)ceil(distVR[v][k] - 1e-9));\n }\n \n // Build tree\n set active;\n for(int i = 0; i < N; i++) if(P[i] > 0) active.insert(i);\n \n vector B(M, 0);\n for(int v : active) {\n int cur = v;\n while(cur != 0 && parentEdge[cur] != -1) {\n B[parentEdge[cur]] = 1;\n cur = parent[cur];\n }\n }\n \n // Activate intermediate vertices on tree (they're reachable, might help)\n set treeVerts;\n treeVerts.insert(0);\n for(int v : active) {\n int cur = v;\n while(cur != -1) { treeVerts.insert(cur); cur = parent[cur]; }\n }\n \n // Try using tree vertices to reduce costs\n for(int iter = 0; iter < 50; iter++) {\n bool improved = false;\n for(int k = 0; k < K; k++) {\n int curV = assignment[k];\n for(int v : treeVerts) {\n if(v == curV || distVR[v][k] > 5000) continue;\n int newR = (int)ceil(distVR[v][k] - 1e-9);\n int oldR = (int)ceil(distVR[curV][k] - 1e-9);\n if(newR < oldR && newR <= 5000) {\n assignment[k] = v;\n improved = true;\n }\n }\n }\n if(!improved) break;\n \n fill(P.begin(), P.end(), 0);\n for(int k = 0; k < K; k++) {\n int v = assignment[k];\n P[v] = max(P[v], (int)ceil(distVR[v][k] - 1e-9));\n }\n }\n \n // Output\n for(int i = 0; i < N; i++) cout << P[i] << \" \\n\"[i==N-1];\n for(int j = 0; j < M; j++) cout << B[j] << \" \\n\"[j==M-1];\n \n return 0;\n}","ahc021":"#include \nusing namespace std;\n\nconst int N = 30;\nint b[N][N];\nvector> ops;\n\nvoid do_swap(int x1, int y1, int x2, int y2) {\n ops.push_back({x1, y1, x2, y2});\n swap(b[x1][y1], b[x2][y2]);\n}\n\nvoid sift_down(int x, int y) {\n while (x < N - 1) {\n int min_child_y = (b[x + 1][y + 1] < b[x + 1][y]) ? (y + 1) : y;\n if (b[x][y] > b[x + 1][min_child_y]) {\n do_swap(x, y, x + 1, min_child_y);\n x = x + 1;\n y = min_child_y;\n } else {\n break;\n }\n }\n}\n\nbool has_violation(int x, int y) {\n if (x >= N - 1) return false;\n return b[x][y] > b[x + 1][y] || b[x][y] > b[x + 1][y + 1];\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int x = 0; x < N; x++) {\n for (int y = 0; y <= x; y++) {\n cin >> b[x][y];\n }\n }\n \n // Process violations iteratively - prioritize by value (larger values first)\n bool changed = true;\n while (changed) {\n changed = false;\n // Collect all violations with their values\n vector> violations; // (value, x, y)\n for (int x = N - 2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) {\n if (has_violation(x, y)) {\n violations.push_back({b[x][y], x, y});\n }\n }\n }\n \n // Sort by value descending (fix larger values first)\n sort(violations.rbegin(), violations.rend());\n \n for (auto& [val, x, y] : violations) {\n if (has_violation(x, y)) {\n sift_down(x, y);\n changed = true;\n }\n }\n }\n \n cout << ops.size() << \"\\n\";\n for (auto& [x1, y1, x2, y2] : ops) {\n cout << x1 << \" \" << y1 << \" \" << x2 << \" \" << y2 << \"\\n\";\n }\n \n return 0;\n}","toyota2023summer-final":"#include \nusing namespace std;\n\nint D, N, ex, ey;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nvector> grid;\n\nvector> getReachable(bool findContainers) {\n vector> result;\n vector> vis(D, vector(D, false));\n queue> q;\n q.push({ex, ey});\n vis[ex][ey] = true;\n \n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n \n if (findContainers && grid[x][y] >= 0) {\n result.push_back({x, y});\n continue;\n }\n if (!findContainers && grid[x][y] == -1 && !(x == ex && y == ey)) {\n result.push_back({x, y});\n }\n if (grid[x][y] >= 0) continue;\n \n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && !vis[nx][ny] && grid[nx][ny] != -2) {\n vis[nx][ny] = true;\n q.push({nx, ny});\n }\n }\n }\n return result;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> D >> N;\n ex = 0; ey = (D - 1) / 2;\n grid.assign(D, vector(D, -1));\n \n for (int i = 0; i < N; i++) {\n int x, y; cin >> x >> y;\n grid[x][y] = -2;\n }\n \n int total = D * D - 1 - N;\n \n vector> bfsOrder;\n map, int> posToIdx;\n {\n vector> vis(D, vector(D, false));\n queue> q;\n q.push({ex, ey});\n vis[ex][ey] = true;\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n if (grid[x][y] == -1 && !(x == ex && y == ey)) {\n posToIdx[{x, y}] = bfsOrder.size();\n bfsOrder.push_back({x, y});\n }\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && !vis[nx][ny] && grid[nx][ny] != -2) {\n vis[nx][ny] = true;\n q.push({nx, ny});\n }\n }\n }\n }\n \n for (int d = 0; d < total; d++) {\n int t; cin >> t;\n auto reach = getReachable(false);\n \n int targetIdx = total - 1 - t;\n pair best = reach[0];\n int bestDist = abs(posToIdx[best] - targetIdx);\n for (auto& pos : reach) {\n int dist = abs(posToIdx[pos] - targetIdx);\n if (dist < bestDist || (dist == bestDist && posToIdx[pos] > posToIdx[best])) {\n bestDist = dist;\n best = pos;\n }\n }\n \n grid[best.first][best.second] = t;\n cout << best.first << \" \" << best.second << \"\\n\";\n cout.flush();\n }\n \n for (int i = 0; i < total; i++) {\n auto reach = getReachable(true);\n pair best = reach[0];\n for (auto& pos : reach) {\n if (grid[pos.first][pos.second] < grid[best.first][best.second]) {\n best = pos;\n }\n }\n cout << best.first << \" \" << best.second << \"\\n\";\n grid[best.first][best.second] = -1;\n }\n \n return 0;\n}","ahc024":"#include \nusing namespace std;\n\nint n, m;\nint dx[] = {0, 0, 1, -1};\nint dy[] = {1, -1, 0, 0};\n\nset> getAdj(vector>& g) {\n set> adj;\n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n int c = g[i][j];\n if (i == 0 || i == n-1 || j == 0 || j == n-1) {\n int a = min(0, c), b = max(0, c);\n if (a != b) adj.insert({a, b});\n }\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n) {\n int nc = g[ni][nj];\n if (c != nc) {\n int a = min(c, nc), b = max(c, nc);\n adj.insert({a, b});\n }\n }\n }\n }\n }\n return adj;\n}\n\nbool isConnected(vector>& g, int c) {\n if (c == 0) return true;\n int si = -1, sj = -1, cnt = 0;\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) {\n if (g[i][j] == c) { if (si < 0) { si = i; sj = j; } cnt++; }\n }\n if (cnt == 0) return true;\n queue> q;\n vector> vis(n, vector(n, false));\n q.push({si, sj}); vis[si][sj] = true;\n int found = 1;\n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n && !vis[ni][nj] && g[ni][nj] == c) {\n vis[ni][nj] = true; found++; q.push({ni, nj});\n }\n }\n }\n return found == cnt;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> n >> m;\n vector> grid(n, vector(n));\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n cin >> grid[i][j];\n \n auto origAdj = getAdj(grid);\n vector> best = grid;\n int bestScore = 0;\n \n // Try greedy shrinking - change cells to 0 when safe\n auto tryGrid = grid;\n for (int iter = 0; iter < 5; iter++) {\n vector> cells;\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++)\n if (tryGrid[i][j] != 0) cells.push_back({i, j});\n \n shuffle(cells.begin(), cells.end(), mt19937(iter * 12345));\n \n for (auto [i, j] : cells) {\n int old = tryGrid[i][j];\n tryGrid[i][j] = 0;\n \n auto newAdj = getAdj(tryGrid);\n bool valid = (newAdj == origAdj);\n if (valid) {\n for (int c = 1; c <= m && valid; c++)\n if (!isConnected(tryGrid, c)) valid = false;\n }\n \n if (!valid) tryGrid[i][j] = old;\n }\n \n int score = 0;\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++)\n if (tryGrid[i][j] == 0) score++;\n \n if (score > bestScore) {\n bestScore = score;\n best = tryGrid;\n }\n }\n \n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n cout << best[i][j];\n if (j < n-1) cout << \" \";\n }\n cout << \"\\n\";\n }\n \n return 0;\n}","ahc025":"#include \nusing namespace std;\n\nint N, D, Q;\nint query_count = 0;\n\nchar query(const vector& L, const vector& R) {\n cout << L.size() << \" \" << R.size();\n for (int x : L) cout << \" \" << x;\n for (int x : R) cout << \" \" << x;\n cout << \"\\n\";\n cout.flush();\n char c;\n cin >> c;\n query_count++;\n return c;\n}\n\nvector items;\n\nvoid merge_sort(int l, int r) {\n if (r - l <= 1) return;\n int m = (l + r) / 2;\n merge_sort(l, m);\n merge_sort(m, r);\n \n vector left(items.begin() + l, items.begin() + m);\n vector right(items.begin() + m, items.begin() + r);\n \n int i = 0, j = 0, k = l;\n while (i < (int)left.size() && j < (int)right.size()) {\n if (query_count >= Q) {\n while (i < (int)left.size()) items[k++] = left[i++];\n while (j < (int)right.size()) items[k++] = right[j++];\n return;\n }\n char c = query({left[i]}, {right[j]});\n if (c != '>') items[k++] = left[i++];\n else items[k++] = right[j++];\n }\n while (i < (int)left.size()) items[k++] = left[i++];\n while (j < (int)right.size()) items[k++] = right[j++];\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> D >> Q;\n \n items.resize(N);\n iota(items.begin(), items.end(), 0);\n merge_sort(0, N);\n \n // Estimate weights using remaining queries\n vector w(N);\n for (int i = 0; i < N; i++) w[i] = i + 1;\n \n for (int j = N - 1; j >= N / 2 && query_count + 10 < Q; j--) {\n int lo = 1, hi = j;\n while (lo < hi && query_count < Q - N) {\n int mid = (lo + hi) / 2;\n vector L, R = {items[j]};\n for (int t = 0; t < mid; t++) L.push_back(items[t]);\n char c = query(L, R);\n if (c == '>' || c == '=') hi = mid;\n else lo = mid + 1;\n }\n double sum = 0;\n for (int t = 0; t < lo; t++) sum += w[t];\n w[j] = sum;\n }\n \n // Greedy assignment\n vector set_weight(D, 0);\n vector assignment(N);\n \n for (int i = N - 1; i >= 0; i--) {\n int best = 0;\n for (int j = 1; j < D; j++)\n if (set_weight[j] < set_weight[best]) best = j;\n assignment[items[i]] = best;\n set_weight[best] += w[i];\n }\n \n while (query_count < Q) query({items[0]}, {items[1]});\n \n for (int i = 0; i < N; i++)\n cout << assignment[i] << \" \\n\"[i == N - 1];\n \n return 0;\n}","ahc026":"#include \nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n, m;\n cin >> n >> m;\n \n vector> stacks(m);\n vector pos(n + 1);\n \n for (int i = 0; i < m; i++) {\n int h = n / m;\n for (int j = 0; j < h; j++) {\n int x;\n cin >> x;\n stacks[i].push_back(x);\n pos[x] = i;\n }\n }\n \n vector> ops;\n \n for (int v = 1; v <= n; v++) {\n int stack_id = pos[v];\n \n int idx = 0;\n while (stacks[stack_id][idx] != v) idx++;\n \n if (idx < (int)stacks[stack_id].size() - 1) {\n int move_start = idx + 1;\n int bottom_box = stacks[stack_id][move_start];\n \n int max_moving = 0;\n int min_moving = INT_MAX;\n for (int j = move_start; j < (int)stacks[stack_id].size(); j++) {\n max_moving = max(max_moving, stacks[stack_id][j]);\n min_moving = min(min_moving, stacks[stack_id][j]);\n }\n \n int best_dest = -1;\n int best_score = INT_MIN;\n \n for (int i = 0; i < m; i++) {\n if (i == stack_id) continue;\n \n int score = 0;\n \n if (stacks[i].empty()) {\n // Empty stack - excellent, no re-moves from below\n score = n * 2 + 100;\n } else {\n int min_in_dest = INT_MAX;\n for (int b : stacks[i]) {\n min_in_dest = min(min_in_dest, b);\n }\n \n if (min_in_dest > min_moving) {\n // Great! All dest boxes extracted after our min\n // Our group won't be moved again due to dest boxes\n score = n * 2;\n } else {\n // We'll be moved when extracting min_in_dest\n // Prefer later moves (higher min_in_dest)\n score = min_in_dest;\n }\n \n // Bonus if our group integrates well (top > max_moving)\n if (stacks[i].back() > max_moving) {\n score += 30;\n }\n }\n \n // Penalty for tall stacks\n score -= (int)stacks[i].size() * 2;\n \n if (score > best_score) {\n best_score = score;\n best_dest = i;\n }\n }\n \n ops.push_back({bottom_box, best_dest + 1});\n \n for (int j = move_start; j < (int)stacks[stack_id].size(); j++) {\n int box = stacks[stack_id][j];\n stacks[best_dest].push_back(box);\n pos[box] = best_dest;\n }\n stacks[stack_id].resize(move_start);\n }\n \n ops.push_back({v, 0});\n stacks[stack_id].pop_back();\n }\n \n for (auto& [a, b] : ops) {\n cout << a << \" \" << b << \"\\n\";\n }\n \n return 0;\n}","ahc027":"#include \nusing namespace std;\n\nint N;\nvector h, v;\nvector> d;\n\nint di[] = {0, 1, 0, -1};\nint dj[] = {1, 0, -1, 0};\nchar dirChar[] = {'R', 'D', 'L', 'U'};\n\nbool canMove(int i, int j, int dir) {\n int ni = i + di[dir];\n int nj = j + dj[dir];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) return false;\n if (dir == 0) return v[i][j] == '0';\n else if (dir == 1) return h[i][j] == '0';\n else if (dir == 2) return j > 0 && v[i][j-1] == '0';\n else return i > 0 && h[i-1][j] == '0';\n}\n\nlong double evaluate(const string& path) {\n int L = path.size();\n vector> lastVisit(N, vector(N, -L));\n lastVisit[0][0] = 0;\n \n long double totalSum = 0;\n int ci = 0, cj = 0;\n \n for (int t = 1; t <= 2 * L; t++) {\n char c = path[(t - 1) % L];\n int dir = (c == 'R') ? 0 : (c == 'D') ? 1 : (c == 'L') ? 2 : 3;\n ci += di[dir]; cj += dj[dir];\n \n if (t >= L) {\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (i == ci && j == cj) continue;\n totalSum += (long double)d[i][j] * (t - lastVisit[i][j]);\n }\n }\n }\n lastVisit[ci][cj] = t;\n }\n return totalSum / L;\n}\n\nstring generatePath(bool highFirst) {\n vector> visited(N, vector(N, false));\n string path;\n \n function dfs = [&](int i, int j) {\n visited[i][j] = true;\n vector> children;\n for (int dir = 0; dir < 4; dir++) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (ni >= 0 && ni < N && nj >= 0 && nj < N && !visited[ni][nj] && canMove(i, j, dir)) {\n children.push_back({d[ni][nj], dir});\n }\n }\n if (highFirst) sort(children.rbegin(), children.rend());\n else sort(children.begin(), children.end());\n \n for (auto [dval, dir] : children) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (!visited[ni][nj]) {\n path += dirChar[dir];\n dfs(ni, nj);\n path += dirChar[(dir + 2) % 4];\n }\n }\n };\n dfs(0, 0);\n return path;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N - 1);\n v.resize(N);\n d.resize(N, vector(N));\n \n for (int i = 0; i < N - 1; i++) cin >> h[i];\n for (int i = 0; i < N; i++) cin >> v[i];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n cin >> d[i][j];\n \n string bestPath;\n long double bestScore = 1e18;\n \n // Try both orderings\n for (int highFirst = 0; highFirst <= 1; highFirst++) {\n string path = generatePath(highFirst);\n long double score = evaluate(path);\n if (score < bestScore) {\n bestScore = score;\n bestPath = path;\n }\n }\n \n // Try adding extra loops for very high-d cells if we have room\n int maxLen = 100000;\n if (bestPath.size() < maxLen - 4 * N) {\n // Find highest d cell and path to it\n int maxD = 0, mi = 0, mj = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (d[i][j] > maxD) { maxD = d[i][j]; mi = i; mj = j; }\n \n // BFS to find path from (0,0) to (mi,mj)\n vector> parent(N, vector(N, -1));\n queue> q;\n q.push({0, 0});\n parent[0][0] = -2;\n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n if (i == mi && j == mj) break;\n for (int dir = 0; dir < 4; dir++) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (ni >= 0 && ni < N && nj >= 0 && nj < N && parent[ni][nj] == -1 && canMove(i, j, dir)) {\n parent[ni][nj] = (dir + 2) % 4;\n q.push({ni, nj});\n }\n }\n }\n \n string toTarget, fromTarget;\n int ci = mi, cj = mj;\n while (ci != 0 || cj != 0) {\n int pdir = parent[ci][cj];\n fromTarget += dirChar[pdir];\n toTarget += dirChar[(pdir + 2) % 4];\n ci += di[pdir]; cj += dj[pdir];\n }\n reverse(toTarget.begin(), toTarget.end());\n \n string extraLoop = toTarget + fromTarget;\n while (bestPath.size() + extraLoop.size() <= maxLen) {\n string candidate = bestPath + extraLoop;\n long double score = evaluate(candidate);\n if (score < bestScore) {\n bestScore = score;\n bestPath = candidate;\n } else break;\n }\n }\n \n cout << bestPath << endl;\n return 0;\n}","ahc028":"#include \nusing namespace std;\n\nint overlap(const string& a, const string& b) {\n int maxOv = min((int)a.length(), (int)b.length());\n for (int ov = maxOv; ov >= 1; ov--) {\n if (a.substr(a.length() - ov) == b.substr(0, ov)) {\n return ov;\n }\n }\n return 0;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, si, sj;\n cin >> N >> M >> si >> sj;\n \n vector A(N);\n map>> charPos;\n for (int i = 0; i < N; i++) {\n cin >> A[i];\n for (int j = 0; j < N; j++) {\n charPos[A[i][j]].push_back({i, j});\n }\n }\n \n vector t(M);\n for (int i = 0; i < M; i++) {\n cin >> t[i];\n }\n \n // Greedy superstring construction\n vector remaining = t;\n \n while (remaining.size() > 1) {\n int bestOv = -1;\n int bestI = -1, bestJ = -1;\n \n for (int i = 0; i < (int)remaining.size(); i++) {\n for (int j = 0; j < (int)remaining.size(); j++) {\n if (i != j) {\n int ov = overlap(remaining[i], remaining[j]);\n if (ov > bestOv) {\n bestOv = ov;\n bestI = i;\n bestJ = j;\n }\n }\n }\n }\n \n string merged = remaining[bestI] + remaining[bestJ].substr(bestOv);\n \n vector newRemaining;\n for (int k = 0; k < (int)remaining.size(); k++) {\n if (k != bestI && k != bestJ) {\n if (merged.find(remaining[k]) == string::npos) {\n newRemaining.push_back(remaining[k]);\n }\n }\n }\n newRemaining.push_back(merged);\n remaining = newRemaining;\n }\n \n string superstring = remaining[0];\n \n // Type the superstring using nearest neighbor\n int curI = si, curJ = sj;\n \n for (char c : superstring) {\n int bestDist = INT_MAX;\n int bI = -1, bJ = -1;\n for (auto [i, j] : charPos[c]) {\n int dist = abs(i - curI) + abs(j - curJ);\n if (dist < bestDist) {\n bestDist = dist;\n bI = i;\n bJ = j;\n }\n }\n cout << bI << \" \" << bJ << \"\\n\";\n curI = bI;\n curJ = bJ;\n }\n \n return 0;\n}","ahc030":"#include \nusing namespace std;\n\nint N, M;\ndouble eps;\nvector>> shapes;\nvector> grid;\n\nint queryDrill(int i, int j) {\n cout << \"q 1 \" << i << \" \" << j << \"\\n\" << flush;\n int v; cin >> v;\n grid[i][j] = v;\n return v;\n}\n\nint queryDivine(const vector>& cells) {\n cout << \"q \" << cells.size();\n for (auto& [i, j] : cells) cout << \" \" << i << \" \" << j;\n cout << \"\\n\" << flush;\n int v; cin >> v;\n return v;\n}\n\nint submit(const set>& oil) {\n cout << \"a \" << oil.size();\n for (auto& [i, j] : oil) cout << \" \" << i << \" \" << j;\n cout << \"\\n\" << flush;\n int r; cin >> r;\n return r;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> eps;\n shapes.resize(M);\n for (int m = 0; m < M; m++) {\n int d; cin >> d;\n shapes[m].resize(d);\n for (int i = 0; i < d; i++) {\n cin >> shapes[m][i].first >> shapes[m][i].second;\n }\n }\n \n grid.assign(N, vector(N, -1));\n set> has_oil;\n \n // When eps is small, use row divination first\n vector rowEstimate(N, -1);\n if (eps <= 0.1) {\n for (int i = 0; i < N; i++) {\n vector> row;\n for (int j = 0; j < N; j++) row.push_back({i, j});\n int est = queryDivine(row);\n rowEstimate[i] = est;\n }\n }\n \n // Drill cells - prioritize rows with higher estimates\n vector order(N);\n iota(order.begin(), order.end(), 0);\n if (eps <= 0.1) {\n sort(order.begin(), order.end(), [&](int a, int b) {\n return rowEstimate[a] > rowEstimate[b];\n });\n }\n \n for (int i : order) {\n for (int j = 0; j < N; j++) {\n int v = queryDrill(i, j);\n if (v > 0) has_oil.insert({i, j});\n }\n }\n \n submit(has_oil);\n return 0;\n}","ahc031":"#include \nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int W, D, N;\n cin >> W >> D >> N;\n \n vector> a(D, vector(N));\n for (int d = 0; d < D; d++) {\n for (int k = 0; k < N; k++) {\n cin >> a[d][k];\n }\n }\n \n for (int d = 0; d < D; d++) {\n vector h(N);\n int totalH = 0;\n \n // Calculate minimum height needed for each reservation\n for (int k = 0; k < N; k++) {\n h[k] = (a[d][k] + W - 1) / W; // ceil(a[k] / W)\n if (h[k] == 0) h[k] = 1;\n totalH += h[k];\n }\n \n if (totalH > W) {\n int excess = totalH - W;\n \n // Calculate slack for each: extra area at current height\n vector> slack(N);\n for (int k = 0; k < N; k++) {\n slack[k] = {h[k] * W - a[d][k], k};\n }\n sort(slack.begin(), slack.end(), greater>());\n \n // Reduce heights of those with most slack first\n for (int i = 0; i < N && excess > 0; i++) {\n int k = slack[i].second;\n while (h[k] > 1 && excess > 0) {\n int newSlack = (h[k] - 1) * W - a[d][k];\n if (newSlack >= 0) {\n h[k]--;\n excess--;\n } else {\n break;\n }\n }\n }\n \n // If still excess, reduce even with penalties (larger reservations last)\n for (int k = 0; k < N && excess > 0; k++) {\n while (h[k] > 1 && excess > 0) {\n h[k]--;\n excess--;\n }\n }\n } else if (totalH < W) {\n int extra = W - totalH;\n // Distribute extra space, prioritizing larger reservations\n while (extra > 0) {\n for (int k = N - 1; k >= 0 && extra > 0; k--) {\n h[k]++;\n extra--;\n }\n }\n }\n \n // Output rectangles\n int y = 0;\n for (int k = 0; k < N; k++) {\n cout << y << \" 0 \" << y + h[k] << \" \" << W << \"\\n\";\n y += h[k];\n }\n }\n \n return 0;\n}","ahc032":"#include \nusing namespace std;\n\nconst long long P = 998244353;\nint N, M, K;\nvector> a_init;\nvector, 3>> stamps;\n\nlong long calcScore(const vector>& a) {\n long long s = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n s += a[i][j];\n return s;\n}\n\nvoid applyOp(vector>& a, int m, int p, int q) {\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n a[p+i][q+j] = (a[p+i][q+j] + stamps[m][i][j]) % P;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(0);\n \n cin >> N >> M >> K;\n a_init.assign(N, vector(N));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n cin >> a_init[i][j];\n a_init[i][j] %= P;\n }\n \n stamps.resize(M);\n for (int m = 0; m < M; m++)\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n cin >> stamps[m][i][j];\n \n auto start = chrono::steady_clock::now();\n \n vector> best_ops;\n long long best_score = calcScore(a_init);\n \n mt19937 rng(42);\n \n for (int trial = 0; chrono::duration(chrono::steady_clock::now() - start).count() < 1.8; trial++) {\n vector> ops;\n auto a = a_init;\n \n // Greedy with randomness\n for (int op = 0; op < K; op++) {\n vector> cands;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N-3; p++)\n for (int q = 0; q <= N-3; q++) {\n long long gain = 0;\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n gain += (a[p+i][q+j] + stamps[m][i][j]) % P - a[p+i][q+j];\n if (gain > 0) cands.push_back({gain, m, p, q});\n }\n if (cands.empty()) break;\n sort(cands.rbegin(), cands.rend());\n int pick = (trial == 0) ? 0 : rng() % min((int)cands.size(), 2 + trial/2);\n auto [g, m, p, q] = cands[pick];\n applyOp(a, m, p, q);\n ops.push_back({m, p, q});\n }\n \n long long score = calcScore(a);\n \n // Local optimization: try replacing each operation\n for (int iter = 0; iter < 3 && chrono::duration(chrono::steady_clock::now() - start).count() < 1.8; iter++) {\n bool improved = false;\n for (int idx = 0; idx < (int)ops.size(); idx++) {\n auto orig = ops[idx];\n \n // Rebuild state without operation idx\n auto a2 = a_init;\n for (int k = 0; k < (int)ops.size(); k++)\n if (k != idx) {\n auto [m,p,q] = ops[k];\n applyOp(a2, m, p, q);\n }\n \n long long bestGain = 0;\n int bm=-1, bp=-1, bq=-1;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N-3; p++)\n for (int q = 0; q <= N-3; q++) {\n long long gain = 0;\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n gain += (a2[p+i][q+j] + stamps[m][i][j]) % P - a2[p+i][q+j];\n if (gain > bestGain) { bestGain = gain; bm=m; bp=p; bq=q; }\n }\n \n if (bm != -1 && (bm != get<0>(orig) || bp != get<1>(orig) || bq != get<2>(orig))) {\n ops[idx] = {bm, bp, bq};\n applyOp(a2, bm, bp, bq);\n long long ns = calcScore(a2);\n if (ns > score) {\n score = ns;\n a = a2;\n improved = true;\n } else {\n ops[idx] = orig;\n }\n }\n }\n \n // Try adding more operations\n while (ops.size() < (size_t)K) {\n long long bestGain = 0;\n int bm=-1, bp=-1, bq=-1;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N-3; p++)\n for (int q = 0; q <= N-3; q++) {\n long long gain = 0;\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n gain += (a[p+i][q+j] + stamps[m][i][j]) % P - a[p+i][q+j];\n if (gain > bestGain) { bestGain = gain; bm=m; bp=p; bq=q; }\n }\n if (bm == -1) break;\n applyOp(a, bm, bp, bq);\n ops.push_back({bm, bp, bq});\n score += bestGain;\n improved = true;\n }\n \n if (!improved) break;\n }\n \n if (score > best_score) {\n best_score = score;\n best_ops = ops;\n }\n }\n \n cout << best_ops.size() << \"\\n\";\n for (auto& [m,p,q] : best_ops) cout << m << \" \" << p << \" \" << q << \"\\n\";\n}","ahc033":"#include \nusing namespace std;\n\nconst int N = 5;\nint A[N][N];\nint grid[N][N];\nint cr[N], cc[N], hold[N];\nint next_in[N];\nstring ans[N];\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n; cin >> n;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n cin >> A[i][j];\n \n memset(grid, -1, sizeof(grid));\n memset(hold, -1, sizeof(hold));\n memset(next_in, 0, sizeof(next_in));\n for (int i = 0; i < N; i++) { cr[i] = i; cc[i] = 0; }\n \n for (int t = 0; t < 5000; t++) {\n // Step 1: Bring in containers\n for (int i = 0; i < N; i++) {\n if (next_in[i] < N && grid[i][0] == -1) {\n bool blocked = false;\n for (int c = 0; c < N; c++)\n if (cr[c] == i && cc[c] == 0 && hold[c] != -1)\n blocked = true;\n if (!blocked) grid[i][0] = A[i][next_in[i]++];\n }\n }\n \n // Decide moves\n char moves[N];\n for (int c = 0; c < N; c++) moves[c] = '.';\n \n for (int c = 0; c < N; c++) {\n int r = cr[c], col = cc[c];\n \n if (hold[c] == -1) {\n if (grid[r][col] != -1) {\n moves[c] = 'P';\n } else if (col > 0) {\n moves[c] = 'L';\n }\n } else {\n int target_row = hold[c] / N;\n if (col < N-1) {\n bool can_move = (c == 0 || grid[r][col+1] == -1);\n if (can_move) moves[c] = 'R';\n } else {\n moves[c] = 'Q';\n }\n }\n }\n \n // Step 2: Execute moves\n for (int c = 0; c < N; c++) {\n char m = moves[c];\n if (m == 'P') {\n hold[c] = grid[cr[c]][cc[c]];\n grid[cr[c]][cc[c]] = -1;\n } else if (m == 'Q') {\n grid[cr[c]][cc[c]] = hold[c];\n hold[c] = -1;\n } else if (m == 'R') cc[c]++;\n else if (m == 'L') cc[c]--;\n else if (m == 'U') cr[c]--;\n else if (m == 'D') cr[c]++;\n }\n \n // Step 3: Dispatch\n for (int i = 0; i < N; i++) grid[i][N-1] = -1;\n \n for (int c = 0; c < N; c++) ans[c] += moves[c];\n \n // Check if done\n bool done = true;\n for (int i = 0; i < N; i++) if (next_in[i] < N) done = false;\n for (int c = 0; c < N; c++) if (hold[c] != -1) done = false;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (grid[i][j] != -1) done = false;\n if (done) break;\n }\n \n // Trim trailing dots\n size_t maxlen = 0;\n for (int i = 0; i < N; i++) maxlen = max(maxlen, ans[i].size());\n \n while (maxlen > 1) {\n bool all_dot = true;\n for (int i = 0; i < N; i++) {\n if (ans[i].size() >= maxlen && ans[i][maxlen-1] != '.') all_dot = false;\n }\n if (!all_dot) break;\n maxlen--;\n for (int i = 0; i < N; i++)\n if (ans[i].size() > maxlen) ans[i].resize(maxlen);\n }\n \n for (int i = 0; i < N; i++) cout << ans[i] << \"\\n\";\n return 0;\n}","ahc034":"#include \nusing namespace std;\n\nint N;\nvector> h;\nvector ops;\nint cx = 0, cy = 0;\nint load = 0;\n\nvoid move_one(char dir) {\n ops.push_back(string(1, dir));\n if (dir == 'U') cx--;\n else if (dir == 'D') cx++;\n else if (dir == 'L') cy--;\n else if (dir == 'R') cy++;\n}\n\nvoid move_to(int tx, int ty) {\n while (cx < tx) move_one('D');\n while (cx > tx) move_one('U');\n while (cy < ty) move_one('R');\n while (cy > ty) move_one('L');\n}\n\nvoid do_load(int d) {\n if (d <= 0) return;\n ops.push_back(\"+\" + to_string(d));\n load += d;\n h[cx][cy] -= d;\n}\n\nvoid do_unload(int d) {\n if (d <= 0) return;\n ops.push_back(\"-\" + to_string(d));\n load -= d;\n h[cx][cy] += d;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N, vector(N));\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n cin >> h[i][j];\n }\n }\n \n while (true) {\n int si = -1, sj = -1, best_dist = INT_MAX;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (h[i][j] > 0) {\n int dist = abs(i - cx) + abs(j - cy);\n if (dist < best_dist) {\n best_dist = dist;\n si = i;\n sj = j;\n }\n }\n }\n }\n \n if (si == -1) break;\n \n move_to(si, sj);\n do_load(h[cx][cy]);\n \n while (load > 0) {\n int ti = -1, tj = -1;\n best_dist = INT_MAX;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (h[i][j] < 0) {\n int dist = abs(i - cx) + abs(j - cy);\n if (dist < best_dist) {\n best_dist = dist;\n ti = i;\n tj = j;\n }\n }\n }\n }\n \n if (ti == -1) break;\n \n move_to(ti, tj);\n do_unload(min(load, -h[cx][cy]));\n }\n }\n \n for (const auto& op : ops) {\n cout << op << \"\\n\";\n }\n \n return 0;\n}","ahc035":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, T;\n cin >> N >> M >> T;\n\n int seed_count = 2 * N * (N - 1);\n vector> X(seed_count, vector(M, 0));\n\n for (int i = 0; i < seed_count; i++) {\n for (int j = 0; j < M; j++) {\n cin >> X[i][j];\n }\n }\n\n for (int t = 0; t < T; t++) {\n // Find max value for each criterion\n vector maxVal(M, -1);\n for (int l = 0; l < M; l++) {\n for (int i = 0; i < seed_count; i++) {\n maxVal[l] = max(maxVal[l], X[i][l]);\n }\n }\n \n // Calculate score for each seed (bonus for having max values)\n vector> seed_scores(seed_count);\n for (int i = 0; i < seed_count; i++) {\n double score = 0;\n for (int l = 0; l < M; l++) {\n if (X[i][l] == maxVal[l]) {\n score += 1000;\n }\n score += X[i][l];\n }\n seed_scores[i] = {score, i};\n }\n \n sort(seed_scores.begin(), seed_scores.end(), greater>());\n \n vector selected(N * N);\n for (int i = 0; i < N * N; i++) {\n selected[i] = seed_scores[i].second;\n }\n \n auto getValue = [&](int idx) {\n int total = 0;\n for (int l = 0; l < M; l++) total += X[idx][l];\n return total;\n };\n \n sort(selected.begin(), selected.end(), [&](int a, int b) {\n return getValue(a) > getValue(b);\n });\n \n vector> pos_order;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n pos_order.push_back({i, j});\n }\n }\n \n double cx = (N - 1) / 2.0;\n double cy = (N - 1) / 2.0;\n sort(pos_order.begin(), pos_order.end(), [&](auto& a, auto& b) {\n double da = abs(a.first - cx) + abs(a.second - cy);\n double db = abs(b.first - cx) + abs(b.second - cy);\n if (da != db) return da < db;\n if (a.first != b.first) return a.first < b.first;\n return a.second < b.second;\n });\n \n vector> A(N, vector(N, -1));\n for (int i = 0; i < N * N; i++) {\n A[pos_order[i].first][pos_order[i].second] = selected[i];\n }\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n cout << A[i][j];\n if (j < N - 1) cout << \" \";\n else cout << \"\\n\";\n }\n }\n cout.flush();\n\n for (int i = 0; i < seed_count; i++) {\n for (int j = 0; j < M; j++) {\n cin >> X[i][j];\n }\n }\n }\n\n return 0;\n}","ahc038":"#include \nusing namespace std;\n\nint N, M, V;\nconst int DX[] = {0, 1, 0, -1};\nconst int DY[] = {1, 0, -1, 0};\n\nint rx, ry;\nvector dirs;\nvector holding;\nint numF;\n\npair fingertip(int i) { return {rx + DX[dirs[i]], ry + DY[dirs[i]]}; }\nbool valid(int x, int y) { return x >= 0 && x < N && y >= 0 && y < N; }\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> V;\n vector grid(N), target(N);\n for (int i = 0; i < N; i++) cin >> grid[i];\n for (int i = 0; i < N; i++) cin >> target[i];\n \n numF = min(V - 1, 4);\n cout << numF + 1 << \"\\n\";\n for (int i = 1; i <= numF; i++) cout << \"0 1\\n\";\n cout << \"0 0\\n\";\n \n rx = ry = 0;\n dirs.assign(numF, 0);\n holding.assign(numF, false);\n \n set> pickup, dropS;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n if (grid[i][j] == '1' && target[i][j] == '0') pickup.insert({i, j});\n if (target[i][j] == '1' && grid[i][j] == '0') dropS.insert({i, j});\n }\n \n vector ops;\n \n auto makeOp = [&](char mv, vector& rot, vector& act) {\n string s; s += mv;\n for (int i = 0; i < numF; i++) s += rot[i];\n s += '.';\n for (int i = 0; i < numF; i++) s += act[i];\n ops.push_back(s);\n };\n \n while (ops.size() < 95000 && (!pickup.empty() || !dropS.empty() || \n any_of(holding.begin(), holding.end(), [](bool h){return h;}))) {\n \n vector rot(numF, '.'), act(numF, '.');\n bool acted = false;\n \n // Try pick/drop at current positions\n for (int i = 0; i < numF; i++) {\n auto [fx, fy] = fingertip(i);\n if (!valid(fx, fy)) continue;\n if (!holding[i] && pickup.count({fx, fy})) {\n act[i] = 'P'; pickup.erase({fx, fy}); holding[i] = true; acted = true;\n } else if (holding[i] && dropS.count({fx, fy})) {\n act[i] = 'P'; dropS.erase({fx, fy}); holding[i] = false; acted = true;\n }\n }\n if (acted) { makeOp('.', rot, act); continue; }\n \n // Find best target for any fingertip\n int bestDist = INT_MAX, bestF = -1, bestDir = -1;\n pair bestTarget;\n bool forDrop = false;\n \n for (int i = 0; i < numF; i++) {\n auto& targets = holding[i] ? dropS : pickup;\n for (auto& t : targets) {\n for (int d = 0; d < 4; d++) {\n int nrx = t.first - DX[d], nry = t.second - DY[d];\n if (!valid(nrx, nry)) continue;\n int dist = abs(nrx - rx) + abs(nry - ry);\n if (dirs[i] != d) dist++;\n if (dist < bestDist) {\n bestDist = dist; bestF = i; bestDir = d; \n bestTarget = t; forDrop = holding[i];\n }\n }\n }\n }\n \n if (bestF == -1) break;\n \n int trx = bestTarget.first - DX[bestDir], tr_y = bestTarget.second - DY[bestDir];\n char mv = '.';\n \n // Move towards target root position\n if (rx < trx && valid(rx + 1, ry)) { mv = 'D'; rx++; }\n else if (rx > trx && valid(rx - 1, ry)) { mv = 'U'; rx--; }\n else if (ry < tr_y && valid(rx, ry + 1)) { mv = 'R'; ry++; }\n else if (ry > tr_y && valid(rx, ry - 1)) { mv = 'L'; ry--; }\n \n // Rotate fingertip towards target direction\n if (dirs[bestF] != bestDir) {\n int diff = (bestDir - dirs[bestF] + 4) % 4;\n if (diff == 1) { rot[bestF] = 'R'; dirs[bestF] = (dirs[bestF] + 1) % 4; }\n else if (diff == 3) { rot[bestF] = 'L'; dirs[bestF] = (dirs[bestF] + 3) % 4; }\n else { rot[bestF] = 'R'; dirs[bestF] = (dirs[bestF] + 1) % 4; }\n }\n \n if (mv == '.' && rot[bestF] == '.') {\n // Stuck - try any move\n if (valid(rx + 1, ry)) { mv = 'D'; rx++; }\n else if (valid(rx - 1, ry)) { mv = 'U'; rx--; }\n else if (valid(rx, ry + 1)) { mv = 'R'; ry++; }\n else if (valid(rx, ry - 1)) { mv = 'L'; ry--; }\n }\n \n makeOp(mv, rot, act);\n }\n \n for (auto& op : ops) cout << op << \"\\n\";\n return 0;\n}","ahc039":"#include \nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N;\n cin >> N;\n \n vector> mackerel(N), sardine(N);\n \n for (int i = 0; i < N; i++)\n cin >> mackerel[i].first >> mackerel[i].second;\n for (int i = 0; i < N; i++)\n cin >> sardine[i].first >> sardine[i].second;\n \n vector xs, ys;\n for (auto& p : mackerel) { xs.push_back(p.first); ys.push_back(p.second); }\n for (auto& p : sardine) { xs.push_back(p.first); ys.push_back(p.second); }\n \n sort(xs.begin(), xs.end()); xs.erase(unique(xs.begin(), xs.end()), xs.end());\n sort(ys.begin(), ys.end()); ys.erase(unique(ys.begin(), ys.end()), ys.end());\n \n int nx = xs.size(), ny = ys.size();\n map x_idx, y_idx;\n for (int i = 0; i < nx; i++) x_idx[xs[i]] = i;\n for (int i = 0; i < ny; i++) y_idx[ys[i]] = i;\n \n vector> grid(ny + 1, vector(nx + 1, 0));\n \n for (auto& p : mackerel)\n grid[y_idx[p.second] + 1][x_idx[p.first] + 1]++;\n for (auto& p : sardine)\n grid[y_idx[p.second] + 1][x_idx[p.first] + 1]--;\n \n // Build 2D prefix sum\n for (int i = 1; i <= ny; i++)\n for (int j = 1; j <= nx; j++)\n grid[i][j] += grid[i-1][j] + grid[i][j-1] - grid[i-1][j-1];\n \n auto query = [&](int y1, int x1, int y2, int x2) -> int {\n return grid[y2+1][x2+1] - grid[y1][x2+1] - grid[y2+1][x1] + grid[y1][x1];\n };\n \n int best_score = 0;\n int bx1 = 0, by1 = 0, bx2 = 0, by2 = 0;\n \n mt19937 rng(42);\n \n // Random sampling\n for (int iter = 0; iter < 500000; iter++) {\n int i1 = rng() % N, i2 = rng() % N;\n int x1i = x_idx[mackerel[i1].first];\n int y1i = y_idx[mackerel[i1].second];\n int x2i = x_idx[mackerel[i2].first];\n int y2i = y_idx[mackerel[i2].second];\n \n if (x1i > x2i) swap(x1i, x2i);\n if (y1i > y2i) swap(y1i, y2i);\n \n int score = query(y1i, x1i, y2i, x2i);\n if (score > best_score) {\n best_score = score;\n bx1 = x1i; by1 = y1i; bx2 = x2i; by2 = y2i;\n }\n }\n \n // Local search\n bool improved = true;\n while (improved) {\n improved = false;\n for (int dx1 : {-1, 0, 1}) {\n for (int dy1 : {-1, 0, 1}) {\n for (int dx2 : {-1, 0, 1}) {\n for (int dy2 : {-1, 0, 1}) {\n int nx1 = bx1 + dx1, ny1 = by1 + dy1;\n int nx2 = bx2 + dx2, ny2 = by2 + dy2;\n if (nx1 < 0 || ny1 < 0 || nx2 >= nx || ny2 >= ny) continue;\n if (nx1 > nx2 || ny1 > ny2) continue;\n int score = query(ny1, nx1, ny2, nx2);\n if (score > best_score) {\n best_score = score;\n bx1 = nx1; by1 = ny1; bx2 = nx2; by2 = ny2;\n improved = true;\n }\n }\n }\n }\n }\n }\n \n int outx1 = xs[bx1], outy1 = ys[by1];\n int outx2 = xs[bx2], outy2 = ys[by2];\n \n if (best_score == 0) {\n outx1 = 0; outy1 = 0; outx2 = 1; outy2 = 1;\n }\n \n cout << 4 << \"\\n\";\n cout << outx1 << \" \" << outy1 << \"\\n\";\n cout << outx2 << \" \" << outy1 << \"\\n\";\n cout << outx2 << \" \" << outy2 << \"\\n\";\n cout << outx1 << \" \" << outy2 << \"\\n\";\n \n return 0;\n}","ahc040":"#include \nusing namespace std;\n\nint N, T;\nlong long sigma;\nvector w, h;\n\nstruct PlacedRect { long long x1, y1, x2, y2; int id; };\n\ntuple simulate(const vector>& ops) {\n vector placed;\n long long W = 0, H = 0;\n for (auto& [p, r, d, b] : ops) {\n long long rw = w[p], rh = h[p];\n if (r) swap(rw, rh);\n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n placed.push_back({x, y, x + rw, y + rh, p});\n W = max(W, x + rw); H = max(H, y + rh);\n }\n return {W, H};\n}\n\nmt19937 rng(12345);\n\nvector> genGreedy() {\n vector> ops;\n vector placed;\n long long curW = 0, curH = 0;\n for (int i = 0; i < N; i++) {\n long long best = LLONG_MAX; tuple bc = {0,'U',-1};\n for (int r = 0; r < 2; r++) for (char d : {'U','L'}) for (int b = -1; b < i; b++) {\n long long rw = w[i], rh = h[i]; if (r) swap(rw, rh);\n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n long long sc = max(curW, x+rw) + max(curH, y+rh);\n if (sc < best) { best = sc; bc = {r, d, b}; }\n }\n auto [r, d, b] = bc;\n long long rw = w[i], rh = h[i]; if (r) swap(rw, rh);\n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n placed.push_back({x, y, x+rw, y+rh, i}); curW = max(curW, x+rw); curH = max(curH, y+rh);\n ops.push_back({i, r, d, b});\n }\n return ops;\n}\n\nvector> genStrip(char dir, int rotMode) {\n vector> ops;\n for (int i = 0; i < N; i++) {\n int r = (rotMode == 0) ? 0 : (rotMode == 1) ? 1 : (w[i] > h[i] ? 1 : 0);\n ops.push_back({i, r, dir, -1});\n }\n return ops;\n}\n\nvector> genChain(char dir) {\n vector> ops;\n for (int i = 0; i < N; i++) {\n int r = (dir == 'U') ? (w[i] < h[i] ? 1 : 0) : (h[i] < w[i] ? 1 : 0);\n ops.push_back({i, r, dir, i > 0 ? i-1 : -1});\n }\n return ops;\n}\n\nvector> mutate(vector> ops, int intensity = 1) {\n int numMut = intensity + rng() % (intensity + 2);\n for (int m = 0; m < numMut; m++) {\n int i = rng() % N;\n auto& [p, r, d, b] = ops[i];\n int choice = rng() % 3;\n if (choice == 0) r = 1 - r;\n else if (choice == 1) d = (d == 'U') ? 'L' : 'U';\n else b = (int)(rng() % (i + 1)) - 1;\n }\n return ops;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> T >> sigma;\n w.resize(N); h.resize(N);\n for (int i = 0; i < N; i++) cin >> w[i] >> h[i];\n \n vector>>> candidates;\n \n auto addCandidate = [&](vector> ops) {\n auto [sw, sh] = simulate(ops);\n candidates.push_back({sw + sh, ops});\n };\n \n addCandidate(genGreedy());\n addCandidate(genStrip('U', 0));\n addCandidate(genStrip('U', 1));\n addCandidate(genStrip('U', 2));\n addCandidate(genStrip('L', 0));\n addCandidate(genStrip('L', 1));\n addCandidate(genStrip('L', 2));\n addCandidate(genChain('U'));\n addCandidate(genChain('L'));\n \n sort(candidates.begin(), candidates.end());\n auto bestOps = candidates[0].second;\n long long bestSim = candidates[0].first;\n \n // Hill climbing with simulated annealing\n for (int iter = 0; iter < 20000 && (int)candidates.size() < T * 2; iter++) {\n int srcIdx = (rng() % 100 < 70) ? 0 : rng() % min((int)candidates.size(), 5);\n auto ops = mutate(candidates[srcIdx].second, 1 + iter / 5000);\n auto [sw, sh] = simulate(ops);\n long long score = sw + sh;\n \n double threshold = bestSim * (1.0 + 0.1 * exp(-iter / 3000.0));\n if (score <= threshold) {\n candidates.push_back({score, ops});\n if (score < bestSim) { \n bestSim = score; \n bestOps = ops;\n }\n }\n }\n \n sort(candidates.begin(), candidates.end());\n if ((int)candidates.size() > T) candidates.resize(T);\n \n while ((int)candidates.size() < T) {\n auto ops = mutate(bestOps, 2);\n auto [sw, sh] = simulate(ops);\n candidates.push_back({sw + sh, ops});\n }\n \n sort(candidates.begin(), candidates.end());\n \n long long bestObserved = LLONG_MAX;\n int bestObservedIdx = 0;\n \n for (int t = 0; t < T; t++) {\n vector>* ops;\n if (t < (int)candidates.size()) {\n ops = &candidates[t].second;\n } else {\n // Generate new mutation based on best observed\n static vector> tempOps;\n tempOps = mutate(candidates[bestObservedIdx].second, 2);\n ops = &tempOps;\n }\n \n cout << ops->size() << \"\\n\";\n for (auto& [p, r, d, b] : *ops) cout << p << \" \" << r << \" \" << d << \" \" << b << \"\\n\";\n cout.flush();\n \n long long W, H; \n cin >> W >> H;\n \n if (W + H < bestObserved) {\n bestObserved = W + H;\n bestObservedIdx = t < (int)candidates.size() ? t : bestObservedIdx;\n }\n }\n \n return 0;\n}","ahc041":"#include \nusing namespace std;\n\nint N, M, H;\nvector A;\nvector> adj;\nvector parent_arr;\nvector depth_arr;\n\nvoid dfs(int u) {\n // Sort neighbors by descending beauty - visit high beauty first to place them deep\n vector> neighbors;\n for (int v : adj[u]) {\n if (depth_arr[v] == -1) {\n neighbors.push_back({-A[v], v}); // negative for descending sort\n }\n }\n sort(neighbors.begin(), neighbors.end());\n \n for (auto& [neg_beauty, v] : neighbors) {\n if (depth_arr[v] == -1 && depth_arr[u] < H) {\n parent_arr[v] = u;\n depth_arr[v] = depth_arr[u] + 1;\n dfs(v);\n }\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> H;\n \n A.resize(N);\n for (int i = 0; i < N; i++) {\n cin >> A[i];\n }\n \n adj.resize(N);\n for (int i = 0; i < M; i++) {\n int u, v;\n cin >> u >> v;\n adj[u].push_back(v);\n adj[v].push_back(u);\n }\n \n for (int i = 0; i < N; i++) {\n int x, y;\n cin >> x >> y;\n }\n \n parent_arr.resize(N, -1);\n depth_arr.resize(N, -1);\n \n // Sort vertices by ascending beauty - low beauty vertices become roots first\n vector order(N);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int a, int b) {\n return A[a] < A[b];\n });\n \n // Build trees using DFS from low-beauty roots\n for (int start : order) {\n if (depth_arr[start] != -1) continue;\n \n depth_arr[start] = 0;\n parent_arr[start] = -1;\n dfs(start);\n }\n \n // Output\n for (int i = 0; i < N; i++) {\n cout << parent_arr[i];\n if (i < N - 1) cout << \" \";\n }\n cout << \"\\n\";\n \n return 0;\n}","ahc042":"#include \nusing namespace std;\n\nint N;\n\nstruct State {\n vector board;\n vector> ops;\n \n void L(int r) { ops.push_back({'L', r}); for (int j = 0; j < N-1; j++) board[r][j] = board[r][j+1]; board[r][N-1] = '.'; }\n void R(int r) { ops.push_back({'R', r}); for (int j = N-1; j > 0; j--) board[r][j] = board[r][j-1]; board[r][0] = '.'; }\n void U(int c) { ops.push_back({'U', c}); for (int i = 0; i < N-1; i++) board[i][c] = board[i+1][c]; board[N-1][c] = '.'; }\n void D(int c) { ops.push_back({'D', c}); for (int i = N-1; i > 0; i--) board[i][c] = board[i-1][c]; board[0][c] = '.'; }\n \n int count_oni() {\n int c = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (board[i][j] == 'x') c++;\n return c;\n }\n \n void apply(int type, int idx, int dist) {\n if (type == 0) { for (int t = 0; t < dist; t++) U(idx); for (int t = 0; t < dist; t++) D(idx); }\n else if (type == 1) { for (int t = 0; t < dist; t++) D(idx); for (int t = 0; t < dist; t++) U(idx); }\n else if (type == 2) { for (int t = 0; t < dist; t++) L(idx); for (int t = 0; t < dist; t++) R(idx); }\n else { for (int t = 0; t < dist; t++) R(idx); for (int t = 0; t < dist; t++) L(idx); }\n }\n};\n\nstruct Batch { int type, idx, dist, cnt; };\n\nvector get_batches(const vector& board) {\n vector batches;\n for (int j = 0; j < N; j++) {\n int first_fuku = N;\n for (int i = 0; i < N; i++) if (board[i][j] == 'o') { first_fuku = i; break; }\n int last_oni = -1, cnt = 0;\n for (int i = 0; i < first_fuku; i++) if (board[i][j] == 'x') { last_oni = i; cnt++; }\n if (cnt > 0) batches.push_back({0, j, last_oni + 1, cnt});\n \n int last_fuku = -1;\n for (int i = N-1; i >= 0; i--) if (board[i][j] == 'o') { last_fuku = i; break; }\n int first_oni = N; cnt = 0;\n for (int i = N-1; i > last_fuku; i--) if (board[i][j] == 'x') { first_oni = i; cnt++; }\n if (cnt > 0) batches.push_back({1, j, N - first_oni, cnt});\n }\n for (int i = 0; i < N; i++) {\n int first_fuku = N;\n for (int j = 0; j < N; j++) if (board[i][j] == 'o') { first_fuku = j; break; }\n int last_oni = -1, cnt = 0;\n for (int j = 0; j < first_fuku; j++) if (board[i][j] == 'x') { last_oni = j; cnt++; }\n if (cnt > 0) batches.push_back({2, i, last_oni + 1, cnt});\n \n int last_fuku = -1;\n for (int j = N-1; j >= 0; j--) if (board[i][j] == 'o') { last_fuku = j; break; }\n int first_oni = N; cnt = 0;\n for (int j = N-1; j > last_fuku; j--) if (board[i][j] == 'x') { first_oni = j; cnt++; }\n if (cnt > 0) batches.push_back({3, i, N - first_oni, cnt});\n }\n return batches;\n}\n\nvector> solve(vector init_board, int strategy, mt19937& rng) {\n State st;\n st.board = init_board;\n \n while (st.count_oni() > 0) {\n auto batches = get_batches(st.board);\n if (batches.empty()) break;\n \n int best = -1;\n double best_score = 1e18;\n \n for (int i = 0; i < (int)batches.size(); i++) {\n auto& b = batches[i];\n double score;\n if (strategy == 0) score = (double)(2 * b.dist) / b.cnt;\n else if (strategy == 1) score = (double)(2 * b.dist) / b.cnt + (rng() % 1000) * 0.0001;\n else if (strategy == 2) score = (double)(2 * b.dist) / (b.cnt * b.cnt);\n else if (strategy == 3) score = b.dist;\n else if (strategy == 4) score = (double)b.dist / b.cnt;\n else score = (double)(2 * b.dist) / b.cnt - b.cnt * 0.01;\n \n if (score < best_score) { best_score = score; best = i; }\n }\n \n st.apply(batches[best].type, batches[best].idx, batches[best].dist);\n }\n \n return st.ops;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n vector board(N);\n for (int i = 0; i < N; i++) cin >> board[i];\n \n mt19937 rng(42);\n vector> best_ops;\n \n for (int trial = 0; trial < 200; trial++) {\n int strategy = (trial < 6) ? trial : 1;\n auto ops = solve(board, strategy, rng);\n if (best_ops.empty() || ops.size() < best_ops.size()) {\n best_ops = ops;\n }\n }\n \n for (auto& [d, p] : best_ops) cout << d << \" \" << p << \"\\n\";\n \n return 0;\n}","ahc044":"#include \nusing namespace std;\n\nint N, L;\nvector T;\n\nlong long simulate(const vector& a, const vector& b, vector& t) {\n fill(t.begin(), t.end(), 0);\n int x = 0;\n for (int week = 0; week < L; week++) {\n t[x]++;\n x = (t[x] & 1) ? a[x] : b[x];\n }\n long long error = 0;\n for (int i = 0; i < N; i++) {\n error += abs(t[i] - T[i]);\n }\n return error;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> L;\n T.resize(N);\n for (int i = 0; i < N; i++) cin >> T[i];\n \n mt19937 rng(42);\n \n vector weighted;\n for (int i = 0; i < N; i++) {\n int cnt = max(1, T[i] / 100);\n for (int j = 0; j < cnt; j++) weighted.push_back(i);\n }\n \n vector sorted_idx(N);\n iota(sorted_idx.begin(), sorted_idx.end(), 0);\n sort(sorted_idx.begin(), sorted_idx.end(), [](int a, int b) { return T[a] > T[b]; });\n \n vector best_a(N), best_b(N), t(N);\n long long global_best = LLONG_MAX;\n \n auto start = chrono::steady_clock::now();\n double time_limit = 1.85;\n \n for (int restart = 0; ; restart++) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > time_limit) break;\n \n vector a(N), b(N);\n \n if (restart == 0) {\n for (int i = 0; i < N; i++) {\n a[sorted_idx[i]] = sorted_idx[(i + 1) % N];\n b[sorted_idx[i]] = sorted_idx[(i + 1) % N];\n }\n } else {\n for (int i = 0; i < N; i++) {\n a[i] = weighted[rng() % weighted.size()];\n b[i] = weighted[rng() % weighted.size()];\n }\n }\n \n long long cur_error = simulate(a, b, t);\n long long local_best = cur_error;\n vector local_a = a, local_b = b;\n \n double restart_budget = min(0.25, (time_limit - elapsed) * 0.7);\n double restart_start = elapsed;\n \n while (true) {\n now = chrono::steady_clock::now();\n elapsed = chrono::duration(now - start).count();\n if (elapsed > time_limit || elapsed - restart_start > restart_budget) break;\n \n double progress = (elapsed - restart_start) / restart_budget;\n double temp = 2000.0 * pow(0.0001, progress);\n \n int i = rng() % N;\n int old_a = a[i], old_b = b[i];\n \n int choice = rng() % 4;\n if (choice == 0) {\n a[i] = rng() % N;\n } else if (choice == 1) {\n b[i] = rng() % N;\n } else if (choice == 2) {\n a[i] = weighted[rng() % weighted.size()];\n } else {\n b[i] = weighted[rng() % weighted.size()];\n }\n \n long long new_error = simulate(a, b, t);\n double delta = new_error - cur_error;\n \n if (delta <= 0 || exp(-delta / temp) > (rng() % 1000000) / 1000000.0) {\n cur_error = new_error;\n if (new_error < local_best) {\n local_best = new_error;\n local_a = a;\n local_b = b;\n }\n } else {\n a[i] = old_a;\n b[i] = old_b;\n }\n }\n \n if (local_best < global_best) {\n global_best = local_best;\n best_a = local_a;\n best_b = local_b;\n }\n }\n \n for (int i = 0; i < N; i++) {\n cout << best_a[i] << \" \" << best_b[i] << \"\\n\";\n }\n \n return 0;\n}","ahc045":"#include \nusing namespace std;\n\nint queries_used = 0;\nint Q_limit;\n\nvector> query(vector cities) {\n if (queries_used >= Q_limit || cities.size() < 2) return {};\n cout << \"? \" << cities.size();\n for (int c : cities) cout << \" \" << c;\n cout << endl;\n \n vector> edges;\n for (size_t i = 0; i + 1 < cities.size(); i++) {\n int a, b;\n cin >> a >> b;\n edges.emplace_back(a, b);\n }\n queries_used++;\n return edges;\n}\n\ndouble estDist(double x1, double y1, double x2, double y2) {\n return sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2));\n}\n\nuint64_t morton(double px, double py) {\n uint32_t ix = (uint32_t)(px);\n uint32_t iy = (uint32_t)(py);\n uint64_t result = 0;\n for (int i = 0; i < 16; i++) {\n result |= ((uint64_t)((ix >> i) & 1) << (2 * i));\n result |= ((uint64_t)((iy >> i) & 1) << (2 * i + 1));\n }\n return result;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, Q, L, W;\n cin >> N >> M >> Q >> L >> W;\n Q_limit = Q;\n \n vector G(M);\n for (int i = 0; i < M; i++) cin >> G[i];\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) {\n int lx, rx, ly, ry;\n cin >> lx >> rx >> ly >> ry;\n x[i] = (lx + rx) / 2.0;\n y[i] = (ly + ry) / 2.0;\n }\n \n // Use Morton code for better 2D locality\n vector order(N);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int a, int b) {\n return morton(x[a], y[a]) < morton(x[b], y[b]);\n });\n \n vector> groups(M);\n int idx = 0;\n for (int i = 0; i < M; i++) {\n for (int j = 0; j < G[i]; j++) {\n groups[i].push_back(order[idx++]);\n }\n }\n \n vector>> edges(M);\n \n for (int k = 0; k < M; k++) {\n int g = groups[k].size();\n if (g == 1) continue;\n \n // Sort within group for better query locality\n sort(groups[k].begin(), groups[k].end(), [&](int a, int b) {\n return morton(x[a], y[a]) < morton(x[b], y[b]);\n });\n \n vector> all_edges;\n \n if (g <= L && queries_used < Q) {\n edges[k] = query(groups[k]);\n } else {\n int step = max(1, L - 1); // Overlap by 1\n for (int i = 0; i < g && queries_used < Q; i += step) {\n int end = min(i + L, g);\n if (end - i >= 2) {\n vector subset(groups[k].begin() + i, groups[k].begin() + end);\n auto e = query(subset);\n all_edges.insert(all_edges.end(), e.begin(), e.end());\n }\n if (end >= g) break;\n }\n \n map city_to_local;\n for (int i = 0; i < g; i++) city_to_local[groups[k][i]] = i;\n \n vector parent(g);\n iota(parent.begin(), parent.end(), 0);\n function find = [&](int u) -> int {\n return parent[u] == u ? u : parent[u] = find(parent[u]);\n };\n \n // Sort edges by estimated distance for Kruskal\n sort(all_edges.begin(), all_edges.end(), [&](auto& a, auto& b) {\n double da = estDist(x[a.first], y[a.first], x[a.second], y[a.second]);\n double db = estDist(x[b.first], y[b.first], x[b.second], y[b.second]);\n return da < db;\n });\n \n for (auto& e : all_edges) {\n int u = city_to_local[e.first];\n int v = city_to_local[e.second];\n if (find(u) != find(v)) {\n parent[find(u)] = find(v);\n edges[k].push_back(e);\n }\n }\n \n // Fallback: connect components using shortest estimated edges\n while ((int)edges[k].size() < g - 1) {\n double best_dist = 1e18;\n int best_u = -1, best_v = -1;\n for (int i = 0; i < g; i++) {\n for (int j = i + 1; j < g; j++) {\n if (find(i) != find(j)) {\n double d = estDist(x[groups[k][i]], y[groups[k][i]], \n x[groups[k][j]], y[groups[k][j]]);\n if (d < best_dist) {\n best_dist = d;\n best_u = i;\n best_v = j;\n }\n }\n }\n }\n if (best_u >= 0) {\n parent[find(best_u)] = find(best_v);\n edges[k].push_back({groups[k][best_u], groups[k][best_v]});\n } else break;\n }\n }\n }\n \n cout << \"!\" << endl;\n for (int k = 0; k < M; k++) {\n for (int c : groups[k]) cout << c << \" \";\n cout << \"\\n\";\n for (auto& e : edges[k]) {\n cout << e.first << \" \" << e.second << \"\\n\";\n }\n }\n \n return 0;\n}","ahc046":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M;\n cin >> N >> M;\n \n vector> targets(M);\n for (int i = 0; i < M; i++) {\n cin >> targets[i].first >> targets[i].second;\n }\n \n vector actions;\n int curR = targets[0].first, curC = targets[0].second;\n \n for (int i = 1; i < M; i++) {\n int tR = targets[i].first, tC = targets[i].second;\n \n int moveCost = abs(tR - curR) + abs(tC - curC);\n int bestCost = moveCost;\n int bestStrategy = 0;\n \n // Edge target strategies (slide directly to target on edge)\n if (tR == 0 && curR > 0) {\n int cost = abs(tC - curC) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 1; }\n }\n if (tR == N - 1 && curR < N - 1) {\n int cost = abs(tC - curC) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 2; }\n }\n if (tC == 0 && curC > 0) {\n int cost = abs(tR - curR) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 3; }\n }\n if (tC == N - 1 && curC < N - 1) {\n int cost = abs(tR - curR) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 4; }\n }\n \n // Slide-first strategies (slide to edge first, then move to target)\n if (curR > 0) {\n int cost = 1 + tR + abs(tC - curC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 5; }\n }\n if (curR < N - 1) {\n int cost = 1 + (N - 1 - tR) + abs(tC - curC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 6; }\n }\n if (curC > 0) {\n int cost = 1 + tC + abs(tR - curR);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 7; }\n }\n if (curC < N - 1) {\n int cost = 1 + (N - 1 - tC) + abs(tR - curR);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 8; }\n }\n \n switch (bestStrategy) {\n case 0:\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n break;\n case 1:\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n actions.push_back(\"S U\"); curR = 0;\n break;\n case 2:\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n actions.push_back(\"S D\"); curR = N - 1;\n break;\n case 3:\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n actions.push_back(\"S L\"); curC = 0;\n break;\n case 4:\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n actions.push_back(\"S R\"); curC = N - 1;\n break;\n case 5:\n actions.push_back(\"S U\"); curR = 0;\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n break;\n case 6:\n actions.push_back(\"S D\"); curR = N - 1;\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n break;\n case 7:\n actions.push_back(\"S L\"); curC = 0;\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n break;\n case 8:\n actions.push_back(\"S R\"); curC = N - 1;\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n break;\n }\n }\n \n for (const string& action : actions) {\n cout << action << \"\\n\";\n }\n \n return 0;\n}"},"4":{"ahc001":"#include \nusing namespace std;\n\nconst int W = 10000;\nint n;\nvector px, py, rr;\nint a[201], b[201], c[201], d[201];\n\nbool canExpand(int i, int dir) {\n int na = a[i], nb = b[i], nc = c[i], nd = d[i];\n if (dir == 0) na--;\n else if (dir == 1) nc++;\n else if (dir == 2) nb--;\n else nd++;\n \n if (na < 0 || nc > W || nb < 0 || nd > W) return false;\n \n for (int j = 0; j < n; j++) {\n if (i == j) continue;\n if (!(nc <= a[j] || c[j] <= na || nd <= b[j] || d[j] <= nb)) return false;\n }\n return true;\n}\n\nvoid expand(int i, int dir) {\n if (dir == 0) a[i]--;\n else if (dir == 1) c[i]++;\n else if (dir == 2) b[i]--;\n else d[i]++;\n}\n\nlong long area(int i) {\n return (long long)(c[i] - a[i]) * (d[i] - b[i]);\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> n;\n px.resize(n); py.resize(n); rr.resize(n);\n \n for (int i = 0; i < n; i++) {\n cin >> px[i] >> py[i] >> rr[i];\n a[i] = px[i]; b[i] = py[i]; c[i] = px[i]+1; d[i] = py[i]+1;\n }\n \n auto start = chrono::high_resolution_clock::now();\n \n while (true) {\n auto now = chrono::high_resolution_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > 4.8) break;\n \n bool changed = false;\n \n vector order(n);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int i, int j) {\n return rr[i] - area(i) > rr[j] - area(j);\n });\n \n for (int i : order) {\n for (int dir = 0; dir < 4; dir++) {\n if (canExpand(i, dir)) {\n expand(i, dir);\n changed = true;\n }\n }\n }\n \n if (!changed) break;\n }\n \n // Shrink rectangles that are too big\n for (int iter = 0; iter < 1000; iter++) {\n for (int i = 0; i < n; i++) {\n if (area(i) <= rr[i]) continue;\n for (int dir = 0; dir < 4; dir++) {\n int na = a[i], nb = b[i], nc = c[i], nd = d[i];\n if (dir == 0) na++;\n else if (dir == 1) nc--;\n else if (dir == 2) nb++;\n else nd--;\n \n if (na >= nc || nb >= nd) continue;\n if (!(na <= px[i] && px[i] < nc && nb <= py[i] && py[i] < nd)) continue;\n \n long long newArea = (long long)(nc - na) * (nd - nb);\n if (newArea >= rr[i]) {\n a[i] = na; b[i] = nb; c[i] = nc; d[i] = nd;\n }\n }\n }\n }\n \n for (int i = 0; i < n; i++) {\n cout << a[i] << \" \" << b[i] << \" \" << c[i] << \" \" << d[i] << \"\\n\";\n }\n \n return 0;\n}","ahc002":"#include \nusing namespace std;\n\nconst int N = 50;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nconst char dc[] = {'U', 'D', 'L', 'R'};\n\nint t[N][N], p[N][N];\nint si, sj;\nmt19937 rng(42);\n\nint countMoves(int x, int y, const bitset<2500>& used) {\n int cnt = 0;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < N && ny >= 0 && ny < N && !used[t[nx][ny]]) cnt++;\n }\n return cnt;\n}\n\nint countMoves2(int x, int y, const bitset<2500>& used) {\n int cnt = 0;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx < 0 || nx >= N || ny < 0 || ny >= N || used[t[nx][ny]]) continue;\n cnt++;\n for (int d2 = 0; d2 < 4; d2++) {\n int nnx = nx + dx[d2], nny = ny + dy[d2];\n if (nnx >= 0 && nnx < N && nny >= 0 && nny < N && \n !used[t[nnx][nny]] && t[nnx][nny] != t[nx][ny]) cnt++;\n }\n }\n return cnt;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> si >> sj;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> t[i][j];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> p[i][j];\n \n struct State {\n int x, y, score, priority;\n bitset<2500> usedTiles;\n string path;\n };\n \n string bestPath = \"\";\n int bestScore = 0;\n auto startTime = chrono::steady_clock::now();\n \n const int BEAM_WIDTH = 700;\n vector beam;\n State init;\n init.x = si; init.y = sj;\n init.score = p[si][sj];\n init.usedTiles.set(t[si][sj]);\n init.path = \"\";\n init.priority = init.score * 1000 + countMoves2(si, sj, init.usedTiles);\n beam.push_back(init);\n bestScore = init.score;\n \n while (!beam.empty()) {\n if (chrono::duration_cast(chrono::steady_clock::now() - startTime).count() > 1800) {\n for (const auto& state : beam) {\n if (state.score > bestScore) {\n bestScore = state.score;\n bestPath = state.path;\n }\n }\n break;\n }\n \n vector nextBeam;\n nextBeam.reserve(beam.size() * 4);\n \n for (const auto& state : beam) {\n bool canExtend = false;\n for (int d = 0; d < 4; d++) {\n int nx = state.x + dx[d];\n int ny = state.y + dy[d];\n if (nx < 0 || nx >= N || ny < 0 || ny >= N) continue;\n if (state.usedTiles[t[nx][ny]]) continue;\n \n canExtend = true;\n State newState;\n newState.x = nx; newState.y = ny;\n newState.score = state.score + p[nx][ny];\n newState.usedTiles = state.usedTiles;\n newState.usedTiles.set(t[nx][ny]);\n newState.path = state.path + dc[d];\n \n int futureMoves = countMoves2(nx, ny, newState.usedTiles);\n newState.priority = newState.score * 1000 + futureMoves * 5;\n nextBeam.push_back(move(newState));\n }\n if (!canExtend && state.score > bestScore) {\n bestScore = state.score;\n bestPath = state.path;\n }\n }\n \n if (nextBeam.size() > BEAM_WIDTH) {\n nth_element(nextBeam.begin(), nextBeam.begin() + BEAM_WIDTH, nextBeam.end(),\n [](const State& a, const State& b) { return a.priority > b.priority; });\n nextBeam.resize(BEAM_WIDTH);\n }\n \n beam = move(nextBeam);\n }\n \n // Random greedy with remaining time\n while (chrono::duration_cast(chrono::steady_clock::now() - startTime).count() < 1950) {\n int x = si, y = sj;\n int score = p[si][sj];\n string path = \"\";\n bitset<2500> usedTiles;\n usedTiles.set(t[si][sj]);\n \n while (true) {\n vector> moves;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d];\n int ny = y + dy[d];\n if (nx < 0 || nx >= N || ny < 0 || ny >= N) continue;\n if (usedTiles[t[nx][ny]]) continue;\n bitset<2500> tmpUsed = usedTiles;\n tmpUsed.set(t[nx][ny]);\n int fm = countMoves2(nx, ny, tmpUsed);\n moves.push_back({p[nx][ny] * 100 + fm * 5, d, p[nx][ny]});\n }\n if (moves.empty()) break;\n sort(moves.begin(), moves.end(), greater>());\n \n int choice = 0;\n if (moves.size() > 1 && rng() % 100 < 25) {\n choice = rng() % min((int)moves.size(), 2);\n }\n \n int d = get<1>(moves[choice]);\n x += dx[d]; y += dy[d];\n score += p[x][y];\n usedTiles.set(t[x][y]);\n path += dc[d];\n }\n if (score > bestScore) {\n bestScore = score;\n bestPath = path;\n }\n }\n \n cout << bestPath << endl;\n return 0;\n}","ahc003":"#include \nusing namespace std;\n\nconst int N = 30;\ndouble h[N][N-1], v[N-1][N];\nint h_cnt[N][N-1], v_cnt[N-1][N];\ndouble h_row[N], v_col[N];\nint h_row_cnt[N], v_col_cnt[N];\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n fill(&h[0][0], &h[0][0] + N*(N-1), 5000.0);\n fill(&v[0][0], &v[0][0] + (N-1)*N, 5000.0);\n fill(&h_cnt[0][0], &h_cnt[0][0] + N*(N-1), 0);\n fill(&v_cnt[0][0], &v_cnt[0][0] + (N-1)*N, 0);\n fill(h_row, h_row + N, 5000.0);\n fill(v_col, v_col + N, 5000.0);\n fill(h_row_cnt, h_row_cnt + N, 0);\n fill(v_col_cnt, v_col_cnt + N, 0);\n \n auto getH = [&](int i, int j) {\n if (h_cnt[i][j] > 0) return h[i][j];\n if (h_row_cnt[i] > 0) return h_row[i];\n return 5000.0;\n };\n \n auto getV = [&](int i, int j) {\n if (v_cnt[i][j] > 0) return v[i][j];\n if (v_col_cnt[j] > 0) return v_col[j];\n return 5000.0;\n };\n \n for (int q = 0; q < 1000; q++) {\n int si, sj, ti, tj;\n cin >> si >> sj >> ti >> tj;\n \n auto idx = [](int i, int j) { return i * N + j; };\n vector dist(N*N, 1e18);\n vector prv(N*N, -1);\n \n priority_queue, vector>, greater<>> pq;\n dist[idx(si, sj)] = 0;\n pq.push({0, idx(si, sj)});\n \n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > dist[u]) continue;\n int i = u / N, j = u % N;\n \n auto relax = [&](int ni, int nj, double w) {\n int nu = idx(ni, nj);\n if (dist[u] + w < dist[nu]) {\n dist[nu] = dist[u] + w;\n prv[nu] = u;\n pq.push({dist[nu], nu});\n }\n };\n \n if (i > 0) relax(i-1, j, getV(i-1, j));\n if (i < N-1) relax(i+1, j, getV(i, j));\n if (j > 0) relax(i, j-1, getH(i, j-1));\n if (j < N-1) relax(i, j+1, getH(i, j));\n }\n \n string path = \"\";\n vector> edges;\n \n int cur = idx(ti, tj);\n while (prv[cur] != -1) {\n int ci = cur / N, cj = cur % N;\n int pi = prv[cur] / N, pj = prv[cur] % N;\n \n if (ci < pi) { path += 'U'; edges.emplace_back(1, ci, cj); }\n else if (ci > pi) { path += 'D'; edges.emplace_back(1, pi, pj); }\n else if (cj < pj) { path += 'L'; edges.emplace_back(0, ci, cj); }\n else { path += 'R'; edges.emplace_back(0, pi, pj); }\n \n cur = prv[cur];\n }\n \n reverse(path.begin(), path.end());\n cout << path << \"\\n\" << flush;\n \n int feedback;\n cin >> feedback;\n \n double est = 0;\n for (auto& [t, ei, ej] : edges) {\n est += (t == 0) ? getH(ei, ej) : getV(ei, ej);\n }\n \n double ratio = feedback / est;\n \n for (auto& [t, ei, ej] : edges) {\n double implied = (t == 0) ? getH(ei, ej) * ratio : getV(ei, ej) * ratio;\n \n if (t == 0) {\n int cnt = ++h_cnt[ei][ej];\n double alpha = 1.0 / (1.0 + cnt);\n h[ei][ej] = h[ei][ej] * (1 - alpha) + implied * alpha;\n } else {\n int cnt = ++v_cnt[ei][ej];\n double alpha = 1.0 / (1.0 + cnt);\n v[ei][ej] = v[ei][ej] * (1 - alpha) + implied * alpha;\n }\n }\n \n // Update row/column averages\n for (int i = 0; i < N; i++) {\n double sum = 0; int cnt = 0;\n for (int j = 0; j < N-1; j++) {\n if (h_cnt[i][j] > 0) { sum += h[i][j]; cnt++; }\n }\n if (cnt > 0) { h_row[i] = sum / cnt; h_row_cnt[i] = cnt; }\n }\n \n for (int j = 0; j < N; j++) {\n double sum = 0; int cnt = 0;\n for (int i = 0; i < N-1; i++) {\n if (v_cnt[i][j] > 0) { sum += v[i][j]; cnt++; }\n }\n if (cnt > 0) { v_col[j] = sum / cnt; v_col_cnt[j] = cnt; }\n }\n }\n \n return 0;\n}","ahc004":"#include \nusing namespace std;\n\nconst int N = 20;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n, m;\n cin >> n >> m;\n \n vector strs(m);\n for(int i = 0; i < m; i++) cin >> strs[i];\n \n vector order(m);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int a, int b) {\n return strs[a].size() > strs[b].size();\n });\n \n char grid[N][N];\n fill(&grid[0][0], &grid[N][0], '.');\n \n // Greedy placement with max overlap preference\n for(int idx : order) {\n const string& s = strs[idx];\n int bestR = -1, bestC, bestD, bestOv = -1;\n \n for(int r = 0; r < N; r++) {\n for(int c = 0; c < N; c++) {\n for(int d = 0; d < 2; d++) {\n bool can = true;\n int ov = 0;\n for(int p = 0; p < (int)s.size() && can; p++) {\n int ni = d ? (r + p) % N : r;\n int nj = d ? c : (c + p) % N;\n if(grid[ni][nj] != '.' && grid[ni][nj] != s[p]) can = false;\n if(grid[ni][nj] != '.') ov++;\n }\n if(can && ov > bestOv) {\n bestOv = ov;\n bestR = r; bestC = c; bestD = d;\n }\n }\n }\n }\n \n if(bestR >= 0) {\n for(int p = 0; p < (int)s.size(); p++) {\n int ni = bestD ? (bestR + p) % N : bestR;\n int nj = bestD ? bestC : (bestC + p) % N;\n grid[ni][nj] = s[p];\n }\n }\n }\n \n // Fill remaining cells randomly\n mt19937 rng(42);\n for(int i = 0; i < N; i++) {\n for(int j = 0; j < N; j++) {\n if(grid[i][j] == '.') grid[i][j] = 'A' + rng() % 8;\n }\n }\n \n // Count function for SA\n auto countMatched = [&]() {\n int cnt = 0;\n for(const auto& s : strs) {\n bool found = false;\n for(int r = 0; r < N && !found; r++) {\n for(int c = 0; c < N && !found; c++) {\n for(int d = 0; d < 2 && !found; d++) {\n bool ok = true;\n for(int p = 0; p < (int)s.size() && ok; p++) {\n int ni = d ? (r + p) % N : r;\n int nj = d ? c : (c + p) % N;\n if(grid[ni][nj] != s[p]) ok = false;\n }\n if(ok) found = true;\n }\n }\n }\n if(found) cnt++;\n }\n return cnt;\n };\n \n // Simple SA to improve\n char bestGrid[N][N];\n memcpy(bestGrid, grid, sizeof(grid));\n int bestScore = countMatched();\n int curScore = bestScore;\n \n auto start = chrono::high_resolution_clock::now();\n double T = 2.0;\n \n while(true) {\n auto now = chrono::high_resolution_clock::now();\n if(chrono::duration(now - start).count() > 2.7) break;\n \n int i = rng() % N, j = rng() % N;\n char old = grid[i][j];\n char newc = 'A' + rng() % 8;\n if(newc == old) continue;\n \n grid[i][j] = newc;\n int newScore = countMatched();\n \n if(newScore >= curScore || (rng() & 0xFFFF) < 65536.0 * exp((newScore - curScore) / T)) {\n curScore = newScore;\n if(newScore > bestScore) {\n bestScore = newScore;\n memcpy(bestGrid, grid, sizeof(grid));\n }\n } else {\n grid[i][j] = old;\n }\n T *= 0.9999;\n }\n \n for(int i = 0; i < N; i++) {\n cout << string(bestGrid[i], bestGrid[i] + N) << '\\n';\n }\n}","ahc005":"#include \nusing namespace std;\n\nint N, si, sj;\nvector grid;\n\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nconst char dir_char[] = {'U', 'D', 'L', 'R'};\n\ninline bool is_road(int i, int j) {\n return i >= 0 && i < N && j >= 0 && j < N && grid[i][j] != '#';\n}\n\npair>, vector>>> dijkstra(int si, int sj) {\n vector> dist(N, vector(N, INT_MAX));\n vector>> parent(N, vector>(N, {-1,-1}));\n priority_queue, vector>, greater<>> pq;\n dist[si][sj] = 0; pq.push({0, si, sj});\n while (!pq.empty()) {\n auto [d, i, j] = pq.top(); pq.pop();\n if (d > dist[i][j]) continue;\n for (int k = 0; k < 4; k++) {\n int ni = i + dx[k], nj = j + dy[k];\n if (is_road(ni, nj)) {\n int c = grid[ni][nj] - '0';\n if (dist[i][j] + c < dist[ni][nj]) {\n dist[ni][nj] = dist[i][j] + c;\n parent[ni][nj] = {i, j};\n pq.push({dist[ni][nj], ni, nj});\n }\n }\n }\n }\n return {dist, parent};\n}\n\nstring get_path(int i1, int j1, int i2, int j2, vector>>& parent) {\n if (i1 == i2 && j1 == j2) return \"\";\n string path;\n int ci = i2, cj = j2;\n while (ci != i1 || cj != j1) {\n auto [pi, pj] = parent[ci][cj];\n for (int k = 0; k < 4; k++) if (pi + dx[k] == ci && pj + dy[k] == cj) { path += dir_char[k]; break; }\n ci = pi; cj = pj;\n }\n reverse(path.begin(), path.end());\n return path;\n}\n\nint calc_path_time(const string& path) {\n int time = 0, ci = si, cj = sj;\n for (char c : path) {\n if (c == 'U') ci--; else if (c == 'D') ci++; else if (c == 'L') cj--; else cj++;\n time += grid[ci][cj] - '0';\n }\n return time;\n}\n\nstring solve(double alpha) {\n vector> visible(N, vector(N, false));\n int visible_count = 0, total_roads = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (is_road(i, j)) total_roads++;\n \n auto mark_visible = [&](int i, int j) {\n if (!visible[i][j]) { visible[i][j] = true; visible_count++; }\n for (int jj = j - 1; jj >= 0 && is_road(i, jj); jj--) if (!visible[i][jj]) { visible[i][jj] = true; visible_count++; }\n for (int jj = j + 1; jj < N && is_road(i, jj); jj++) if (!visible[i][jj]) { visible[i][jj] = true; visible_count++; }\n for (int ii = i - 1; ii >= 0 && is_road(ii, j); ii--) if (!visible[ii][j]) { visible[ii][j] = true; visible_count++; }\n for (int ii = i + 1; ii < N && is_road(ii, j); ii++) if (!visible[ii][j]) { visible[ii][j] = true; visible_count++; }\n };\n \n auto count_new_visible = [&](int i, int j) {\n int cnt = !visible[i][j];\n for (int jj = j - 1; jj >= 0 && is_road(i, jj); jj--) cnt += !visible[i][jj];\n for (int jj = j + 1; jj < N && is_road(i, jj); jj++) cnt += !visible[i][jj];\n for (int ii = i - 1; ii >= 0 && is_road(ii, j); ii--) cnt += !visible[ii][j];\n for (int ii = i + 1; ii < N && is_road(ii, j); ii++) cnt += !visible[ii][j];\n return cnt;\n };\n \n auto [dist_from_start, parent_from_start] = dijkstra(si, sj);\n int cur_i = si, cur_j = sj;\n string result;\n mark_visible(cur_i, cur_j);\n \n while (visible_count < total_roads) {\n auto [dist, parent] = dijkstra(cur_i, cur_j);\n int best_i = -1, best_j = -1;\n double best_score = -1e18;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (dist[i][j] == INT_MAX || dist[i][j] == 0) continue;\n int nv = count_new_visible(i, j);\n if (nv == 0) continue;\n double cost = dist[i][j] + alpha * dist_from_start[i][j];\n double score = (double)nv / cost;\n if (score > best_score) { best_score = score; best_i = i; best_j = j; }\n }\n }\n \n if (best_i == -1) break;\n \n string path = get_path(cur_i, cur_j, best_i, best_j, parent);\n result += path;\n int ti = cur_i, tj = cur_j;\n for (char c : path) {\n if (c == 'U') ti--; else if (c == 'D') ti++; else if (c == 'L') tj--; else tj++;\n mark_visible(ti, tj);\n }\n cur_i = best_i; cur_j = best_j;\n }\n \n if (cur_i != si || cur_j != sj) {\n auto [dist, parent] = dijkstra(cur_i, cur_j);\n result += get_path(cur_i, cur_j, si, sj, parent);\n }\n return result;\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> si >> sj;\n grid.resize(N);\n for (int i = 0; i < N; i++) cin >> grid[i];\n \n string best_result;\n int best_time = INT_MAX;\n \n for (double alpha : {0.0, 0.03, 0.06, 0.1, 0.15, 0.2, 0.25, 0.3}) {\n string result = solve(alpha);\n int time = calc_path_time(result);\n if (time < best_time) { best_time = time; best_result = result; }\n }\n \n cout << best_result << endl;\n return 0;\n}","future-contest-2022-qual":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K, R;\n cin >> N >> M >> K >> R;\n \n vector> d(N, vector(K));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < K; j++)\n cin >> d[i][j];\n \n vector> deps(N), rdeps(N);\n for (int i = 0; i < R; i++) {\n int u, v;\n cin >> u >> v;\n u--; v--;\n deps[v].push_back(u);\n rdeps[u].push_back(v);\n }\n \n vector taskStatus(N, -1);\n vector memberTask(M, -1), memberStartDay(M, 0);\n \n double initSkill = 40.0 / sqrt(K);\n vector> skillEst(M, vector(K, initSkill));\n vector> skillLo(M, vector(K, 0.0));\n \n auto estimateTime = [&](int task, int member) -> double {\n double w = 0;\n for (int k = 0; k < K; k++)\n w += max(0.0, (double)d[task][k] - skillEst[member][k]);\n return max(1.0, w);\n };\n \n auto avgTime = [&](int task) -> double {\n double sum = 0;\n for (int j = 0; j < M; j++) sum += estimateTime(task, j);\n return sum / M;\n };\n \n // Calculate weighted depth (considering task difficulty)\n vector wdepth(N);\n for (int i = N - 1; i >= 0; i--) {\n wdepth[i] = avgTime(i);\n double maxChild = 0;\n for (int v : rdeps[i])\n maxChild = max(maxChild, wdepth[v]);\n wdepth[i] += maxChild;\n }\n \n // Downstream task count\n vector downstream(N, 0);\n for (int i = N - 1; i >= 0; i--) {\n downstream[i] = (int)rdeps[i].size();\n for (int v : rdeps[i])\n downstream[i] += downstream[v];\n }\n \n for (int day = 1; ; day++) {\n // Recalculate weighted depth periodically\n if (day % 50 == 1) {\n for (int i = N - 1; i >= 0; i--) {\n if (taskStatus[i] == 1) { wdepth[i] = 0; continue; }\n wdepth[i] = avgTime(i);\n double maxChild = 0;\n for (int v : rdeps[i])\n maxChild = max(maxChild, wdepth[v]);\n wdepth[i] += maxChild;\n }\n }\n \n vector availTasks;\n for (int i = 0; i < N; i++) {\n if (taskStatus[i] != -1) continue;\n bool ok = true;\n for (int dep : deps[i])\n if (taskStatus[dep] != 1) { ok = false; break; }\n if (ok) availTasks.push_back(i);\n }\n \n vector freeMembers;\n for (int j = 0; j < M; j++)\n if (memberTask[j] == -1) freeMembers.push_back(j);\n \n // Create candidate pairs and score them\n vector> candidates; // (score, task, member, time)\n for (int task : availTasks) {\n for (int member : freeMembers) {\n double t = estimateTime(task, member);\n // Higher wdepth = more critical, want to minimize time for critical tasks\n double score = wdepth[task] / max(1.0, t);\n candidates.push_back({-score, task, member, t});\n }\n }\n sort(candidates.begin(), candidates.end());\n \n vector> assignments;\n vector usedMember(M, false), usedTask(N, false);\n \n for (auto& [score, task, member, t] : candidates) {\n if (usedMember[member] || usedTask[task]) continue;\n usedMember[member] = true;\n usedTask[task] = true;\n assignments.push_back({member + 1, task + 1});\n taskStatus[task] = 0;\n memberTask[member] = task;\n memberStartDay[member] = day;\n }\n \n cout << assignments.size();\n for (auto& [a, b] : assignments) cout << \" \" << a << \" \" << b;\n cout << \"\\n\";\n cout.flush();\n \n int n; cin >> n;\n if (n == -1) break;\n \n for (int i = 0; i < n; i++) {\n int f; cin >> f; f--;\n int task = memberTask[f];\n int timeTaken = day - memberStartDay[f] + 1;\n taskStatus[task] = 1;\n memberTask[f] = -1;\n \n if (timeTaken == 1) {\n for (int k = 0; k < K; k++) {\n skillLo[f][k] = max(skillLo[f][k], (double)d[task][k]);\n skillEst[f][k] = max(skillEst[f][k], (double)d[task][k]);\n }\n } else {\n double wEst = (double)timeTaken;\n double currW = 0;\n for (int k = 0; k < K; k++)\n currW += max(0.0, (double)d[task][k] - skillEst[f][k]);\n \n if (currW > 0.5) {\n double factor = wEst / currW;\n factor = 0.6 * factor + 0.4;\n factor = max(0.5, min(1.5, factor));\n \n for (int k = 0; k < K; k++) {\n double gap = d[task][k] - skillEst[f][k];\n if (gap > 0) {\n double newSkill = d[task][k] - gap * factor;\n skillEst[f][k] = max(skillLo[f][k], newSkill);\n }\n }\n } else if (wEst > 4) {\n for (int k = 0; k < K; k++) {\n if (d[task][k] > skillLo[f][k] + 0.5) {\n skillEst[f][k] = max(skillLo[f][k], \n skillEst[f][k] - (wEst - 3) * d[task][k] / (avgTime(task) * K + 1));\n }\n }\n }\n }\n }\n }\n return 0;\n}","ahc006":"#include \nusing namespace std;\n\nconst int N = 1000, M = 50, CX = 400, CY = 400;\nint ordA[N], ordB[N], ordC[N], ordD[N];\nmt19937 rng(chrono::steady_clock::now().time_since_epoch().count());\n\ninline int dist(int x1, int y1, int x2, int y2) {\n return abs(x1 - x2) + abs(y1 - y2);\n}\n\nint buildRoute(const vector& sel, vector>& ev) {\n ev.clear();\n ev.reserve(2 * M);\n bool picked[N] = {}, done[N] = {};\n int cx = CX, cy = CY, cost = 0;\n \n for (int i = 0; i < 2*M; i++) {\n int best = -1, bd = 1e9;\n bool isDel = false;\n for (int j : sel) {\n if (!picked[j]) {\n int d = dist(cx, cy, ordA[j], ordB[j]);\n if (d < bd) { bd = d; best = j; isDel = false; }\n } else if (!done[j]) {\n int d = dist(cx, cy, ordC[j], ordD[j]);\n if (d < bd) { bd = d; best = j; isDel = true; }\n }\n }\n cost += bd;\n if (isDel) { cx = ordC[best]; cy = ordD[best]; done[best] = true; }\n else { cx = ordA[best]; cy = ordB[best]; picked[best] = true; }\n ev.push_back({best, isDel});\n }\n return cost + dist(cx, cy, CX, CY);\n}\n\nint calcCost(const vector>& ev) {\n int cx = CX, cy = CY, cost = 0;\n for (auto& [idx, isDel] : ev) {\n int nx = isDel ? ordC[idx] : ordA[idx];\n int ny = isDel ? ordD[idx] : ordB[idx];\n cost += dist(cx, cy, nx, ny);\n cx = nx; cy = ny;\n }\n return cost + dist(cx, cy, CX, CY);\n}\n\nbool validSwap(vector>& ev, int i, int j) {\n swap(ev[i], ev[j]);\n map pickPos;\n for (int k = 0; k < (int)ev.size(); k++) {\n if (!ev[k].second) pickPos[ev[k].first] = k;\n else if (pickPos.find(ev[k].first) == pickPos.end() || pickPos[ev[k].first] > k) {\n swap(ev[i], ev[j]);\n return false;\n }\n }\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n auto st = chrono::steady_clock::now();\n for (int i = 0; i < N; i++) cin >> ordA[i] >> ordB[i] >> ordC[i] >> ordD[i];\n \n auto elapsed = [&]() {\n return chrono::duration(chrono::steady_clock::now() - st).count();\n };\n \n vector> byDist(N);\n for (int i = 0; i < N; i++) {\n byDist[i] = {dist(CX, CY, ordA[i], ordB[i]) + dist(CX, CY, ordC[i], ordD[i]), i};\n }\n sort(byDist.begin(), byDist.end());\n \n vector sel(M), unsel(N-M);\n for (int i = 0; i < M; i++) sel[i] = byDist[i].second;\n for (int i = 0; i < N-M; i++) unsel[i] = byDist[M+i].second;\n \n vector> ev, bestEv;\n int cost = buildRoute(sel, ev);\n int bestCost = cost;\n vector bestSel = sel;\n bestEv = ev;\n \n double temp = 3000.0;\n \n while (elapsed() < 1.8) {\n int si = rng() % M;\n int ui = rng() % (N-M);\n swap(sel[si], unsel[ui]);\n \n int nc = buildRoute(sel, ev);\n int delta = nc - cost;\n \n if (delta < 0 || (rng() % 10000) < 10000 * exp(-delta / temp)) {\n cost = nc;\n if (nc < bestCost) {\n bestCost = nc;\n bestSel = sel;\n bestEv = ev;\n }\n } else {\n swap(sel[si], unsel[ui]);\n }\n temp *= 0.99995;\n }\n \n // Light 2-opt on best route at the end\n bool improved = true;\n while (improved && elapsed() < 1.95) {\n improved = false;\n for (int i = 0; i < 2*M - 1 && !improved; i++) {\n for (int j = i + 1; j < 2*M && !improved; j++) {\n if (bestEv[i].first == bestEv[j].first) continue;\n int oldCost = bestCost;\n if (validSwap(bestEv, i, j)) {\n int nc = calcCost(bestEv);\n if (nc < bestCost) {\n bestCost = nc;\n improved = true;\n } else {\n swap(bestEv[i], bestEv[j]);\n }\n }\n }\n }\n }\n \n cout << M;\n for (int x : bestSel) cout << \" \" << (x+1);\n cout << \"\\n\" << (2*M+2) << \" \" << CX << \" \" << CY;\n for (auto& [idx, isDel] : bestEv) {\n if (isDel) cout << \" \" << ordC[idx] << \" \" << ordD[idx];\n else cout << \" \" << ordA[idx] << \" \" << ordB[idx];\n }\n cout << \" \" << CX << \" \" << CY << \"\\n\";\n \n return 0;\n}","ahc007":"#include \nusing namespace std;\n\nclass UnionFind {\n vector parent, rank_;\npublic:\n UnionFind(int n) : parent(n), rank_(n, 0) {\n iota(parent.begin(), parent.end(), 0);\n }\n int find(int x) {\n if (parent[x] != x) parent[x] = find(parent[x]);\n return parent[x];\n }\n bool unite(int x, int y) {\n int px = find(x), py = find(y);\n if (px == py) return false;\n if (rank_[px] < rank_[py]) swap(px, py);\n parent[py] = px;\n if (rank_[px] == rank_[py]) rank_[px]++;\n return true;\n }\n};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n const int N = 400, M = 1995;\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) {\n cin >> x[i] >> y[i];\n }\n \n vector u(M), v(M), d(M);\n for (int i = 0; i < M; i++) {\n cin >> u[i] >> v[i];\n double dx = x[u[i]] - x[v[i]];\n double dy = y[u[i]] - y[v[i]];\n d[i] = (int)round(sqrt(dx * dx + dy * dy));\n }\n \n UnionFind uf(N);\n int components = N;\n \n for (int i = 0; i < M; i++) {\n int l;\n cin >> l;\n \n int pu = uf.find(u[i]);\n int pv = uf.find(v[i]);\n \n bool already_connected = (pu == pv);\n double ratio = (double)l / d[i];\n \n bool adopt = false;\n \n if (!already_connected) {\n int useful_remaining = 0;\n int same_pair_remaining = 0;\n \n for (int j = i + 1; j < M; j++) {\n int uj = uf.find(u[j]);\n int vj = uf.find(v[j]);\n if (uj != vj) {\n useful_remaining++;\n if ((uj == pu && vj == pv) || (uj == pv && vj == pu)) {\n same_pair_remaining++;\n }\n }\n }\n \n int needed = components - 1;\n \n // Must accept if no alternatives\n if (same_pair_remaining == 0) {\n adopt = true;\n }\n // Safety: running low on useful edges\n else if (useful_remaining < needed * 2) {\n adopt = true;\n }\n else {\n // Expected minimum of (k+1) uniform [1,3] samples = 1 + 2/(k+2)\n double k = same_pair_remaining;\n double expected_min = 1.0 + 2.0 / (k + 2.0);\n \n // Be more accepting - larger buffer helps avoid missing good opportunities\n double threshold = expected_min + 0.25;\n \n if (ratio <= threshold) {\n adopt = true;\n }\n }\n }\n \n if (adopt) {\n uf.unite(u[i], v[i]);\n components--;\n }\n \n cout << (adopt ? 1 : 0) << \"\\n\" << flush;\n }\n \n return 0;\n}","ahc008":"#include \nusing namespace std;\n\nint N, M;\nvector> pets;\nvector> humans;\nbool blocked[32][32];\n\nbool pet_at(int x, int y) {\n for (auto& p : pets) if (p[0] == x && p[1] == y) return true;\n return false;\n}\n\nbool pet_adjacent(int x, int y) {\n int dx[] = {0, -1, 1, 0, 0}, dy[] = {0, 0, 0, -1, 1};\n for (int d = 0; d < 5; d++) if (pet_at(x+dx[d], y+dy[d])) return true;\n return false;\n}\n\nbool can_place(int x, int y) {\n if (x < 1 || x > 30 || y < 1 || y > 30 || blocked[x][y]) return false;\n for (auto& h : humans) if (h[0] == x && h[1] == y) return false;\n return !pet_adjacent(x, y);\n}\n\nbool passable(int x, int y) {\n return x >= 1 && x <= 30 && y >= 1 && y <= 30 && !blocked[x][y];\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N; pets.resize(N);\n for (int i = 0; i < N; i++) cin >> pets[i][0] >> pets[i][1] >> pets[i][2];\n cin >> M; humans.resize(M);\n for (int i = 0; i < M; i++) cin >> humans[i][0] >> humans[i][1];\n \n set> target;\n for (int i = 1; i <= 30; i++) {\n for (int c : {7, 14, 21, 28}) {\n target.insert({i, c});\n target.insert({c, i});\n }\n }\n \n int dx[] = {-1, 1, 0, 0}, dy[] = {0, 0, -1, 1};\n char wc[] = {'u', 'd', 'l', 'r'}, mc[] = {'U', 'D', 'L', 'R'};\n \n for (int turn = 0; turn < 300; turn++) {\n string action(M, '.');\n \n for (int i = 0; i < M; i++) {\n int hx = humans[i][0], hy = humans[i][1];\n int best = -1, bestd = -1;\n \n for (int d = 0; d < 4; d++) {\n int nx = hx + dx[d], ny = hy + dy[d];\n if (can_place(nx, ny)) {\n int sc = target.count({nx, ny}) ? 100 : 1;\n if (sc > best) { best = sc; bestd = d; }\n }\n }\n \n if (bestd >= 0) {\n action[i] = wc[bestd];\n } else {\n int minD = INT_MAX, moveD = -1;\n for (auto& [tx, ty] : target) {\n if (blocked[tx][ty]) continue;\n int dist = abs(hx-tx) + abs(hy-ty);\n if (dist > 0 && dist < minD) minD = dist;\n }\n for (int d = 0; d < 4; d++) {\n int nx = hx + dx[d], ny = hy + dy[d];\n if (!passable(nx, ny) || pet_at(nx, ny)) continue;\n for (auto& [tx, ty] : target) {\n if (blocked[tx][ty]) continue;\n if (abs(nx-tx) + abs(ny-ty) < minD) {\n minD = abs(nx-tx) + abs(ny-ty);\n moveD = d;\n }\n }\n }\n if (moveD >= 0) action[i] = mc[moveD];\n }\n }\n \n cout << action << \"\\n\" << flush;\n \n for (int i = 0; i < M; i++) {\n char a = action[i];\n for (int d = 0; d < 4; d++) {\n if (a == wc[d]) blocked[humans[i][0]+dx[d]][humans[i][1]+dy[d]] = true;\n if (a == mc[d]) { humans[i][0] += dx[d]; humans[i][1] += dy[d]; }\n }\n }\n \n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (char c : s) {\n if (c == 'U') pets[i][0]--;\n else if (c == 'D') pets[i][0]++;\n else if (c == 'L') pets[i][1]--;\n else if (c == 'R') pets[i][1]++;\n }\n }\n }\n return 0;\n}","ahc009":"#include \nusing namespace std;\n\nint N = 20;\nint si, sj, ti, tj;\ndouble p;\nbool hwall[20][19];\nbool vwall[19][20];\n\nbool canMove(int i, int j, char dir) {\n if (dir == 'U') return i > 0 && !vwall[i-1][j];\n if (dir == 'D') return i < 19 && !vwall[i][j];\n if (dir == 'L') return j > 0 && !hwall[i][j-1];\n if (dir == 'R') return j < 19 && !hwall[i][j];\n return false;\n}\n\npair doMove(int i, int j, char dir) {\n if (!canMove(i, j, dir)) return {i, j};\n if (dir == 'U') return {i-1, j};\n if (dir == 'D') return {i+1, j};\n if (dir == 'L') return {i, j-1};\n if (dir == 'R') return {i, j+1};\n return {i, j};\n}\n\ndouble evaluate(const string& s) {\n if (s.empty() || s.size() > 200) return -1;\n vector> prob(N, vector(N, 0));\n prob[si][sj] = 1.0;\n double expectedScore = 0;\n for (int t = 1; t <= (int)s.size(); t++) {\n char dir = s[t-1];\n vector> newProb(N, vector(N, 0));\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (prob[i][j] < 1e-18) continue;\n auto [ni, nj] = doMove(i, j, dir);\n if (ni == ti && nj == tj) {\n expectedScore += (1-p) * prob[i][j] * (401 - t);\n } else {\n newProb[ni][nj] += (1-p) * prob[i][j];\n }\n newProb[i][j] += p * prob[i][j];\n }\n }\n prob = newProb;\n }\n return expectedScore;\n}\n\nstring bfsWithOrder(vector& order) {\n vector> dist(N, vector(N, -1));\n vector>> parent(N, vector>(N, {-1,-1}));\n vector> fromDir(N, vector(N, ' '));\n queue> q;\n q.push({si, sj});\n dist[si][sj] = 0;\n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (char d : order) {\n auto [ni, nj] = doMove(i, j, d);\n if (ni == i && nj == j) continue;\n if (dist[ni][nj] == -1) {\n dist[ni][nj] = dist[i][j] + 1;\n parent[ni][nj] = {i, j};\n fromDir[ni][nj] = d;\n q.push({ni, nj});\n }\n }\n }\n string path;\n int ci = ti, cj = tj;\n while (ci != si || cj != sj) {\n path += fromDir[ci][cj];\n auto [pi, pj] = parent[ci][cj];\n ci = pi; cj = pj;\n }\n reverse(path.begin(), path.end());\n return path;\n}\n\nmt19937 rng(12345);\nstring best;\ndouble bestScore = -1;\nconst char dirs[] = {'U', 'D', 'L', 'R'};\n\nvoid updateBest(const string& s) {\n if (s.size() > 200 || s.empty()) return;\n double score = evaluate(s);\n if (score > bestScore) {\n bestScore = score;\n best = s;\n }\n}\n\nchrono::steady_clock::time_point startTime;\n\nbool timeUp(int ms = 1900) {\n return chrono::duration_cast(chrono::steady_clock::now() - startTime).count() > ms;\n}\n\nvoid localSearch() {\n while (!timeUp()) {\n bool improved = false;\n \n // Try removing each character\n for (size_t i = 0; i < best.size() && !improved && !timeUp(); i++) {\n string trial = best.substr(0, i) + best.substr(i + 1);\n if (!trial.empty()) {\n double score = evaluate(trial);\n if (score > bestScore) { bestScore = score; best = trial; improved = true; }\n }\n }\n \n // Try changing each character\n for (size_t i = 0; i < best.size() && !improved && !timeUp(); i++) {\n for (char d : dirs) {\n if (d == best[i]) continue;\n string trial = best;\n trial[i] = d;\n double score = evaluate(trial);\n if (score > bestScore) { bestScore = score; best = trial; improved = true; break; }\n }\n }\n \n // Try inserting characters\n if (best.size() < 200) {\n for (size_t i = 0; i <= best.size() && !improved && !timeUp(); i++) {\n for (char d : dirs) {\n string trial = best.substr(0, i) + d + best.substr(i);\n if (trial.size() <= 200) {\n double score = evaluate(trial);\n if (score > bestScore) { bestScore = score; best = trial; improved = true; break; }\n }\n }\n }\n }\n \n // Try duplicating characters\n if (best.size() < 200) {\n for (size_t i = 0; i < best.size() && !improved && !timeUp(); i++) {\n string trial = best.substr(0, i+1) + best[i] + best.substr(i+1);\n if (trial.size() <= 200) {\n double score = evaluate(trial);\n if (score > bestScore) { bestScore = score; best = trial; improved = true; }\n }\n }\n }\n \n if (!improved) break;\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n startTime = chrono::steady_clock::now();\n \n cin >> si >> sj >> ti >> tj >> p;\n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < 19; j++) hwall[i][j] = (s[j] == '1');\n }\n for (int i = 0; i < 19; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) vwall[i][j] = (s[j] == '1');\n }\n \n vector order = {'U', 'D', 'L', 'R'};\n set pathSet;\n \n for (int iter = 0; iter < 200 && !timeUp(500); iter++) {\n shuffle(order.begin(), order.end(), rng);\n pathSet.insert(bfsWithOrder(order));\n }\n vector paths(pathSet.begin(), pathSet.end());\n \n for (const string& path : paths) {\n if (timeUp(1200)) break;\n int pathLen = path.size();\n \n // Strategy 1: Uniform move repetition\n for (int rep = 1; rep * pathLen <= 200; rep++) {\n string result;\n for (char c : path) for (int i = 0; i < rep; i++) result += c;\n updateBest(result);\n }\n \n // Strategy 2: Path multiplication\n for (int rep = 1; rep * pathLen <= 200; rep++) {\n string result;\n for (int i = 0; i < rep; i++) result += path;\n updateBest(result);\n }\n \n // Strategy 3: Wall-aware repetition\n for (int bonus = 1; bonus <= 8; bonus++) {\n for (int baseR = 1; baseR <= 12 && baseR * pathLen <= 200; baseR++) {\n string result;\n int ci = si, cj = sj;\n for (char c : path) {\n auto [ni, nj] = doMove(ci, cj, c);\n bool safeAfter = !canMove(ni, nj, c);\n int reps = safeAfter ? baseR + bonus : baseR;\n for (int i = 0; i < reps && result.size() < 200; i++) result += c;\n ci = ni; cj = nj;\n }\n updateBest(result);\n }\n }\n \n // Strategy 4: Combined repetition\n for (int pathRep = 1; pathRep <= 10; pathRep++) {\n for (int moveRep = 1; moveRep * pathLen * pathRep <= 200 && moveRep <= 10; moveRep++) {\n string result;\n for (int pr = 0; pr < pathRep; pr++)\n for (char c : path) for (int mr = 0; mr < moveRep; mr++) result += c;\n updateBest(result);\n }\n }\n \n // Strategy 5: Progressive repetition (increasing)\n for (int startRep = 1; startRep <= 5; startRep++) {\n for (int endRep = startRep; endRep <= 12; endRep++) {\n string result;\n for (int i = 0; i < pathLen && result.size() < 200; i++) {\n int rep = startRep + (endRep - startRep) * i / max(1, pathLen - 1);\n for (int j = 0; j < rep && result.size() < 200; j++) result += path[i];\n }\n updateBest(result);\n }\n }\n \n // Strategy 6: Progressive repetition (decreasing)\n for (int startRep = 2; startRep <= 12; startRep++) {\n for (int endRep = 1; endRep < startRep; endRep++) {\n string result;\n for (int i = 0; i < pathLen && result.size() < 200; i++) {\n int rep = startRep - (startRep - endRep) * i / max(1, pathLen - 1);\n for (int j = 0; j < rep && result.size() < 200; j++) result += path[i];\n }\n updateBest(result);\n }\n }\n \n // Strategy 7: Path mult with extra repetition at end\n for (int pathRep = 2; pathRep * pathLen <= 200; pathRep++) {\n for (int extra = 1; extra <= 5; extra++) {\n string result;\n for (int i = 0; i < pathRep - 1; i++) result += path;\n for (char c : path) for (int j = 0; j < extra && result.size() < 200; j++) result += c;\n updateBest(result);\n }\n }\n }\n \n localSearch();\n \n cout << best << endl;\n return 0;\n}","ahc010":"#include \nusing namespace std;\n\nconst int N = 30;\nint tiles[N][N];\nint rotation[N][N];\n\nconst int di[] = {0, -1, 0, 1};\nconst int dj[] = {-1, 0, 1, 0};\n\nconst int to_arr[8][4] = {\n {1, 0, -1, -1}, {3, -1, -1, 0}, {-1, -1, 3, 2}, {-1, 2, 1, -1},\n {1, 0, 3, 2}, {3, 2, 1, 0}, {2, -1, 0, -1}, {-1, 3, -1, 1},\n};\n\ninline int getState(int i, int j) {\n int t = tiles[i][j], r = rotation[i][j];\n if (t < 4) return (t + r) % 4;\n if (t < 6) return 4 + (t - 4 + r) % 2;\n return 6 + (t - 6 + r) % 2;\n}\n\nint traceLoop(int si, int sj, int sd) {\n int i = si, j = sj, d = sd, length = 0;\n do {\n int state = getState(i, j);\n int d2 = to_arr[state][d];\n if (d2 == -1) return 0;\n length++;\n if (length > 4 * N * N) return 0;\n i += di[d2]; j += dj[d2];\n if ((unsigned)i >= N || (unsigned)j >= N) return 0;\n d = (d2 + 2) % 4;\n } while (i != si || j != sj || d != sd);\n return length;\n}\n\npair computeTopTwoLoops() {\n static bool visited[N][N][4];\n memset(visited, 0, sizeof(visited));\n int top1 = 0, top2 = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n int state = getState(i, j);\n for (int d = 0; d < 4; d++) {\n if (to_arr[state][d] == -1 || visited[i][j][d]) continue;\n int len = traceLoop(i, j, d);\n if (len > 0) {\n if (len > top1) { top2 = top1; top1 = len; }\n else if (len > top2) { top2 = len; }\n int ci = i, cj = j, cd = d;\n do {\n visited[ci][cj][cd] = true;\n int st = getState(ci, cj);\n int d2 = to_arr[st][cd];\n ci += di[d2]; cj += dj[d2];\n cd = (d2 + 2) % 4;\n } while (ci != i || cj != j || cd != d);\n }\n }\n }\n }\n return {top1, top2};\n}\n\nint best_rotation[N][N];\nlong long best_score;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) {\n tiles[i][j] = s[j] - '0';\n rotation[i][j] = 0;\n }\n }\n \n mt19937 rng(42);\n auto start_time = chrono::steady_clock::now();\n \n auto [l1, l2] = computeTopTwoLoops();\n best_score = (long long)l1 * l2;\n memcpy(best_rotation, rotation, sizeof(rotation));\n long long current_score = best_score;\n \n const double TIME_LIMIT = 1.9;\n \n while (true) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start_time).count();\n if (elapsed > TIME_LIMIT) break;\n \n double T = 1000.0 * pow(0.0001, elapsed / TIME_LIMIT);\n \n int i = rng() % N, j = rng() % N;\n int old_rot = rotation[i][j];\n int new_rot = (old_rot + 1 + rng() % 3) % 4;\n \n rotation[i][j] = new_rot;\n auto [nl1, nl2] = computeTopTwoLoops();\n long long new_score = (long long)nl1 * nl2;\n \n double delta = (double)(new_score - current_score);\n if (delta >= 0 || uniform_real_distribution(0, 1)(rng) < exp(delta / T)) {\n current_score = new_score;\n if (new_score > best_score) {\n best_score = new_score;\n memcpy(best_rotation, rotation, sizeof(rotation));\n }\n } else {\n rotation[i][j] = old_rot;\n }\n }\n \n string result;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n result += ('0' + best_rotation[i][j]);\n cout << result << endl;\n \n return 0;\n}","ahc011":"#include \nusing namespace std;\n\nint N, T;\nint dr[] = {-1, 1, 0, 0};\nint dc[] = {0, 0, -1, 1};\nchar dc_char[] = {'U', 'D', 'L', 'R'};\n\nint hexChar(char c) {\n return (c >= '0' && c <= '9') ? c - '0' : c - 'a' + 10;\n}\n\nint calcScore(const vector>& board) {\n vector> adj(N * N);\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (board[i][j] == 0) continue;\n if (i + 1 < N && board[i+1][j] != 0 && (board[i][j] & 8) && (board[i+1][j] & 2)) {\n adj[i*N+j].push_back((i+1)*N+j);\n adj[(i+1)*N+j].push_back(i*N+j);\n }\n if (j + 1 < N && board[i][j+1] != 0 && (board[i][j] & 4) && (board[i][j+1] & 1)) {\n adj[i*N+j].push_back(i*N+j+1);\n adj[i*N+j+1].push_back(i*N+j);\n }\n }\n }\n vector vis(N * N, false);\n int maxTree = 0;\n for (int s = 0; s < N * N; s++) {\n if (vis[s] || board[s/N][s%N] == 0) continue;\n int cnt = 0, edges = 0;\n queue q; q.push(s); vis[s] = true;\n while (!q.empty()) {\n int u = q.front(); q.pop(); cnt++;\n edges += adj[u].size();\n for (int v : adj[u]) if (!vis[v]) { vis[v] = true; q.push(v); }\n }\n if (edges / 2 == cnt - 1) maxTree = max(maxTree, cnt);\n }\n return maxTree;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> T;\n vector> board(N, vector(N));\n int er, ec;\n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) {\n board[i][j] = hexChar(s[j]);\n if (board[i][j] == 0) { er = i; ec = j; }\n }\n }\n \n string best, cur;\n int bestScore = calcScore(board), curScore = bestScore;\n auto bestBoard = board; int bestEr = er, bestEc = ec;\n \n mt19937 rng(42);\n auto start = chrono::steady_clock::now();\n \n while (chrono::duration_cast(chrono::steady_clock::now() - start).count() < 2800) {\n if (cur.size() >= (size_t)T || bestScore >= N * N - 1) break;\n \n vector valid;\n for (int d = 0; d < 4; d++) {\n int nr = er + dr[d], nc = ec + dc[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N) valid.push_back(d);\n }\n int d = valid[rng() % valid.size()];\n int nr = er + dr[d], nc = ec + dc[d];\n \n swap(board[er][ec], board[nr][nc]);\n cur += dc_char[d];\n int newScore = calcScore(board);\n \n double temp = 1.0 - (double)cur.size() / T;\n bool accept = newScore > curScore || (rng() % 1000 < 100 * temp);\n \n if (accept) {\n er = nr; ec = nc; curScore = newScore;\n if (curScore > bestScore || (curScore == bestScore && cur.size() < best.size())) {\n bestScore = curScore; best = cur;\n bestBoard = board; bestEr = er; bestEc = ec;\n }\n } else {\n cur.pop_back();\n swap(board[er][ec], board[nr][nc]);\n }\n \n if (cur.size() > T / 2 && rng() % 100 < 5) {\n board = bestBoard; er = bestEr; ec = bestEc;\n cur = best; curScore = bestScore;\n }\n }\n \n cout << best << endl;\n return 0;\n}","ahc012":"#include \nusing namespace std;\n\ntypedef long long ll;\n\nint N, K;\nvector a(10);\nvector> berries;\nvector> cuts;\nvector> sides;\n\ninline int side(ll x1, ll y1, ll x2, ll y2, ll px, ll py) {\n __int128 cross = (__int128)(x2 - x1) * (py - y1) - (__int128)(y2 - y1) * (px - x1);\n if (cross > 0) return 1;\n if (cross < 0) return -1;\n return 0;\n}\n\nint calcScore() {\n int numCuts = cuts.size();\n unordered_map pieceCount;\n \n for (int j = 0; j < N; j++) {\n bool onLine = false;\n uint64_t h = 0;\n for (int i = 0; i < numCuts; i++) {\n if (sides[i][j] == 0) { onLine = true; break; }\n h = h * 3ULL + (uint64_t)(sides[i][j] + 1);\n }\n if (!onLine) pieceCount[h]++;\n }\n \n vector b(11, 0);\n for (auto& [sig, cnt] : pieceCount) {\n if (cnt >= 1 && cnt <= 10) b[cnt]++;\n }\n \n int total = 0;\n for (int d = 1; d <= 10; d++) total += min(a[d-1], b[d]);\n return total;\n}\n\nvoid updateSides(int idx) {\n while ((int)sides.size() <= idx) sides.push_back(vector(N));\n for (int j = 0; j < N; j++) {\n sides[idx][j] = side(cuts[idx][0], cuts[idx][1], cuts[idx][2], cuts[idx][3],\n berries[j].first, berries[j].second);\n }\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> K;\n for (int i = 0; i < 10; i++) cin >> a[i];\n \n berries.resize(N);\n for (int i = 0; i < N; i++) cin >> berries[i].first >> berries[i].second;\n \n mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());\n \n auto randLine = [&]() -> array {\n ll px = (ll)(rng() % 20001) - 10000;\n ll py = (ll)(rng() % 20001) - 10000;\n ll qx = (ll)(rng() % 20001) - 10000;\n ll qy = (ll)(rng() % 20001) - 10000;\n while (px == qx && py == qy) { qx = (ll)(rng() % 20001) - 10000; qy = (ll)(rng() % 20001) - 10000; }\n return {px, py, qx, qy};\n };\n \n auto perpBisector = [&](int i, int j) -> array {\n if (i == j) return randLine();\n ll dx = berries[j].first - berries[i].first;\n ll dy = berries[j].second - berries[i].second;\n ll mx = berries[i].first + berries[j].first;\n ll my = berries[i].second + berries[j].second;\n return {mx - dy * 1000, my + dx * 1000, mx + dy * 1000, my - dx * 1000};\n };\n \n auto radialLine = [&](double angle) -> array {\n ll px = (ll)(cos(angle) * 15000);\n ll py = (ll)(sin(angle) * 15000);\n if (px == 0 && py == 0) px = 1;\n return {px, py, -px, -py};\n };\n \n int bestScore = 0;\n vector> bestCuts;\n \n auto start = chrono::steady_clock::now();\n \n for (int restart = 0; ; restart++) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration_cast(now - start).count();\n if (elapsed > 2850) break;\n \n cuts.clear();\n sides.clear();\n int numCuts = 25 + rng() % 35;\n \n for (int i = 0; i < numCuts; i++) {\n int strategy = rng() % 4;\n if (strategy == 0) cuts.push_back(randLine());\n else if (strategy == 1) cuts.push_back(perpBisector(rng() % N, rng() % N));\n else if (strategy == 2) cuts.push_back(radialLine((double)(rng() % 10000) / 10000.0 * M_PI * 2));\n else {\n int b1 = rng() % N, b2 = rng() % N;\n if (b1 != b2) {\n cuts.push_back({berries[b1].first, berries[b1].second, berries[b2].first, berries[b2].second});\n } else cuts.push_back(randLine());\n }\n updateSides(i);\n }\n \n int curScore = calcScore();\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n \n for (int iter = 0; ; iter++) {\n now = chrono::steady_clock::now();\n elapsed = chrono::duration_cast(now - start).count();\n if (elapsed > 2850) break;\n \n double progress = elapsed / 2850.0;\n double temp = 3.0 * (1.0 - progress) + 0.1;\n int moveType = rng() % 100;\n \n if (moveType < 75 && !cuts.empty()) {\n int idx = rng() % cuts.size();\n auto oldCut = cuts[idx];\n auto oldSide = sides[idx];\n \n int strat = rng() % 4;\n if (strat == 0) cuts[idx] = randLine();\n else if (strat == 1) cuts[idx] = perpBisector(rng() % N, rng() % N);\n else if (strat == 2) cuts[idx] = radialLine((double)(rng() % 10000) / 10000.0 * M_PI * 2);\n else {\n int b1 = rng() % N, b2 = rng() % N;\n if (b1 != b2) cuts[idx] = {berries[b1].first, berries[b1].second, berries[b2].first, berries[b2].second};\n else cuts[idx] = randLine();\n }\n updateSides(idx);\n \n int newScore = calcScore();\n double acceptProb = exp((newScore - curScore) / temp);\n if (newScore > curScore || (double)(rng() % 1000000) / 1000000.0 < acceptProb) {\n curScore = newScore;\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n } else {\n cuts[idx] = oldCut;\n sides[idx] = oldSide;\n }\n } else if (moveType < 90 && cuts.size() < (size_t)min(K, 80)) {\n int strat = rng() % 4;\n if (strat == 0) cuts.push_back(randLine());\n else if (strat == 1) cuts.push_back(perpBisector(rng() % N, rng() % N));\n else if (strat == 2) cuts.push_back(radialLine((double)(rng() % 10000) / 10000.0 * M_PI * 2));\n else {\n int b1 = rng() % N, b2 = rng() % N;\n if (b1 != b2) cuts.push_back({berries[b1].first, berries[b1].second, berries[b2].first, berries[b2].second});\n else cuts.push_back(randLine());\n }\n updateSides(cuts.size() - 1);\n \n int newScore = calcScore();\n if (newScore >= curScore) {\n curScore = newScore;\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n } else {\n cuts.pop_back();\n sides.pop_back();\n }\n } else if (cuts.size() > 10) {\n int idx = rng() % cuts.size();\n auto oldCut = cuts[idx];\n auto oldSide = sides[idx];\n cuts.erase(cuts.begin() + idx);\n sides.erase(sides.begin() + idx);\n \n int newScore = calcScore();\n if (newScore >= curScore) {\n curScore = newScore;\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n } else {\n cuts.insert(cuts.begin() + idx, oldCut);\n sides.insert(sides.begin() + idx, oldSide);\n }\n }\n }\n }\n \n cout << bestCuts.size() << \"\\n\";\n for (auto& c : bestCuts) cout << c[0] << \" \" << c[1] << \" \" << c[2] << \" \" << c[3] << \"\\n\";\n \n return 0;\n}","ahc014":"#include \nusing namespace std;\n\nint N, M, c;\nset> dots;\nset> usedSegs;\nvector> ops;\n\nbool inGrid(int x, int y) { return x >= 0 && x < N && y >= 0 && y < N; }\nlong long wt(int x, int y) { return (long long)(x-c)*(x-c) + (long long)(y-c)*(y-c) + 1; }\n\nvoid addSeg(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g == 0) return;\n dx /= g; dy /= g;\n for (int i = 0; i < g; i++) {\n int a = x1+i*dx, b = y1+i*dy, e = a+dx, f = b+dy;\n if (a > e || (a == e && b > f)) { swap(a,e); swap(b,f); }\n usedSegs.insert({a,b,e,f});\n }\n}\n\nbool segUsed(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g == 0) return true;\n dx /= g; dy /= g;\n for (int i = 0; i < g; i++) {\n int a = x1+i*dx, b = y1+i*dy, e = a+dx, f = b+dy;\n if (a > e || (a == e && b > f)) { swap(a,e); swap(b,f); }\n if (usedSegs.count({a,b,e,f})) return true;\n }\n return false;\n}\n\nbool dotOnSeg(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g <= 1) return false;\n dx /= g; dy /= g;\n for (int i = 1; i < g; i++)\n if (dots.count({x1+i*dx, y1+i*dy})) return true;\n return false;\n}\n\nbool isValidRect(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4) {\n int v1x = x2-x1, v1y = y2-y1;\n int v2x = x3-x2, v2y = y3-y2;\n if (v1x == 0 && v1y == 0) return false;\n if (v2x == 0 && v2y == 0) return false;\n if (v1x*v2x + v1y*v2y != 0) return false;\n bool axis1 = (v1x == 0 || v1y == 0);\n bool diag1 = (abs(v1x) == abs(v1y));\n if (!axis1 && !diag1) return false;\n bool axis2 = (v2x == 0 || v2y == 0);\n bool diag2 = (abs(v2x) == abs(v2y));\n if (!axis2 && !diag2) return false;\n if (x4 != x1 + v2x || y4 != y1 + v2y) return false;\n return true;\n}\n\nbool tryAdd(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4) {\n if (!inGrid(x1,y1) || dots.count({x1,y1})) return false;\n if (!dots.count({x2,y2}) || !dots.count({x3,y3}) || !dots.count({x4,y4})) return false;\n set> pts = {{x1,y1},{x2,y2},{x3,y3},{x4,y4}};\n if (pts.size() != 4) return false;\n if (!isValidRect(x1,y1,x2,y2,x3,y3,x4,y4)) return false;\n if (dotOnSeg(x1,y1,x2,y2) || dotOnSeg(x2,y2,x3,y3) || \n dotOnSeg(x3,y3,x4,y4) || dotOnSeg(x4,y4,x1,y1)) return false;\n if (segUsed(x1,y1,x2,y2) || segUsed(x2,y2,x3,y3) || \n segUsed(x3,y3,x4,y4) || segUsed(x4,y4,x1,y1)) return false;\n \n dots.insert({x1,y1});\n addSeg(x1,y1,x2,y2); addSeg(x2,y2,x3,y3);\n addSeg(x3,y3,x4,y4); addSeg(x4,y4,x1,y1);\n ops.push_back({x1,y1,x2,y2,x3,y3,x4,y4});\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M;\n c = (N-1) / 2;\n for (int i = 0; i < M; i++) { int x, y; cin >> x >> y; dots.insert({x, y}); }\n \n auto tstart = chrono::steady_clock::now();\n mt19937 rng(42);\n \n int fails = 0;\n while (chrono::duration(chrono::steady_clock::now() - tstart).count() < 4.5) {\n vector> dl(dots.begin(), dots.end());\n shuffle(dl.begin(), dl.end(), rng);\n int sz = min((int)dl.size(), 100);\n \n vector>> candidates;\n \n for (int i = 0; i < sz; i++) {\n for (int j = 0; j < sz; j++) {\n if (i == j) continue;\n for (int k = 0; k < sz; k++) {\n if (k == i || k == j) continue;\n auto [ax, ay] = dl[i];\n auto [bx, by] = dl[j];\n auto [cx, cy] = dl[k];\n \n // Try: new point D, with corners D-A-B-C (A opposite to C, B opposite to D)\n // D = A + C - B\n int dx = ax + cx - bx, dy = ay + cy - by;\n if (inGrid(dx, dy) && !dots.count({dx, dy})) {\n long long w = wt(dx, dy);\n candidates.push_back({w, {dx, dy, ax, ay, bx, by, cx, cy}});\n }\n }\n }\n }\n \n sort(candidates.begin(), candidates.end(), greater<>());\n \n bool found = false;\n for (auto& [w, arr] : candidates) {\n if (tryAdd(arr[0],arr[1],arr[2],arr[3],arr[4],arr[5],arr[6],arr[7])) {\n found = true;\n break;\n }\n }\n \n if (!found) {\n if (++fails > 200) break;\n } else {\n fails = 0;\n }\n }\n \n cout << ops.size() << \"\\n\";\n for (auto& op : ops) {\n for (int i = 0; i < 8; i++) cout << op[i] << \" \\n\"[i==7];\n }\n return 0;\n}","ahc015":"#include \nusing namespace std;\n\nconst int N = 10;\n\nstruct State {\n int grid[N][N];\n \n State() { memset(grid, 0, sizeof(grid)); }\n \n int countEmpty() const {\n int cnt = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (grid[i][j] == 0) cnt++;\n return cnt;\n }\n \n void place(int p, int flavor) {\n int cnt = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (grid[i][j] == 0 && ++cnt == p) { grid[i][j] = flavor; return; }\n }\n \n void tilt(char dir) {\n if (dir == 'F') {\n for (int j = 0; j < N; j++) {\n int w = 0;\n for (int i = 0; i < N; i++) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[w++][j] = v; }\n }\n } else if (dir == 'B') {\n for (int j = 0; j < N; j++) {\n int w = N - 1;\n for (int i = N - 1; i >= 0; i--) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[w--][j] = v; }\n }\n } else if (dir == 'L') {\n for (int i = 0; i < N; i++) {\n int w = 0;\n for (int j = 0; j < N; j++) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[i][w++] = v; }\n }\n } else {\n for (int i = 0; i < N; i++) {\n int w = N - 1;\n for (int j = N - 1; j >= 0; j--) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[i][w--] = v; }\n }\n }\n }\n \n long long calcScore() const {\n bool vis[N][N] = {};\n long long sum = 0;\n int dx[] = {-1, 1, 0, 0}, dy[] = {0, 0, -1, 1};\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (grid[i][j] && !vis[i][j]) {\n int f = grid[i][j], sz = 0;\n queue> q; q.push({i, j}); vis[i][j] = true;\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop(); sz++;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < N && ny >= 0 && ny < N && !vis[nx][ny] && grid[nx][ny] == f) {\n vis[nx][ny] = true; q.push({nx, ny});\n }\n }\n }\n sum += (long long)sz * sz;\n }\n }\n }\n return sum;\n }\n};\n\nmt19937 rng(12345);\nconst char dirs[] = {'F', 'B', 'L', 'R'};\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int f[101];\n for (int t = 1; t <= 100; t++) cin >> f[t];\n \n State state;\n \n for (int t = 1; t <= 100; t++) {\n int p; cin >> p;\n state.place(p, f[t]);\n \n int depth = min(12, 100 - t);\n int numSims = 25;\n \n char bestDir = 'F';\n long long bestScore = -1;\n \n for (char dir : dirs) {\n long long totalScore = 0;\n \n for (int sim = 0; sim < numSims; sim++) {\n State s = state;\n s.tilt(dir);\n \n for (int step = 1; step <= depth && t + step <= 100; step++) {\n int empty = s.countEmpty();\n if (empty == 0) break;\n int randPos = (rng() % empty) + 1;\n s.place(randPos, f[t + step]);\n \n // Greedy tilt\n char simBest = 'F';\n long long simBestScore = -1;\n for (char d : dirs) {\n State tmp = s;\n tmp.tilt(d);\n long long sc = tmp.calcScore();\n if (sc > simBestScore) { simBestScore = sc; simBest = d; }\n }\n s.tilt(simBest);\n }\n totalScore += s.calcScore();\n }\n \n if (totalScore > bestScore) {\n bestScore = totalScore;\n bestDir = dir;\n }\n }\n \n state.tilt(bestDir);\n cout << bestDir << '\\n' << flush;\n }\n \n return 0;\n}","ahc016":"#include \nusing namespace std;\n\nint N, M;\ndouble eps;\n\nvector get_sorted_degrees(const string& s) {\n vector deg(N, 0);\n int idx = 0;\n for (int i = 0; i < N; i++) {\n for (int j = i + 1; j < N; j++) {\n if (s[idx++] == '1') {\n deg[i]++;\n deg[j]++;\n }\n }\n }\n sort(deg.begin(), deg.end());\n return deg;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(0);\n \n cin >> M >> eps;\n \n // Better N selection based on theoretical analysis\n // Need larger N for higher noise to maintain distinguishability\n double noise_factor = (eps < 0.001) ? 1.0 : 1.0 / max(0.2, 1.0 - 2.0 * eps);\n \n // Base N on M and noise\n if (eps < 0.01) {\n N = (int)ceil(sqrt(2.0 * M)) + 2;\n } else if (eps < 0.05) {\n N = (int)ceil(sqrt(2.5 * M)) + 4;\n } else if (eps < 0.15) {\n N = (int)ceil(sqrt(3.0 * M * noise_factor)) + 8;\n } else if (eps < 0.25) {\n N = (int)ceil(sqrt(4.0 * M * noise_factor)) + 15;\n } else if (eps < 0.35) {\n N = (int)ceil(sqrt(5.0 * M * noise_factor)) + 25;\n } else {\n N = (int)ceil(sqrt(6.0 * M * noise_factor)) + 35;\n }\n \n N = max(N, (int)(2.0 * sqrt(M)));\n N = max(N, 8);\n N = min(N, 100);\n \n cout << N << \"\\n\";\n \n int total = N * (N - 1) / 2;\n \n vector G(M);\n vector> expected_deg(M);\n \n // Create M graphs with linearly spaced edge counts\n for (int i = 0; i < M; i++) {\n string s(total, '0');\n long long edges = (M > 1) ? ((long long)i * total / (M - 1)) : 0;\n \n // Fill edges in a pattern that creates varied degree distribution\n int idx = 0;\n int filled = 0;\n for (int a = 0; a < N && filled < edges; a++) {\n for (int b = a + 1; b < N && filled < edges; b++) {\n int pos = a * (2 * N - a - 1) / 2 + (b - a - 1);\n s[pos] = '1';\n filled++;\n }\n }\n \n G[i] = s;\n \n // Compute expected degree sequence after noise\n vector deg = get_sorted_degrees(s);\n expected_deg[i].resize(N);\n double transform = 1.0 - 2.0 * eps;\n double base = (N - 1) * eps;\n for (int j = 0; j < N; j++) {\n expected_deg[i][j] = deg[j] * transform + base;\n }\n \n cout << s << \"\\n\";\n }\n cout.flush();\n \n for (int q = 0; q < 100; q++) {\n string H;\n cin >> H;\n \n vector deg_h = get_sorted_degrees(H);\n \n int best = 0;\n double best_score = 1e18;\n \n for (int i = 0; i < M; i++) {\n // Weighted L2 distance - weight more heavily at extremes\n double score = 0;\n for (int j = 0; j < N; j++) {\n double diff = deg_h[j] - expected_deg[i][j];\n // Weight endpoints more (more informative)\n double weight = 1.0 + 0.5 * (abs(j - N/2.0) / (N/2.0));\n score += weight * diff * diff;\n }\n \n if (score < best_score) {\n best_score = score;\n best = i;\n }\n }\n \n cout << best << \"\\n\";\n cout.flush();\n }\n \n return 0;\n}","ahc017":"#include \nusing namespace std;\n\nint N, M, D, K;\nvector> edges;\nvector>> adj;\nvector> adjEdge;\nmt19937 rng(42);\nconst long long INF = 1e9;\n\nvector dijkstraMask(int src, const vector& excl) {\n vector dist(N, INF);\n priority_queue, vector>, greater<>> pq;\n dist[src] = 0;\n pq.push({0, src});\n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > dist[u]) continue;\n for (size_t i = 0; i < adj[u].size(); i++) {\n if (excl[adjEdge[u][i]]) continue;\n auto [v, w] = adj[u][i];\n if (dist[u] + w < dist[v]) {\n dist[v] = dist[u] + w;\n pq.push({dist[v], v});\n }\n }\n }\n return dist;\n}\n\nint numSamples;\nvector samples;\nvector> origDist;\nvector assign_;\nvector cnt;\n\ndouble evalDay(int d) {\n vector excl(M, false);\n for (int e = 0; e < M; e++) if (assign_[e] == d) excl[e] = true;\n double tot = 0;\n for (int i = 0; i < numSamples; i++) {\n auto dist = dijkstraMask(samples[i], excl);\n for (int v = 0; v < N; v++) if (v != samples[i])\n tot += min(dist[v], INF) - origDist[i][v];\n }\n return tot;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n auto start = chrono::steady_clock::now();\n \n cin >> N >> M >> D >> K;\n edges.resize(M); adj.resize(N); adjEdge.resize(N);\n \n for (int i = 0; i < M; i++) {\n int u, v, w; cin >> u >> v >> w; u--; v--;\n edges[i] = {u, v, w};\n adj[u].push_back({v, w}); adj[v].push_back({u, w});\n adjEdge[u].push_back(i); adjEdge[v].push_back(i);\n }\n for (int i = 0; i < N; i++) { int x, y; cin >> x >> y; }\n \n vector noEdge(M, false);\n vector crit(M);\n for (int e = 0; e < M; e++) {\n noEdge[e] = true;\n auto dist = dijkstraMask(edges[e][0], noEdge);\n crit[e] = dist[edges[e][1]] - edges[e][2];\n noEdge[e] = false;\n }\n \n numSamples = min(55, N);\n samples.resize(N); iota(samples.begin(), samples.end(), 0);\n shuffle(samples.begin(), samples.end(), rng);\n samples.resize(numSamples);\n \n origDist.resize(numSamples);\n for (int i = 0; i < numSamples; i++) origDist[i] = dijkstraMask(samples[i], noEdge);\n \n double globalBest = 1e18;\n vector globalBestAssign;\n \n for (int restart = 0; restart < 3; restart++) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > 5.0) break;\n \n vector order(M); iota(order.begin(), order.end(), 0);\n if (restart == 0) {\n sort(order.begin(), order.end(), [&](int a, int b) { return crit[a] > crit[b]; });\n } else {\n shuffle(order.begin(), order.end(), rng);\n sort(order.begin(), order.end(), [&](int a, int b) { return crit[a] > crit[b]; });\n }\n \n assign_.assign(M, 0);\n cnt.assign(D + 1, 0);\n vector> dayVertices(D + 1);\n \n for (int e : order) {\n int u = edges[e][0], v = edges[e][1];\n int best = 1, bestScore = INT_MAX;\n for (int d = 1; d <= D; d++) {\n if (cnt[d] >= K) continue;\n int conflict = (dayVertices[d].count(u) ? 1 : 0) + (dayVertices[d].count(v) ? 1 : 0);\n int score = conflict * 10000 + cnt[d] + (restart > 0 ? (int)(rng() % 100) : 0);\n if (score < bestScore) { bestScore = score; best = d; }\n }\n assign_[e] = best; cnt[best]++;\n dayVertices[best].insert(u); dayVertices[best].insert(v);\n }\n \n vector dayCost(D + 1);\n double cur = 0;\n for (int d = 1; d <= D; d++) { dayCost[d] = evalDay(d); cur += dayCost[d]; }\n \n double bestScore = cur;\n vector bestAssign = assign_;\n double temp = max(1.0, cur / D / 3);\n int noImprove = 0;\n \n while (true) {\n now = chrono::steady_clock::now();\n elapsed = chrono::duration(now - start).count();\n double timePerRestart = 5.3 / 3;\n if (elapsed > (restart + 1) * timePerRestart || elapsed > 5.3) break;\n \n if (noImprove > 500) {\n temp = max(temp, bestScore / D / 10);\n noImprove = 0;\n }\n \n int worstDay = 1;\n for (int d = 2; d <= D; d++) if (dayCost[d] > dayCost[worstDay]) worstDay = d;\n \n int moveType = rng() % 5;\n \n if (moveType < 2) {\n int e1 = rng() % M, e2 = rng() % M;\n if (assign_[e1] == assign_[e2]) continue;\n int d1 = assign_[e1], d2 = assign_[e2];\n \n swap(assign_[e1], assign_[e2]);\n double nc1 = evalDay(d1), nc2 = evalDay(d2);\n double delta = (nc1 + nc2) - (dayCost[d1] + dayCost[d2]);\n \n if (delta < 0 || (double)(rng() % 1000000) / 1000000 < exp(-delta / temp)) {\n dayCost[d1] = nc1; dayCost[d2] = nc2; cur += delta;\n if (cur < bestScore) { bestScore = cur; bestAssign = assign_; noImprove = 0; }\n else noImprove++;\n } else { swap(assign_[e1], assign_[e2]); noImprove++; }\n } else if (moveType == 2) {\n int e = rng() % M;\n int oldD = assign_[e], newD = rng() % D + 1;\n if (newD == oldD || cnt[newD] >= K) continue;\n \n assign_[e] = newD; cnt[oldD]--; cnt[newD]++;\n double nc1 = evalDay(oldD), nc2 = evalDay(newD);\n double delta = (nc1 + nc2) - (dayCost[oldD] + dayCost[newD]);\n \n if (delta < 0 || (double)(rng() % 1000000) / 1000000 < exp(-delta / temp)) {\n dayCost[oldD] = nc1; dayCost[newD] = nc2; cur += delta;\n if (cur < bestScore) { bestScore = cur; bestAssign = assign_; noImprove = 0; }\n else noImprove++;\n } else { assign_[e] = oldD; cnt[oldD]++; cnt[newD]--; noImprove++; }\n } else {\n vector worstEdges;\n for (int e = 0; e < M; e++) if (assign_[e] == worstDay) worstEdges.push_back(e);\n if (worstEdges.empty()) continue;\n int e = worstEdges[rng() % worstEdges.size()];\n int newD = rng() % D + 1;\n if (newD == worstDay || cnt[newD] >= K) continue;\n \n assign_[e] = newD; cnt[worstDay]--; cnt[newD]++;\n double nc1 = evalDay(worstDay), nc2 = evalDay(newD);\n double delta = (nc1 + nc2) - (dayCost[worstDay] + dayCost[newD]);\n \n if (delta < 0 || (double)(rng() % 1000000) / 1000000 < exp(-delta / temp)) {\n dayCost[worstDay] = nc1; dayCost[newD] = nc2; cur += delta;\n if (cur < bestScore) { bestScore = cur; bestAssign = assign_; noImprove = 0; }\n else noImprove++;\n } else { assign_[e] = worstDay; cnt[worstDay]++; cnt[newD]--; noImprove++; }\n }\n temp *= 0.999995;\n if (temp < 0.1) temp = 0.1;\n }\n \n if (bestScore < globalBest) {\n globalBest = bestScore;\n globalBestAssign = bestAssign;\n }\n }\n \n for (int i = 0; i < M; i++) cout << globalBestAssign[i] << \" \\n\"[i == M-1];\n return 0;\n}","ahc019":"#include \nusing namespace std;\n\nint D;\nstring f[2][15], r[2][15];\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> D;\n for (int i = 0; i < 2; i++) {\n for (int k = 0; k < D; k++) cin >> f[i][k];\n for (int k = 0; k < D; k++) cin >> r[i][k];\n }\n \n vector b[2];\n for (int i = 0; i < 2; i++) b[i].assign(D * D * D, 0);\n \n auto idx = [&](int x, int y, int z) { return x * D * D + y * D + z; };\n int dx[] = {1, -1, 0, 0, 0, 0};\n int dy[] = {0, 0, 1, -1, 0, 0};\n int dz[] = {0, 0, 0, 0, 1, -1};\n \n int n = 0;\n \n // Step 1: Create large shared blocks from cells valid in both at same position\n for (int x = 0; x < D; x++) {\n for (int y = 0; y < D; y++) {\n for (int z = 0; z < D; z++) {\n bool v0 = (f[0][z][x] == '1' && r[0][z][y] == '1');\n bool v1 = (f[1][z][x] == '1' && r[1][z][y] == '1');\n if (v0 && v1 && b[0][idx(x,y,z)] == 0) {\n n++;\n queue> q;\n q.push({x, y, z});\n b[0][idx(x,y,z)] = b[1][idx(x,y,z)] = n;\n while (!q.empty()) {\n auto [cx, cy, cz] = q.front(); q.pop();\n for (int d = 0; d < 6; d++) {\n int nx = cx + dx[d], ny = cy + dy[d], nz = cz + dz[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && nz >= 0 && nz < D) {\n bool nv0 = (f[0][nz][nx] == '1' && r[0][nz][ny] == '1');\n bool nv1 = (f[1][nz][nx] == '1' && r[1][nz][ny] == '1');\n if (nv0 && nv1 && b[0][idx(nx,ny,nz)] == 0) {\n b[0][idx(nx,ny,nz)] = b[1][idx(nx,ny,nz)] = n;\n q.push({nx, ny, nz});\n }\n }\n }\n }\n }\n }\n }\n }\n \n // Step 2: Find remaining constraints for each arrangement\n vector> extra[2];\n for (int arr = 0; arr < 2; arr++) {\n set needFront, needRight;\n for (int z = 0; z < D; z++) {\n for (int x = 0; x < D; x++) if (f[arr][z][x] == '1') needFront.insert(z * D + x);\n for (int y = 0; y < D; y++) if (r[arr][z][y] == '1') needRight.insert(z * D + y);\n }\n \n // Remove constraints already satisfied by shared blocks\n for (int x = 0; x < D; x++) {\n for (int y = 0; y < D; y++) {\n for (int z = 0; z < D; z++) {\n if (b[arr][idx(x,y,z)] > 0) {\n needFront.erase(z * D + x);\n needRight.erase(z * D + y);\n }\n }\n }\n }\n \n // Greedily pick unit blocks for remaining constraints\n while (!needFront.empty() || !needRight.empty()) {\n int bestX = -1, bestY = -1, bestZ = -1, bestScore = -1;\n for (int z = 0; z < D; z++) {\n for (int x = 0; x < D; x++) {\n if (f[arr][z][x] != '1') continue;\n for (int y = 0; y < D; y++) {\n if (r[arr][z][y] != '1') continue;\n int score = 0;\n if (needFront.count(z * D + x)) score++;\n if (needRight.count(z * D + y)) score++;\n if (score > bestScore) {\n bestScore = score;\n bestX = x; bestY = y; bestZ = z;\n }\n }\n }\n }\n if (bestScore <= 0) break;\n extra[arr].push_back({bestX, bestY, bestZ});\n needFront.erase(bestZ * D + bestX);\n needRight.erase(bestZ * D + bestY);\n }\n }\n \n // Step 3: Assign unit blocks (shared between arrangements)\n int m1 = extra[0].size(), m2 = extra[1].size();\n int totalExtra = max(m1, m2);\n \n for (int i = 0; i < m1; i++) {\n auto [x, y, z] = extra[0][i];\n b[0][idx(x,y,z)] = n + 1 + i;\n }\n for (int i = 0; i < m2; i++) {\n auto [x, y, z] = extra[1][i];\n b[1][idx(x,y,z)] = n + 1 + i;\n }\n \n n += totalExtra;\n \n cout << n << \"\\n\";\n for (int i = 0; i < 2; i++) {\n for (int j = 0; j < D * D * D; j++) {\n if (j) cout << \" \";\n cout << b[i][j];\n }\n cout << \"\\n\";\n }\n \n return 0;\n}","ahc020":"#include \nusing namespace std;\n\nint N, M, K;\nvector> V, R;\nvector> E;\nvector>> adj;\n\ndouble dist(int i, int k) {\n double dx = V[i].first - R[k].first, dy = V[i].second - R[k].second;\n return sqrt(dx*dx + dy*dy);\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> K;\n V.resize(N); R.resize(K); E.resize(M); adj.resize(N);\n \n for(int i = 0; i < N; i++) cin >> V[i].first >> V[i].second;\n for(int j = 0; j < M; j++) {\n int u, v; long long w;\n cin >> u >> v >> w; u--; v--;\n E[j] = {u, v, w};\n adj[u].push_back({v, j});\n adj[v].push_back({u, j});\n }\n for(int k = 0; k < K; k++) cin >> R[k].first >> R[k].second;\n \n // All-pairs shortest paths\n vector> distVV(N, vector(N, LLONG_MAX/2));\n vector> parentV(N, vector(N, -1));\n \n for(int s = 0; s < N; s++) {\n distVV[s][s] = 0;\n priority_queue, vector>, greater<>> pq;\n pq.push({0, s});\n while(!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if(d > distVV[s][u]) continue;\n for(auto [v, eid] : adj[u]) {\n long long w = get<2>(E[eid]);\n if(distVV[s][u] + w < distVV[s][v]) {\n distVV[s][v] = distVV[s][u] + w;\n parentV[s][v] = u;\n pq.push({distVV[s][v], v});\n }\n }\n }\n }\n \n vector bestP(N, 0), bestB(M, 0), bestAssign(K);\n long long bestCost = LLONG_MAX;\n \n // Try different weight factors for initial assignment\n for(double factor : {0.0, 0.001, 0.01, 0.05, 0.1, 0.2}) {\n vector assignment(K);\n for(int k = 0; k < K; k++) {\n int best = -1; double bestScore = 1e18;\n for(int i = 0; i < N; i++) {\n double d = dist(i, k);\n if(d > 5000) continue;\n double score = d * d + factor * distVV[0][i];\n if(score < bestScore) { bestScore = score; best = i; }\n }\n assignment[k] = best;\n }\n \n auto computeP = [&]() {\n vector P(N, 0);\n for(int k = 0; k < K; k++) {\n int v = assignment[k];\n P[v] = max(P[v], (int)ceil(dist(v, k) - 1e-9));\n }\n return P;\n };\n \n auto buildSteinerTree = [&](const vector& P) {\n vector terminals; terminals.push_back(0);\n for(int i = 0; i < N; i++) if(P[i] > 0 && i != 0) terminals.push_back(i);\n \n vector B(M, 0);\n if(terminals.size() <= 1) return B;\n \n set inTree; inTree.insert(0);\n vector minD(N, LLONG_MAX);\n vector minFrom(N, -1);\n for(int t : terminals) if(t != 0) minD[t] = distVV[0][t];\n \n while(inTree.size() < terminals.size()) {\n int best = -1;\n for(int t : terminals) if(inTree.find(t) == inTree.end()) {\n if(best == -1 || minD[t] < minD[best]) best = t;\n }\n if(best == -1) break;\n \n inTree.insert(best);\n int cur = best, src = minFrom[best] == -1 ? 0 : minFrom[best];\n while(cur != src) {\n int p = parentV[src][cur];\n for(auto [nxt, eid] : adj[cur]) if(nxt == p) { B[eid] = 1; break; }\n cur = p;\n }\n \n for(int t : terminals) if(inTree.find(t) == inTree.end()) {\n if(distVV[best][t] < minD[t]) { minD[t] = distVV[best][t]; minFrom[t] = best; }\n }\n }\n return B;\n };\n \n auto getReachable = [&](const vector& B) {\n vector visited(N, false);\n queue q; q.push(0); visited[0] = true;\n vector reach;\n while(!q.empty()) {\n int u = q.front(); q.pop(); reach.push_back(u);\n for(auto [v, eid] : adj[u]) if(B[eid] && !visited[v]) {\n visited[v] = true; q.push(v);\n }\n }\n return reach;\n };\n \n auto calcCost = [&](const vector& P, const vector& B) {\n long long cost = 0;\n for(int i = 0; i < N; i++) cost += (long long)P[i] * P[i];\n for(int j = 0; j < M; j++) if(B[j]) cost += get<2>(E[j]);\n return cost;\n };\n \n vector P = computeP();\n vector B = buildSteinerTree(P);\n \n // Local search using reachable vertices\n for(int iter = 0; iter < 20; iter++) {\n vector reach = getReachable(B);\n bool improved = false;\n for(int k = 0; k < K; k++) {\n int curV = assignment[k];\n double curD = dist(curV, k);\n for(int v : reach) {\n double d = dist(v, k);\n if(d < curD - 0.01 && d <= 5000) {\n assignment[k] = v; curV = v; curD = d;\n improved = true;\n }\n }\n }\n if(!improved) break;\n P = computeP();\n B = buildSteinerTree(P);\n }\n \n long long cost = calcCost(P, B);\n if(cost < bestCost) {\n bestCost = cost; bestP = P; bestB = B; bestAssign = assignment;\n }\n }\n \n for(int i = 0; i < N; i++) cout << bestP[i] << \" \\n\"[i==N-1];\n for(int j = 0; j < M; j++) cout << bestB[j] << \" \\n\"[j==M-1];\n \n return 0;\n}","ahc021":"#include \nusing namespace std;\n\nconst int N = 30;\nint b[N][N];\nvector> ops;\n\nvoid do_swap(int x1, int y1, int x2, int y2) {\n ops.push_back({x1, y1, x2, y2});\n swap(b[x1][y1], b[x2][y2]);\n}\n\nvoid sift_down(int x, int y) {\n while (x < N - 1) {\n int min_child_y = (b[x + 1][y + 1] < b[x + 1][y]) ? (y + 1) : y;\n if (b[x][y] > b[x + 1][min_child_y]) {\n do_swap(x, y, x + 1, min_child_y);\n x = x + 1;\n y = min_child_y;\n } else {\n break;\n }\n }\n}\n\nbool has_violation(int x, int y) {\n if (x >= N - 1) return false;\n return b[x][y] > b[x + 1][y] || b[x][y] > b[x + 1][y + 1];\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int x = 0; x < N; x++) {\n for (int y = 0; y <= x; y++) {\n cin >> b[x][y];\n }\n }\n \n // Process violations iteratively - prioritize by value (larger values first)\n bool changed = true;\n while (changed) {\n changed = false;\n // Collect all violations with their values\n vector> violations; // (value, x, y)\n for (int x = N - 2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) {\n if (has_violation(x, y)) {\n violations.push_back({b[x][y], x, y});\n }\n }\n }\n \n // Sort by value descending (fix larger values first)\n sort(violations.rbegin(), violations.rend());\n \n for (auto& [val, x, y] : violations) {\n if (has_violation(x, y)) {\n sift_down(x, y);\n changed = true;\n }\n }\n }\n \n cout << ops.size() << \"\\n\";\n for (auto& [x1, y1, x2, y2] : ops) {\n cout << x1 << \" \" << y1 << \" \" << x2 << \" \" << y2 << \"\\n\";\n }\n \n return 0;\n}","toyota2023summer-final":"#include \nusing namespace std;\n\nint D, N;\nint ex, ey;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nvector> grid;\n\nvector> findReachableEmpty() {\n vector> result;\n vector> vis(D, vector(D, false));\n queue> q;\n q.push({ex, ey});\n vis[ex][ey] = true;\n \n while (!q.empty()) {\n int x = q.front().first, y = q.front().second;\n q.pop();\n \n // This is an empty square (entrance or regular empty)\n if (!(x == ex && y == ey)) {\n result.push_back({x, y});\n }\n \n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && !vis[nx][ny] && grid[nx][ny] == -1) {\n vis[nx][ny] = true;\n q.push({nx, ny});\n }\n }\n }\n return result;\n}\n\nvector> findReachableContainers() {\n vector> result;\n vector> vis(D, vector(D, false));\n queue> q;\n q.push({ex, ey});\n vis[ex][ey] = true;\n \n while (!q.empty()) {\n int x = q.front().first, y = q.front().second;\n q.pop();\n \n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && !vis[nx][ny] && grid[nx][ny] != -2) {\n vis[nx][ny] = true;\n if (grid[nx][ny] >= 0) {\n // This is a container adjacent to reachable empty square\n result.push_back({nx, ny});\n } else {\n // This is an empty square, continue searching\n q.push({nx, ny});\n }\n }\n }\n }\n return result;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> D >> N;\n ex = 0;\n ey = (D - 1) / 2;\n \n grid.assign(D, vector(D, -1));\n \n for (int i = 0; i < N; i++) {\n int x, y;\n cin >> x >> y;\n grid[x][y] = -2;\n }\n \n int total = D * D - 1 - N;\n \n // Placement phase\n for (int iter = 0; iter < total; iter++) {\n int t;\n cin >> t;\n \n vector> reach = findReachableEmpty();\n \n // Simple strategy: place at the last reachable position (furthest from entrance in BFS order)\n pair best = reach.back();\n \n grid[best.first][best.second] = t;\n cout << best.first << \" \" << best.second << endl;\n }\n \n // Transport phase\n for (int iter = 0; iter < total; iter++) {\n vector> reachable = findReachableContainers();\n \n // Find container with smallest number\n pair best = reachable[0];\n for (auto& pos : reachable) {\n if (grid[pos.first][pos.second] < grid[best.first][best.second]) {\n best = pos;\n }\n }\n \n cout << best.first << \" \" << best.second << \"\\n\";\n grid[best.first][best.second] = -1;\n }\n \n return 0;\n}","ahc024":"#include \nusing namespace std;\n\nint n, m;\nint dx[] = {0, 0, 1, -1};\nint dy[] = {1, -1, 0, 0};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> n >> m;\n vector> grid(n, vector(n));\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n cin >> grid[i][j];\n \n // Output original grid first as valid baseline\n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n cout << grid[i][j];\n if (j < n-1) cout << \" \";\n }\n cout << \"\\n\";\n }\n cout.flush();\n \n // Colors adjacent to 0 (boundary colors)\n set adjToZero;\n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n if (i == 0 || i == n-1 || j == 0 || j == n-1) {\n adjToZero.insert(grid[i][j]);\n }\n }\n }\n \n // Track adjacency edge counts\n map, int> edgeCount;\n auto addEdge = [&](int a, int b) {\n if (a > b) swap(a, b);\n if (a != b) edgeCount[{a, b}]++;\n };\n auto removeEdge = [&](int a, int b) {\n if (a > b) swap(a, b);\n if (a != b) edgeCount[{a, b}]--;\n };\n \n auto best = grid;\n \n // Initialize edge counts\n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n int c = best[i][j];\n if (i == 0 || i == n-1 || j == 0 || j == n-1) {\n addEdge(0, c);\n }\n // Only count right and down to avoid double counting\n if (j + 1 < n && best[i][j+1] != c) addEdge(c, best[i][j+1]);\n if (i + 1 < n && best[i+1][j] != c) addEdge(c, best[i+1][j]);\n }\n }\n \n // Required adjacencies (those with count > 0)\n set> required;\n for (auto& [p, cnt] : edgeCount) {\n if (cnt > 0) required.insert(p);\n }\n \n vector colorCount(m + 1, 0);\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n colorCount[best[i][j]]++;\n \n auto start = chrono::steady_clock::now();\n \n vector> candidates;\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n candidates.push_back({i, j});\n \n mt19937 rng(12345);\n shuffle(candidates.begin(), candidates.end(), rng);\n \n for (auto [i, j] : candidates) {\n auto elapsed = chrono::steady_clock::now() - start;\n if (chrono::duration_cast(elapsed).count() > 1800) break;\n \n int c = best[i][j];\n if (c == 0) continue;\n if (colorCount[c] <= 1) continue;\n \n // Check all neighbors are colors that can be adjacent to 0\n bool canRemove = true;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n) {\n int nc = best[ni][nj];\n if (nc != 0 && adjToZero.find(nc) == adjToZero.end()) {\n canRemove = false;\n break;\n }\n }\n }\n if (!canRemove) continue;\n \n // Cell must touch 0 (boundary or adjacent to 0 cell)\n bool touchesZero = (i == 0 || i == n-1 || j == 0 || j == n-1);\n for (int d = 0; d < 4 && !touchesZero; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n && best[ni][nj] == 0) {\n touchesZero = true;\n }\n }\n if (!touchesZero) continue;\n \n // Must have same-color neighbor for connectivity\n bool hasNeighbor = false;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n && best[ni][nj] == c) {\n hasNeighbor = true;\n break;\n }\n }\n if (!hasNeighbor) continue;\n \n // Try removal - track edge changes\n vector> lostEdges, gainedEdges;\n \n // Lost: boundary edge if on boundary\n if (i == 0 || i == n-1 || j == 0 || j == n-1) {\n lostEdges.push_back({min(0,c), max(0,c)});\n }\n \n // Lost/gained from neighbors\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n) {\n int nc = best[ni][nj];\n if (nc != c && nc != 0) {\n lostEdges.push_back({min(c,nc), max(c,nc)});\n gainedEdges.push_back({0, nc});\n }\n }\n }\n \n // Check if any required edge would be lost\n bool wouldBreak = false;\n map, int> delta;\n for (auto& e : lostEdges) delta[e]--;\n for (auto& e : gainedEdges) delta[e]++;\n \n for (auto& [e, d] : delta) {\n int newCount = edgeCount[e] + d;\n if (required.count(e) && newCount <= 0) {\n wouldBreak = true;\n break;\n }\n }\n if (wouldBreak) continue;\n \n // Check connectivity of color c after removal\n best[i][j] = 0;\n \n int si = -1, sj = -1, total = 0;\n for (int x = 0; x < n; x++) {\n for (int y = 0; y < n; y++) {\n if (best[x][y] == c) {\n if (si < 0) { si = x; sj = y; }\n total++;\n }\n }\n }\n \n bool connected = true;\n if (total > 0) {\n vector> vis(n, vector(n, false));\n queue> q;\n q.push({si, sj});\n vis[si][sj] = true;\n int found = 1;\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < n && ny >= 0 && ny < n && !vis[nx][ny] && best[nx][ny] == c) {\n vis[nx][ny] = true;\n found++;\n q.push({nx, ny});\n }\n }\n }\n connected = (found == total);\n }\n \n if (!connected) {\n best[i][j] = c;\n continue;\n }\n \n // Apply edge changes\n for (auto& [e, d] : delta) {\n edgeCount[e] += d;\n }\n colorCount[c]--;\n }\n \n // Output improved solution\n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) {\n cout << best[i][j];\n if (j < n-1) cout << \" \";\n }\n cout << \"\\n\";\n }\n \n return 0;\n}","ahc025":"#include \nusing namespace std;\n\nint N, D, Q;\nint query_count = 0;\n\nchar query(const vector& L, const vector& R) {\n cout << L.size() << \" \" << R.size();\n for (int x : L) cout << \" \" << x;\n for (int x : R) cout << \" \" << x;\n cout << \"\\n\" << flush;\n char c;\n cin >> c;\n query_count++;\n return c;\n}\n\nvector sorted_items;\n\nvoid merge_sort(int l, int r) {\n if (r - l <= 1) return;\n int m = (l + r) / 2;\n merge_sort(l, m);\n merge_sort(m, r);\n \n vector left(sorted_items.begin() + l, sorted_items.begin() + m);\n vector right(sorted_items.begin() + m, sorted_items.begin() + r);\n \n int i = 0, j = 0, k = l;\n while (i < (int)left.size() && j < (int)right.size()) {\n if (query_count >= Q) {\n while (i < (int)left.size()) sorted_items[k++] = left[i++];\n while (j < (int)right.size()) sorted_items[k++] = right[j++];\n return;\n }\n char c = query({left[i]}, {right[j]});\n if (c != '>') sorted_items[k++] = left[i++];\n else sorted_items[k++] = right[j++];\n }\n while (i < (int)left.size()) sorted_items[k++] = left[i++];\n while (j < (int)right.size()) sorted_items[k++] = right[j++];\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> D >> Q;\n \n sorted_items.resize(N);\n iota(sorted_items.begin(), sorted_items.end(), 0);\n merge_sort(0, N);\n \n vector rank_of(N);\n for (int i = 0; i < N; i++) rank_of[sorted_items[i]] = i;\n \n // Initial weight estimation\n vector w(N);\n for (int i = 0; i < N; i++) w[i] = i + 1;\n \n // Use remaining queries for weight estimation\n int est_budget = min((Q - query_count) / 2, N * 3);\n \n for (int j = N - 1; j >= 1 && est_budget > 0; j--) {\n int lo = 1, hi = j;\n while (lo < hi && est_budget > 0 && query_count < Q) {\n int mid = (lo + hi) / 2;\n vector L, R = {sorted_items[j]};\n for (int t = 0; t < mid; t++) L.push_back(sorted_items[t]);\n char c = query(L, R);\n est_budget--;\n if (c == '>' || c == '=') hi = mid;\n else lo = mid + 1;\n }\n double sum = 0;\n for (int t = 0; t < lo; t++) sum += w[t];\n w[j] = max(w[j], sum * 1.05);\n }\n \n // Greedy assignment\n vector set_weight(D, 0);\n vector assignment(N);\n vector> sets(D);\n \n for (int i = N - 1; i >= 0; i--) {\n int item = sorted_items[i];\n int best = 0;\n for (int j = 1; j < D; j++)\n if (set_weight[j] < set_weight[best]) best = j;\n assignment[item] = best;\n set_weight[best] += w[i];\n sets[best].push_back(item);\n }\n \n // Simple local search: try moving smallest item from heaviest to lightest set\n for (int iter = 0; iter < 50 && query_count + 3 < Q; iter++) {\n // Find heaviest and lightest sets by estimation\n int heavy = 0, light = 0;\n for (int i = 1; i < D; i++) {\n if (set_weight[i] > set_weight[heavy]) heavy = i;\n if (set_weight[i] < set_weight[light]) light = i;\n }\n \n if (heavy == light || sets[heavy].size() <= 1) break;\n \n // Compare them\n if (query_count >= Q) break;\n char cmp = query(sets[heavy], sets[light]);\n \n if (cmp != '>') break; // Already balanced or wrong estimation\n \n // Find lightest item in heavy set\n int min_item = sets[heavy][0];\n int min_rank = rank_of[min_item];\n for (int item : sets[heavy]) {\n if (rank_of[item] < min_rank) {\n min_rank = rank_of[item];\n min_item = item;\n }\n }\n \n // Try moving it\n vector new_heavy, new_light = sets[light];\n for (int item : sets[heavy])\n if (item != min_item) new_heavy.push_back(item);\n new_light.push_back(min_item);\n \n if (new_heavy.empty()) break;\n if (query_count >= Q) break;\n \n char new_cmp = query(new_heavy, new_light);\n \n // Accept if balanced or reversed (but not too much)\n if (new_cmp == '=' || new_cmp == '<') {\n sets[heavy] = new_heavy;\n sets[light] = new_light;\n assignment[min_item] = light;\n set_weight[heavy] -= w[min_rank];\n set_weight[light] += w[min_rank];\n } else {\n break; // Can't improve\n }\n }\n \n while (query_count < Q) query({sorted_items[0]}, {sorted_items[1]});\n \n for (int i = 0; i < N; i++)\n cout << assignment[i] << \" \\n\"[i == N - 1];\n \n return 0;\n}","ahc026":"#include \nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n, m;\n cin >> n >> m;\n \n vector> stacks(m);\n vector pos(n + 1);\n \n for (int i = 0; i < m; i++) {\n int h = n / m;\n for (int j = 0; j < h; j++) {\n int x;\n cin >> x;\n stacks[i].push_back(x);\n pos[x] = i;\n }\n }\n \n vector> ops;\n \n for (int v = 1; v <= n; v++) {\n int stack_id = pos[v];\n \n int idx = 0;\n while (stacks[stack_id][idx] != v) idx++;\n \n if (idx < (int)stacks[stack_id].size() - 1) {\n int move_start = idx + 1;\n int bottom_box = stacks[stack_id][move_start];\n \n int max_moving = 0;\n int min_moving = INT_MAX;\n int cnt = (int)stacks[stack_id].size() - move_start;\n \n // Track which upcoming boxes are in our group\n set upcoming_in_group;\n for (int j = move_start; j < (int)stacks[stack_id].size(); j++) {\n int b = stacks[stack_id][j];\n max_moving = max(max_moving, b);\n min_moving = min(min_moving, b);\n // Check next few boxes we'll need\n if (b <= v + 10) {\n upcoming_in_group.insert(b);\n }\n }\n \n int best_dest = -1;\n int best_score = INT_MIN;\n \n for (int i = 0; i < m; i++) {\n if (i == stack_id) continue;\n \n int score = 0;\n \n if (stacks[i].empty()) {\n // Empty stack - very good, value based on min_moving\n // More valuable for groups with smaller min (more urgent)\n score = n * 3 + (n - min_moving);\n } else {\n int min_in_dest = INT_MAX;\n for (int b : stacks[i]) {\n min_in_dest = min(min_in_dest, b);\n }\n \n if (min_in_dest > min_moving) {\n // Safe - our group won't be re-moved due to dest\n score = n * 3;\n \n // Bonus: if top > max_moving, good stacking\n if (stacks[i].back() > max_moving) {\n score += 50;\n }\n } else {\n // Unsafe - will be re-moved when extracting min_in_dest\n // Prefer later re-moves\n score = min_in_dest;\n \n // Penalty proportional to group size (bigger groups = worse to re-move)\n score -= cnt * 3;\n }\n }\n \n // Penalty for tall stacks\n score -= (int)stacks[i].size() * 2;\n \n // Bonus if upcoming boxes would be accessible\n for (int ub : upcoming_in_group) {\n // Check if ub would be safe in this destination\n if (stacks[i].empty()) {\n score += 5;\n } else {\n int min_d = INT_MAX;\n for (int b : stacks[i]) min_d = min(min_d, b);\n if (min_d > ub) {\n score += 5;\n }\n }\n }\n \n if (score > best_score) {\n best_score = score;\n best_dest = i;\n }\n }\n \n ops.push_back({bottom_box, best_dest + 1});\n \n for (int j = move_start; j < (int)stacks[stack_id].size(); j++) {\n int b = stacks[stack_id][j];\n stacks[best_dest].push_back(b);\n pos[b] = best_dest;\n }\n stacks[stack_id].resize(move_start);\n }\n \n ops.push_back({v, 0});\n stacks[stack_id].pop_back();\n }\n \n for (auto& [a, b] : ops) {\n cout << a << \" \" << b << \"\\n\";\n }\n \n return 0;\n}","ahc027":"#include \nusing namespace std;\n\nint N;\nvector h, v;\nvector> d;\nlong long totalD;\nmt19937 rng(42);\n\nint di[] = {0, 1, 0, -1};\nint dj[] = {1, 0, -1, 0};\nchar dirChar[] = {'R', 'D', 'L', 'U'};\n\nbool canMove(int i, int j, int dir) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) return false;\n if (dir == 0) return v[i][j] == '0';\n if (dir == 1) return h[i][j] == '0';\n if (dir == 2) return j > 0 && v[i][j-1] == '0';\n return i > 0 && h[i-1][j] == '0';\n}\n\nlong double fastEvaluate(const string& path) {\n int L = path.size();\n vector> lastVisit(N, vector(N, 0));\n vector> contrib(N, vector(N, 0));\n long long contribSum = 0;\n int ci = 0, cj = 0;\n \n auto move = [&](int t, char c) {\n int dir = (c == 'R') ? 0 : (c == 'D') ? 1 : (c == 'L') ? 2 : 3;\n ci += di[dir]; cj += dj[dir];\n contribSum -= contrib[ci][cj];\n contrib[ci][cj] = (long long)d[ci][cj] * t;\n contribSum += contrib[ci][cj];\n };\n \n for (int t = 1; t <= L; t++) move(t, path[t-1]);\n \n long double totalSum = 0;\n for (int t = L + 1; t <= 2 * L; t++) {\n totalSum += (long long)totalD * t - contribSum;\n move(t, path[(t-1) % L]);\n }\n return totalSum / L;\n}\n\nstring generatePath(int mode) {\n vector> visited(N, vector(N, false));\n string path;\n \n function dfs = [&](int i, int j) {\n visited[i][j] = true;\n vector> children;\n for (int dir = 0; dir < 4; dir++) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (ni >= 0 && ni < N && nj >= 0 && nj < N && !visited[ni][nj] && canMove(i, j, dir)) {\n children.push_back({d[ni][nj], dir});\n }\n }\n \n if (mode == 0) sort(children.begin(), children.end());\n else if (mode == 1) sort(children.rbegin(), children.rend());\n else shuffle(children.begin(), children.end(), rng);\n \n for (auto [dval, dir] : children) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (!visited[ni][nj]) {\n path += dirChar[dir];\n dfs(ni, nj);\n path += dirChar[(dir + 2) % 4];\n }\n }\n };\n dfs(0, 0);\n return path;\n}\n\nstring getLoopTo(int ti, int tj) {\n vector> par(N, vector(N, -1));\n queue> bfs;\n bfs.push({0, 0});\n par[0][0] = -2;\n \n while (!bfs.empty()) {\n auto [i, j] = bfs.front(); bfs.pop();\n if (i == ti && j == tj) break;\n for (int dir = 0; dir < 4; dir++) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (ni >= 0 && ni < N && nj >= 0 && nj < N && par[ni][nj] == -1 && canMove(i, j, dir)) {\n par[ni][nj] = (dir + 2) % 4;\n bfs.push({ni, nj});\n }\n }\n }\n \n string toTarget, fromTarget;\n int ci = ti, cj = tj;\n while (ci != 0 || cj != 0) {\n int pdir = par[ci][cj];\n fromTarget += dirChar[pdir];\n toTarget += dirChar[(pdir + 2) % 4];\n ci += di[pdir]; cj += dj[pdir];\n }\n reverse(toTarget.begin(), toTarget.end());\n return toTarget + fromTarget;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N - 1);\n v.resize(N);\n d.resize(N, vector(N));\n \n for (int i = 0; i < N - 1; i++) cin >> h[i];\n for (int i = 0; i < N; i++) cin >> v[i];\n totalD = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n cin >> d[i][j];\n totalD += d[i][j];\n }\n \n string bestPath;\n long double bestScore = 1e18;\n \n auto tryPath = [&](const string& path) {\n long double score = fastEvaluate(path);\n if (score < bestScore) {\n bestScore = score;\n bestPath = path;\n }\n return score;\n };\n \n // Deterministic orderings\n for (int mode = 0; mode < 2; mode++) tryPath(generatePath(mode));\n \n // Random search\n auto startTime = chrono::steady_clock::now();\n while (chrono::duration_cast(chrono::steady_clock::now() - startTime).count() < 1000) {\n tryPath(generatePath(2));\n }\n \n // Get top high-d cells for loop candidates\n vector> loopCandidates;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (i != 0 || j != 0)\n loopCandidates.push_back({d[i][j], i, j, getLoopTo(i, j)});\n sort(loopCandidates.rbegin(), loopCandidates.rend());\n \n // Try adding loops greedily\n string currentBest = bestPath;\n long double currentScore = bestScore;\n \n for (int iter = 0; iter < 3; iter++) {\n for (int c = 0; c < min(15, (int)loopCandidates.size()); c++) {\n auto& [dval, ti, tj, loop] = loopCandidates[c];\n if (currentBest.size() + loop.size() > 100000) continue;\n \n string candidate = currentBest + loop;\n long double score = fastEvaluate(candidate);\n if (score < currentScore) {\n currentScore = score;\n currentBest = candidate;\n if (score < bestScore) {\n bestScore = score;\n bestPath = currentBest;\n }\n }\n }\n }\n \n // Try multiple loops to same high-d cell\n for (int c = 0; c < min(5, (int)loopCandidates.size()); c++) {\n auto& [dval, ti, tj, loop] = loopCandidates[c];\n string candidate = bestPath;\n for (int rep = 1; rep <= 10 && candidate.size() + loop.size() <= 100000; rep++) {\n candidate += loop;\n tryPath(candidate);\n }\n }\n \n cout << bestPath << endl;\n return 0;\n}","ahc028":"#include \nusing namespace std;\n\nint N, M, si, sj;\nvector A;\nmap>> charPos;\n\nint overlap(const string& a, const string& b) {\n int maxOv = min((int)a.length(), (int)b.length());\n for (int ov = maxOv; ov >= 1; ov--) {\n if (a.substr(a.length() - ov) == b.substr(0, ov)) return ov;\n }\n return 0;\n}\n\nstring buildSuperstring(vector& t) {\n vector remaining = t;\n \n while (remaining.size() > 1) {\n int bestOv = -1, bestI = -1, bestJ = -1;\n \n for (int i = 0; i < (int)remaining.size(); i++) {\n for (int j = 0; j < (int)remaining.size(); j++) {\n if (i != j) {\n int ov = overlap(remaining[i], remaining[j]);\n if (ov > bestOv) { bestOv = ov; bestI = i; bestJ = j; }\n }\n }\n }\n \n string merged = remaining[bestI] + remaining[bestJ].substr(bestOv);\n \n vector newRemaining;\n for (int k = 0; k < (int)remaining.size(); k++) {\n if (k != bestI && k != bestJ) {\n if (merged.find(remaining[k]) == string::npos)\n newRemaining.push_back(remaining[k]);\n }\n }\n newRemaining.push_back(merged);\n remaining = newRemaining;\n }\n return remaining[0];\n}\n\npair>> computePath(const string& ss) {\n int n = ss.length();\n if (n == 0) return {0, {}};\n \n // dp[pos][idx] = min cost from pos to end, starting at charPos[ss[pos]][idx]\n vector> dp(n);\n \n for (int pos = n - 1; pos >= 0; pos--) {\n char c = ss[pos];\n int sz = charPos[c].size();\n dp[pos].resize(sz);\n \n if (pos == n - 1) {\n for (int idx = 0; idx < sz; idx++) dp[pos][idx] = 0;\n } else {\n char nc = ss[pos + 1];\n for (int idx = 0; idx < sz; idx++) {\n auto [r, col] = charPos[c][idx];\n int best = INT_MAX;\n for (int nidx = 0; nidx < (int)charPos[nc].size(); nidx++) {\n auto [nr, ncol] = charPos[nc][nidx];\n int dist = abs(nr - r) + abs(ncol - col) + 1;\n best = min(best, dist + dp[pos + 1][nidx]);\n }\n dp[pos][idx] = best;\n }\n }\n }\n \n // Find best starting position\n char c0 = ss[0];\n int bestCost = INT_MAX, bestIdx = 0;\n for (int idx = 0; idx < (int)charPos[c0].size(); idx++) {\n auto [r, col] = charPos[c0][idx];\n int dist = abs(r - si) + abs(col - sj) + 1;\n int total = dist + dp[0][idx];\n if (total < bestCost) { bestCost = total; bestIdx = idx; }\n }\n \n // Reconstruct path\n vector> path(n);\n int curI = si, curJ = sj;\n for (int pos = 0; pos < n; pos++) {\n char c = ss[pos];\n int best = INT_MAX, bIdx = 0;\n for (int idx = 0; idx < (int)charPos[c].size(); idx++) {\n auto [r, col] = charPos[c][idx];\n int dist = abs(r - curI) + abs(col - curJ) + 1;\n int total = dist + dp[pos][idx];\n if (total < best) { best = total; bIdx = idx; }\n }\n path[pos] = charPos[c][bIdx];\n curI = path[pos].first;\n curJ = path[pos].second;\n }\n \n return {bestCost, path};\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> si >> sj;\n A.resize(N);\n for (int i = 0; i < N; i++) {\n cin >> A[i];\n for (int j = 0; j < N; j++)\n charPos[A[i][j]].push_back({i, j});\n }\n \n vector t(M);\n for (int i = 0; i < M; i++) cin >> t[i];\n \n string ss = buildSuperstring(t);\n auto [cost, path] = computePath(ss);\n \n for (auto& [i, j] : path)\n cout << i << \" \" << j << \"\\n\";\n \n return 0;\n}","ahc030":"#include \nusing namespace std;\n\nint N, M;\ndouble eps;\nvector>> shapes;\nmap, int> drilled;\nset> confirmed_oil, confirmed_no_oil;\nint qcount = 0;\n\nint queryDrill(int i, int j) {\n pair key = make_pair(i, j);\n if (drilled.count(key)) return drilled[key];\n cout << \"q 1 \" << i << \" \" << j << \"\\n\" << flush;\n qcount++;\n int v; cin >> v;\n drilled[key] = v;\n if (v > 0) confirmed_oil.insert(key);\n else confirmed_no_oil.insert(key);\n return v;\n}\n\nint queryDivine(const vector>& cells) {\n cout << \"q \" << cells.size();\n for (auto& c : cells) cout << \" \" << c.first << \" \" << c.second;\n cout << \"\\n\" << flush;\n qcount++;\n int v; cin >> v;\n return v;\n}\n\nint submit(set> oil) {\n for (auto& c : confirmed_oil) oil.insert(c);\n cout << \"a \" << oil.size();\n for (auto& c : oil) cout << \" \" << c.first << \" \" << c.second;\n cout << \"\\n\" << flush;\n int r; cin >> r;\n return r;\n}\n\nvector>>> placements;\n\nvoid filterPlacements() {\n for (int m = 0; m < M; m++) {\n vector>> valid;\n for (auto& p : placements[m]) {\n bool ok = true;\n for (auto& c : confirmed_no_oil) {\n if (p.count(c)) { ok = false; break; }\n }\n if (ok) valid.push_back(p);\n }\n if (!valid.empty()) placements[m] = valid;\n }\n}\n\nbool allUnique() {\n for (int m = 0; m < M; m++)\n if (placements[m].size() > 1) return false;\n return true;\n}\n\nset> getAnswer() {\n set> answer;\n for (int m = 0; m < M; m++) {\n if (!placements[m].empty()) {\n for (auto& c : placements[m][0]) answer.insert(c);\n }\n }\n return answer;\n}\n\nset> getPossible() {\n set> possible;\n for (int m = 0; m < M; m++)\n for (auto& p : placements[m])\n for (auto& c : p) possible.insert(c);\n return possible;\n}\n\npair getBestCell(const vector>& prob) {\n map, vector> cellToField;\n for (int m = 0; m < M; m++) {\n set> inAny;\n for (auto& p : placements[m])\n for (auto& c : p) inAny.insert(c);\n for (auto& c : inAny)\n cellToField[c].push_back(m);\n }\n \n pair best = {-1, -1};\n double bestScore = -1;\n \n for (auto& [cell, fields] : cellToField) {\n if (drilled.count(cell)) continue;\n \n int eliminates = 0;\n for (int m : fields) {\n for (auto& p : placements[m]) {\n if (p.count(cell)) eliminates++;\n }\n }\n \n // Prefer cells with low probability (likely no oil) that eliminate many\n double score = eliminates * (1.0 - prob[cell.first][cell.second]);\n if (score > bestScore) {\n bestScore = score;\n best = cell;\n }\n }\n return best;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> eps;\n shapes.resize(M);\n \n for (int m = 0; m < M; m++) {\n int d; cin >> d;\n shapes[m].resize(d);\n for (int i = 0; i < d; i++)\n cin >> shapes[m][i].first >> shapes[m][i].second;\n }\n \n placements.resize(M);\n for (int m = 0; m < M; m++) {\n int maxI = 0, maxJ = 0;\n for (auto& c : shapes[m]) {\n maxI = max(maxI, c.first);\n maxJ = max(maxJ, c.second);\n }\n for (int di = 0; di + maxI < N; di++) {\n for (int dj = 0; dj + maxJ < N; dj++) {\n set> cells;\n for (auto& c : shapes[m])\n cells.insert(make_pair(di + c.first, dj + c.second));\n placements[m].push_back(cells);\n }\n }\n }\n \n vector> prob(N, vector(N, 0.5));\n \n // Row divination\n vector rowEst(N);\n for (int i = 0; i < N; i++) {\n vector> row;\n for (int j = 0; j < N; j++) row.push_back({i, j});\n rowEst[i] = queryDivine(row);\n double est = max(0.0, (rowEst[i] - N * eps) / (1 - 2 * eps));\n for (int j = 0; j < N; j++)\n prob[i][j] = min(1.0, est / N);\n }\n \n // Column divination\n vector colEst(N);\n for (int j = 0; j < N; j++) {\n vector> col;\n for (int i = 0; i < N; i++) col.push_back({i, j});\n colEst[j] = queryDivine(col);\n double est = max(0.0, (colEst[j] - N * eps) / (1 - 2 * eps));\n for (int i = 0; i < N; i++)\n prob[i][j] = (prob[i][j] + min(1.0, est / N)) / 2;\n }\n \n while (qcount < 2*N*N - 5 && !allUnique()) {\n auto cell = getBestCell(prob);\n if (cell.first < 0) break;\n \n queryDrill(cell.first, cell.second);\n filterPlacements();\n }\n \n set> answer = allUnique() ? getAnswer() : getPossible();\n for (auto& c : confirmed_no_oil) answer.erase(c);\n \n if (!submit(answer)) {\n answer = getPossible();\n for (auto& c : confirmed_no_oil) answer.erase(c);\n if (!submit(answer)) {\n for (int i = 0; i < N && qcount < 2*N*N - 1; i++)\n for (int j = 0; j < N && qcount < 2*N*N - 1; j++)\n if (!drilled.count({i,j})) queryDrill(i, j);\n submit(confirmed_oil);\n }\n }\n \n return 0;\n}","ahc031":"#include \nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int W, D, N;\n cin >> W >> D >> N;\n \n vector> a(D, vector(N));\n for (int d = 0; d < D; d++) {\n for (int k = 0; k < N; k++) {\n cin >> a[d][k];\n }\n }\n \n for (int d = 0; d < D; d++) {\n vector h(N);\n int totalH = 0;\n \n // Calculate minimum height needed for each reservation\n for (int k = 0; k < N; k++) {\n h[k] = (a[d][k] + W - 1) / W; // ceil(a[k] / W)\n if (h[k] == 0) h[k] = 1;\n totalH += h[k];\n }\n \n if (totalH > W) {\n int excess = totalH - W;\n \n // Calculate slack for each: extra area at current height\n vector> slack(N);\n for (int k = 0; k < N; k++) {\n slack[k] = {h[k] * W - a[d][k], k};\n }\n sort(slack.begin(), slack.end(), greater>());\n \n // Reduce heights of those with most slack first\n for (int i = 0; i < N && excess > 0; i++) {\n int k = slack[i].second;\n while (h[k] > 1 && excess > 0) {\n int newSlack = (h[k] - 1) * W - a[d][k];\n if (newSlack >= 0) {\n h[k]--;\n excess--;\n } else {\n break;\n }\n }\n }\n \n // If still excess, reduce even with penalties (larger reservations last)\n for (int k = 0; k < N && excess > 0; k++) {\n while (h[k] > 1 && excess > 0) {\n h[k]--;\n excess--;\n }\n }\n } else if (totalH < W) {\n int extra = W - totalH;\n // Distribute extra space, prioritizing larger reservations\n while (extra > 0) {\n for (int k = N - 1; k >= 0 && extra > 0; k--) {\n h[k]++;\n extra--;\n }\n }\n }\n \n // Output rectangles\n int y = 0;\n for (int k = 0; k < N; k++) {\n cout << y << \" 0 \" << y + h[k] << \" \" << W << \"\\n\";\n y += h[k];\n }\n }\n \n return 0;\n}","ahc032":"#include \nusing namespace std;\n\nconst long long P = 998244353;\nint N, M, K;\nvector> a_init;\nvector, 3>> stamps;\n\nlong long calcScore(const vector>& a) {\n long long s = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n s += a[i][j];\n return s;\n}\n\nvoid applyOp(vector>& a, int m, int p, int q) {\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n a[p+i][q+j] = (a[p+i][q+j] + stamps[m][i][j]) % P;\n}\n\nlong long calcGain(const vector>& a, int m, int p, int q) {\n long long gain = 0;\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n gain += (a[p+i][q+j] + stamps[m][i][j]) % P - a[p+i][q+j];\n return gain;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(0);\n \n cin >> N >> M >> K;\n a_init.assign(N, vector(N));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n cin >> a_init[i][j];\n a_init[i][j] %= P;\n }\n \n stamps.resize(M);\n for (int m = 0; m < M; m++)\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n cin >> stamps[m][i][j];\n \n auto start = chrono::steady_clock::now();\n auto elapsed = [&]() { return chrono::duration(chrono::steady_clock::now() - start).count(); };\n \n vector> best_ops;\n long long best_score = calcScore(a_init);\n \n mt19937 rng(12345);\n \n for (int trial = 0; elapsed() < 1.85; trial++) {\n vector> ops;\n auto a = a_init;\n \n // Randomized greedy\n for (int op = 0; op < K; op++) {\n vector> cands;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N-3; p++)\n for (int q = 0; q <= N-3; q++) {\n long long gain = calcGain(a, m, p, q);\n if (gain > 0) cands.push_back({gain, m, p, q});\n }\n if (cands.empty()) break;\n sort(cands.rbegin(), cands.rend());\n int pick = (trial == 0) ? 0 : rng() % min((int)cands.size(), 1 + trial);\n auto [g, m, p, q] = cands[pick];\n applyOp(a, m, p, q);\n ops.push_back({m, p, q});\n }\n \n // Local optimization passes\n for (int iter = 0; iter < 5 && elapsed() < 1.85; iter++) {\n bool improved = false;\n \n // Try replacing each operation\n for (int idx = 0; idx < (int)ops.size() && elapsed() < 1.85; idx++) {\n auto orig = ops[idx];\n auto a2 = a_init;\n for (int k = 0; k < (int)ops.size(); k++)\n if (k != idx) {\n auto [m,p,q] = ops[k];\n applyOp(a2, m, p, q);\n }\n \n long long bestGain = 0;\n int bm=-1, bp=-1, bq=-1;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N-3; p++)\n for (int q = 0; q <= N-3; q++) {\n long long gain = calcGain(a2, m, p, q);\n if (gain > bestGain) { bestGain = gain; bm=m; bp=p; bq=q; }\n }\n \n if (bm != -1) {\n ops[idx] = {bm, bp, bq};\n a = a2;\n applyOp(a, bm, bp, bq);\n if (make_tuple(bm,bp,bq) != orig) improved = true;\n }\n }\n \n // Try removing operations that hurt\n for (int idx = (int)ops.size()-1; idx >= 0 && elapsed() < 1.85; idx--) {\n auto a2 = a_init;\n for (int k = 0; k < (int)ops.size(); k++)\n if (k != idx) {\n auto [m,p,q] = ops[k];\n applyOp(a2, m, p, q);\n }\n if (calcScore(a2) >= calcScore(a)) {\n ops.erase(ops.begin() + idx);\n a = a2;\n improved = true;\n }\n }\n \n // Try adding more operations\n while (ops.size() < (size_t)K && elapsed() < 1.85) {\n long long bestGain = 0;\n int bm=-1, bp=-1, bq=-1;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N-3; p++)\n for (int q = 0; q <= N-3; q++) {\n long long gain = calcGain(a, m, p, q);\n if (gain > bestGain) { bestGain = gain; bm=m; bp=p; bq=q; }\n }\n if (bm == -1) break;\n applyOp(a, bm, bp, bq);\n ops.push_back({bm, bp, bq});\n improved = true;\n }\n \n if (!improved) break;\n }\n \n long long score = calcScore(a);\n if (score > best_score) {\n best_score = score;\n best_ops = ops;\n }\n }\n \n cout << best_ops.size() << \"\\n\";\n for (auto& [m,p,q] : best_ops) cout << m << \" \" << p << \" \" << q << \"\\n\";\n}","ahc033":"#include \nusing namespace std;\n\nconst int N = 5;\nint A[N][N];\nint grid[N][N];\nint cr[N], cc[N], hold[N];\nint next_in[N];\nstring ans[N];\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n; cin >> n;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n cin >> A[i][j];\n \n memset(grid, -1, sizeof(grid));\n memset(hold, -1, sizeof(hold));\n memset(next_in, 0, sizeof(next_in));\n for (int i = 0; i < N; i++) { cr[i] = i; cc[i] = 0; }\n \n for (int t = 0; t < 5000; t++) {\n // Step 1: Bring in containers\n for (int i = 0; i < N; i++) {\n if (next_in[i] < N && grid[i][0] == -1) {\n bool blocked = false;\n for (int c = 0; c < N; c++)\n if (cr[c] == i && cc[c] == 0 && hold[c] != -1)\n blocked = true;\n if (!blocked) grid[i][0] = A[i][next_in[i]++];\n }\n }\n \n // Decide moves\n char moves[N];\n for (int c = 0; c < N; c++) moves[c] = '.';\n \n for (int c = 0; c < N; c++) {\n int r = cr[c], col = cc[c];\n \n if (hold[c] == -1) {\n if (grid[r][col] != -1) {\n moves[c] = 'P';\n } else if (col > 0) {\n moves[c] = 'L';\n }\n } else {\n int target_row = hold[c] / N;\n if (col < N-1) {\n bool can_move = (c == 0 || grid[r][col+1] == -1);\n if (can_move) moves[c] = 'R';\n } else {\n moves[c] = 'Q';\n }\n }\n }\n \n // Step 2: Execute moves\n for (int c = 0; c < N; c++) {\n char m = moves[c];\n if (m == 'P') {\n hold[c] = grid[cr[c]][cc[c]];\n grid[cr[c]][cc[c]] = -1;\n } else if (m == 'Q') {\n grid[cr[c]][cc[c]] = hold[c];\n hold[c] = -1;\n } else if (m == 'R') cc[c]++;\n else if (m == 'L') cc[c]--;\n else if (m == 'U') cr[c]--;\n else if (m == 'D') cr[c]++;\n }\n \n // Step 3: Dispatch\n for (int i = 0; i < N; i++) grid[i][N-1] = -1;\n \n for (int c = 0; c < N; c++) ans[c] += moves[c];\n \n // Check if done\n bool done = true;\n for (int i = 0; i < N; i++) if (next_in[i] < N) done = false;\n for (int c = 0; c < N; c++) if (hold[c] != -1) done = false;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (grid[i][j] != -1) done = false;\n if (done) break;\n }\n \n // Trim trailing dots\n size_t maxlen = 0;\n for (int i = 0; i < N; i++) maxlen = max(maxlen, ans[i].size());\n \n while (maxlen > 1) {\n bool all_dot = true;\n for (int i = 0; i < N; i++) {\n if (ans[i].size() >= maxlen && ans[i][maxlen-1] != '.') all_dot = false;\n }\n if (!all_dot) break;\n maxlen--;\n for (int i = 0; i < N; i++)\n if (ans[i].size() > maxlen) ans[i].resize(maxlen);\n }\n \n for (int i = 0; i < N; i++) cout << ans[i] << \"\\n\";\n return 0;\n}","ahc034":"#include \nusing namespace std;\n\nint N;\nvector> h;\nvector ops;\nint cx = 0, cy = 0;\nint load = 0;\n\nvoid do_load(int d) {\n if (d <= 0) return;\n ops.push_back(\"+\" + to_string(d));\n load += d;\n h[cx][cy] -= d;\n}\n\nvoid do_unload(int d) {\n if (d <= 0) return;\n ops.push_back(\"-\" + to_string(d));\n load -= d;\n h[cx][cy] += d;\n}\n\nvoid move_one(char dir) {\n ops.push_back(string(1, dir));\n if (dir == 'U') cx--;\n else if (dir == 'D') cx++;\n else if (dir == 'L') cy--;\n else if (dir == 'R') cy++;\n}\n\nvoid process_cell() {\n // Opportunistically load if positive\n if (h[cx][cy] > 0) {\n do_load(h[cx][cy]);\n }\n // Opportunistically unload if negative and we have load\n if (h[cx][cy] < 0 && load > 0) {\n do_unload(min(load, -h[cx][cy]));\n }\n}\n\nvoid move_to(int tx, int ty, bool opportunistic = false) {\n while (cx < tx) {\n move_one('D');\n if (opportunistic) process_cell();\n }\n while (cx > tx) {\n move_one('U');\n if (opportunistic) process_cell();\n }\n while (cy < ty) {\n move_one('R');\n if (opportunistic) process_cell();\n }\n while (cy > ty) {\n move_one('L');\n if (opportunistic) process_cell();\n }\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N, vector(N));\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n cin >> h[i][j];\n }\n }\n \n while (true) {\n if (load == 0) {\n // Find nearest source\n int si = -1, sj = -1, best_dist = INT_MAX;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (h[i][j] > 0) {\n int dist = abs(i - cx) + abs(j - cy);\n if (dist < best_dist) {\n best_dist = dist;\n si = i; sj = j;\n }\n }\n }\n }\n \n if (si == -1) break;\n \n move_to(si, sj, true);\n if (h[cx][cy] > 0) do_load(h[cx][cy]);\n } else {\n // Find nearest sink\n int ti = -1, tj = -1, best_dist = INT_MAX;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (h[i][j] < 0) {\n int dist = abs(i - cx) + abs(j - cy);\n if (dist < best_dist) {\n best_dist = dist;\n ti = i; tj = j;\n }\n }\n }\n }\n \n if (ti == -1) break;\n \n move_to(ti, tj, true);\n if (h[cx][cy] < 0 && load > 0) {\n do_unload(min(load, -h[cx][cy]));\n }\n }\n }\n \n for (const auto& op : ops) {\n cout << op << \"\\n\";\n }\n \n return 0;\n}","ahc035":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, T;\n cin >> N >> M >> T;\n\n int seed_count = 2 * N * (N - 1);\n vector> X(seed_count, vector(M, 0));\n\n for (int i = 0; i < seed_count; i++) {\n for (int j = 0; j < M; j++) {\n cin >> X[i][j];\n }\n }\n\n for (int t = 0; t < T; t++) {\n // Find max value for each criterion\n vector maxVal(M, -1);\n for (int l = 0; l < M; l++) {\n for (int i = 0; i < seed_count; i++) {\n maxVal[l] = max(maxVal[l], X[i][l]);\n }\n }\n \n // Calculate score for each seed (bonus for having max values)\n vector> seed_scores(seed_count);\n for (int i = 0; i < seed_count; i++) {\n double score = 0;\n for (int l = 0; l < M; l++) {\n if (X[i][l] == maxVal[l]) {\n score += 1000;\n }\n score += X[i][l];\n }\n seed_scores[i] = {score, i};\n }\n \n sort(seed_scores.begin(), seed_scores.end(), greater>());\n \n vector selected(N * N);\n for (int i = 0; i < N * N; i++) {\n selected[i] = seed_scores[i].second;\n }\n \n auto getValue = [&](int idx) {\n int total = 0;\n for (int l = 0; l < M; l++) total += X[idx][l];\n return total;\n };\n \n sort(selected.begin(), selected.end(), [&](int a, int b) {\n return getValue(a) > getValue(b);\n });\n \n vector> pos_order;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n pos_order.push_back({i, j});\n }\n }\n \n double cx = (N - 1) / 2.0;\n double cy = (N - 1) / 2.0;\n sort(pos_order.begin(), pos_order.end(), [&](auto& a, auto& b) {\n double da = abs(a.first - cx) + abs(a.second - cy);\n double db = abs(b.first - cx) + abs(b.second - cy);\n if (da != db) return da < db;\n if (a.first != b.first) return a.first < b.first;\n return a.second < b.second;\n });\n \n vector> A(N, vector(N, -1));\n for (int i = 0; i < N * N; i++) {\n A[pos_order[i].first][pos_order[i].second] = selected[i];\n }\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n cout << A[i][j];\n if (j < N - 1) cout << \" \";\n else cout << \"\\n\";\n }\n }\n cout.flush();\n\n for (int i = 0; i < seed_count; i++) {\n for (int j = 0; j < M; j++) {\n cin >> X[i][j];\n }\n }\n }\n\n return 0;\n}","ahc038":"#include \nusing namespace std;\n\nint N, M, V;\nconst int DX[] = {0, 1, 0, -1};\nconst int DY[] = {1, 0, -1, 0};\n\nint rx, ry;\nvector dirs;\nvector holding;\nint numF;\n\npair fingertip(int i) { return {rx + DX[dirs[i]], ry + DY[dirs[i]]}; }\nbool valid(int x, int y) { return x >= 0 && x < N && y >= 0 && y < N; }\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> V;\n vector grid(N), target(N);\n for (int i = 0; i < N; i++) cin >> grid[i];\n for (int i = 0; i < N; i++) cin >> target[i];\n \n numF = V - 1;\n cout << numF + 1 << \"\\n\";\n for (int i = 1; i <= numF; i++) cout << \"0 1\\n\";\n cout << \"0 0\\n\";\n \n rx = ry = 0;\n dirs.assign(numF, 0);\n holding.assign(numF, false);\n \n set> pickup, dropS;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n if (grid[i][j] == '1' && target[i][j] == '0') pickup.insert({i, j});\n if (target[i][j] == '1' && grid[i][j] == '0') dropS.insert({i, j});\n }\n \n vector ops;\n \n auto makeOp = [&](char mv, vector& rot, vector& act) {\n string s; s += mv;\n for (int i = 0; i < numF; i++) s += rot[i];\n s += '.';\n for (int i = 0; i < numF; i++) s += act[i];\n ops.push_back(s);\n };\n \n while (ops.size() < 95000 && (!pickup.empty() || !dropS.empty() || \n any_of(holding.begin(), holding.end(), [](bool h){return h;}))) {\n \n vector rot(numF, '.'), act(numF, '.');\n bool acted = false;\n \n // Try pick/drop at current positions\n for (int i = 0; i < numF; i++) {\n auto [fx, fy] = fingertip(i);\n if (!valid(fx, fy)) continue;\n if (!holding[i] && pickup.count({fx, fy})) {\n act[i] = 'P'; pickup.erase({fx, fy}); holding[i] = true; acted = true;\n } else if (holding[i] && dropS.count({fx, fy})) {\n act[i] = 'P'; dropS.erase({fx, fy}); holding[i] = false; acted = true;\n }\n }\n if (acted) { makeOp('.', rot, act); continue; }\n \n // Find best target for each fingertip (cached)\n int bestDist = INT_MAX, bestF = -1, bestDir = -1;\n pair bestTarget;\n \n for (int i = 0; i < numF; i++) {\n auto& targets = holding[i] ? dropS : pickup;\n if (targets.empty()) continue;\n \n auto [fx, fy] = fingertip(i);\n for (auto& t : targets) {\n int dist = abs(t.first - fx) + abs(t.second - fy);\n if (dist < bestDist) {\n bestDist = dist;\n bestF = i;\n bestTarget = t;\n }\n }\n }\n \n if (bestF == -1) break;\n \n // Find best direction to reach target\n int tx = bestTarget.first, ty = bestTarget.second;\n bestDist = INT_MAX;\n bestDir = dirs[bestF];\n \n for (int d = 0; d < 4; d++) {\n int nrx = tx - DX[d], nry = ty - DY[d];\n if (!valid(nrx, nry)) continue;\n int diff = (d - dirs[bestF] + 4) % 4;\n int rotCost = min(diff, 4 - diff);\n int dist = abs(nrx - rx) + abs(nry - ry) + rotCost;\n if (dist < bestDist) {\n bestDist = dist;\n bestDir = d;\n }\n }\n \n int trx = tx - DX[bestDir], tr_y = ty - DY[bestDir];\n char mv = '.';\n \n // Move towards target root position\n if (rx < trx && valid(rx + 1, ry)) { mv = 'D'; rx++; }\n else if (rx > trx && valid(rx - 1, ry)) { mv = 'U'; rx--; }\n else if (ry < tr_y && valid(rx, ry + 1)) { mv = 'R'; ry++; }\n else if (ry > tr_y && valid(rx, ry - 1)) { mv = 'L'; ry--; }\n \n // Rotate fingertip towards target direction\n if (dirs[bestF] != bestDir) {\n int diff = (bestDir - dirs[bestF] + 4) % 4;\n if (diff == 1) { rot[bestF] = 'R'; dirs[bestF] = (dirs[bestF] + 1) % 4; }\n else if (diff == 3) { rot[bestF] = 'L'; dirs[bestF] = (dirs[bestF] + 3) % 4; }\n else { rot[bestF] = 'R'; dirs[bestF] = (dirs[bestF] + 1) % 4; }\n }\n \n if (mv == '.' && rot[bestF] == '.') {\n // Stuck - try any move\n if (valid(rx + 1, ry)) { mv = 'D'; rx++; }\n else if (valid(rx - 1, ry)) { mv = 'U'; rx--; }\n else if (valid(rx, ry + 1)) { mv = 'R'; ry++; }\n else if (valid(rx, ry - 1)) { mv = 'L'; ry--; }\n else {\n rot[bestF] = 'R';\n dirs[bestF] = (dirs[bestF] + 1) % 4;\n }\n }\n \n makeOp(mv, rot, act);\n }\n \n for (auto& op : ops) cout << op << \"\\n\";\n return 0;\n}","ahc039":"#include \nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N;\n cin >> N;\n \n vector> mackerel(N), sardine(N);\n for (int i = 0; i < N; i++)\n cin >> mackerel[i].first >> mackerel[i].second;\n for (int i = 0; i < N; i++)\n cin >> sardine[i].first >> sardine[i].second;\n \n vector xs, ys;\n for (auto& p : mackerel) { xs.push_back(p.first); ys.push_back(p.second); }\n for (auto& p : sardine) { xs.push_back(p.first); ys.push_back(p.second); }\n \n sort(xs.begin(), xs.end()); xs.erase(unique(xs.begin(), xs.end()), xs.end());\n sort(ys.begin(), ys.end()); ys.erase(unique(ys.begin(), ys.end()), ys.end());\n \n int nx = xs.size(), ny = ys.size();\n map x_idx, y_idx;\n for (int i = 0; i < nx; i++) x_idx[xs[i]] = i;\n for (int i = 0; i < ny; i++) y_idx[ys[i]] = i;\n \n vector> grid(ny + 1, vector(nx + 1, 0));\n for (auto& p : mackerel) grid[y_idx[p.second] + 1][x_idx[p.first] + 1]++;\n for (auto& p : sardine) grid[y_idx[p.second] + 1][x_idx[p.first] + 1]--;\n \n for (int i = 1; i <= ny; i++)\n for (int j = 1; j <= nx; j++)\n grid[i][j] += grid[i-1][j] + grid[i][j-1] - grid[i-1][j-1];\n \n auto query = [&](int y1, int x1, int y2, int x2) -> int {\n return grid[y2+1][x2+1] - grid[y1][x2+1] - grid[y2+1][x1] + grid[y1][x1];\n };\n \n int best_score = 0;\n int bx1 = 0, by1 = 0, bx2 = 0, by2 = 0;\n \n mt19937 rng(12345);\n \n vector> candidates;\n \n // Random sampling phase\n for (int iter = 0; iter < 300000; iter++) {\n int i1 = rng() % N, i2 = rng() % N;\n int x1i = x_idx[mackerel[i1].first];\n int y1i = y_idx[mackerel[i1].second];\n int x2i = x_idx[mackerel[i2].first];\n int y2i = y_idx[mackerel[i2].second];\n \n if (x1i > x2i) swap(x1i, x2i);\n if (y1i > y2i) swap(y1i, y2i);\n \n int score = query(y1i, x1i, y2i, x2i);\n if (score > best_score - 50) {\n candidates.push_back({score, x1i, y1i, x2i, y2i});\n }\n if (score > best_score) {\n best_score = score;\n bx1 = x1i; by1 = y1i; bx2 = x2i; by2 = y2i;\n }\n }\n \n // Sort candidates and keep top ones\n sort(candidates.rbegin(), candidates.rend());\n if (candidates.size() > 50) candidates.resize(50);\n \n // Optimize each candidate\n for (auto& [sc, cx1, cy1, cx2, cy2] : candidates) {\n // Optimize each edge independently\n for (int round = 0; round < 3; round++) {\n // Optimize x1\n for (int x = 0; x <= cx2; x++) {\n int score = query(cy1, x, cy2, cx2);\n if (score > query(cy1, cx1, cy2, cx2)) cx1 = x;\n }\n // Optimize x2\n for (int x = cx1; x < nx; x++) {\n int score = query(cy1, cx1, cy2, x);\n if (score > query(cy1, cx1, cy2, cx2)) cx2 = x;\n }\n // Optimize y1\n for (int y = 0; y <= cy2; y++) {\n int score = query(y, cx1, cy2, cx2);\n if (score > query(cy1, cx1, cy2, cx2)) cy1 = y;\n }\n // Optimize y2\n for (int y = cy1; y < ny; y++) {\n int score = query(cy1, cx1, y, cx2);\n if (score > query(cy1, cx1, cy2, cx2)) cy2 = y;\n }\n }\n \n int final_score = query(cy1, cx1, cy2, cx2);\n if (final_score > best_score) {\n best_score = final_score;\n bx1 = cx1; by1 = cy1; bx2 = cx2; by2 = cy2;\n }\n }\n \n int outx1 = xs[bx1], outy1 = ys[by1];\n int outx2 = xs[bx2], outy2 = ys[by2];\n \n if (best_score == 0) {\n outx1 = 0; outy1 = 0; outx2 = 1; outy2 = 1;\n }\n \n cout << 4 << \"\\n\";\n cout << outx1 << \" \" << outy1 << \"\\n\";\n cout << outx2 << \" \" << outy1 << \"\\n\";\n cout << outx2 << \" \" << outy2 << \"\\n\";\n cout << outx1 << \" \" << outy2 << \"\\n\";\n \n return 0;\n}","ahc040":"#include \nusing namespace std;\n\nint N, T;\nlong long sigma;\nvector w, h;\n\nstruct PlacedRect { long long x1, y1, x2, y2; int id; };\n\ntuple simulate(const vector>& ops) {\n vector placed;\n long long W = 0, H = 0;\n for (auto& [p, r, d, b] : ops) {\n long long rw = w[p], rh = h[p];\n if (r) swap(rw, rh);\n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n placed.push_back({x, y, x + rw, y + rh, p});\n W = max(W, x + rw); H = max(H, y + rh);\n }\n return {W, H};\n}\n\nmt19937 rng(42);\n\nvector> genGreedy(double wBias = 1.0) {\n vector> ops;\n vector placed;\n long long curW = 0, curH = 0;\n for (int i = 0; i < N; i++) {\n long long best = LLONG_MAX; tuple bc = {0,'U',-1};\n vector bases = {-1};\n for (int j = max(0, i-10); j < i; j++) bases.push_back(j);\n \n for (int r = 0; r < 2; r++) for (char d : {'U','L'}) for (int b : bases) {\n long long rw = w[i], rh = h[i]; if (r) swap(rw, rh);\n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n double sc = wBias * max(curW, x+rw) + max(curH, y+rh);\n if (sc < best) { best = sc; bc = {r, d, b}; }\n }\n auto [r, d, b] = bc;\n long long rw = w[i], rh = h[i]; if (r) swap(rw, rh);\n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n placed.push_back({x, y, x+rw, y+rh, i}); curW = max(curW, x+rw); curH = max(curH, y+rh);\n ops.push_back({i, r, d, b});\n }\n return ops;\n}\n\nvector> genShelf(double widthFactor) {\n long long totalArea = 0;\n for (int i = 0; i < N; i++) totalArea += w[i] * h[i];\n long long targetW = (long long)(sqrt(totalArea) * widthFactor);\n \n vector> ops;\n long long curX = 0, shelfH = 0;\n int lastInShelf = -1;\n \n for (int i = 0; i < N; i++) {\n int r = (h[i] > w[i]) ? 1 : 0;\n long long rw = w[i], rh = h[i]; if (r) swap(rw, rh);\n \n if (curX + rw > targetW && lastInShelf >= 0) {\n ops.push_back({i, r, 'L', lastInShelf});\n curX = rw; shelfH = rh; lastInShelf = i;\n } else {\n if (lastInShelf < 0) {\n ops.push_back({i, r, 'U', -1});\n } else {\n ops.push_back({i, r, 'U', lastInShelf});\n }\n curX += rw; shelfH = max(shelfH, rh); lastInShelf = i;\n }\n }\n return ops;\n}\n\nvector> genStrip(char dir, int rotMode) {\n vector> ops;\n for (int i = 0; i < N; i++) {\n int r = (rotMode == 0) ? 0 : (rotMode == 1) ? 1 : \n ((dir == 'U') ? (w[i] < h[i] ? 1 : 0) : (h[i] < w[i] ? 1 : 0));\n ops.push_back({i, r, dir, -1});\n }\n return ops;\n}\n\nvector> mutate(vector> ops, int intensity) {\n int numMut = 1 + rng() % (intensity + 1);\n for (int m = 0; m < numMut; m++) {\n int i = rng() % N;\n auto& [p, r, d, b] = ops[i];\n int choice = rng() % 3;\n if (choice == 0) r = 1 - r;\n else if (choice == 1) d = (d == 'U') ? 'L' : 'U';\n else if (i > 0) b = (int)(rng() % (i + 1)) - 1;\n }\n return ops;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> T >> sigma;\n w.resize(N); h.resize(N);\n for (int i = 0; i < N; i++) cin >> w[i] >> h[i];\n \n vector>>> candidates;\n \n auto addCandidate = [&](vector> ops) {\n auto [sw, sh] = simulate(ops);\n candidates.push_back({sw + sh, ops});\n };\n \n // Generate diverse initial candidates\n for (double bias : {0.8, 1.0, 1.2}) addCandidate(genGreedy(bias));\n for (double wf : {0.8, 1.0, 1.2, 1.5, 2.0}) addCandidate(genShelf(wf));\n for (char d : {'U', 'L'}) for (int rm = 0; rm < 3; rm++) addCandidate(genStrip(d, rm));\n \n sort(candidates.begin(), candidates.end());\n auto bestOps = candidates[0].second;\n long long bestSim = candidates[0].first;\n \n // Hill climbing\n auto startTime = chrono::steady_clock::now();\n for (int iter = 0; (int)candidates.size() < T * 3; iter++) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration_cast(now - startTime).count() > 2500) break;\n \n int srcIdx = (rng() % 100 < 80) ? 0 : rng() % min((int)candidates.size(), 5);\n auto ops = mutate(candidates[srcIdx].second, 1 + iter / 2000);\n auto [sw, sh] = simulate(ops);\n \n if (sw + sh <= bestSim * 1.05) {\n candidates.push_back({sw + sh, ops});\n if (sw + sh < bestSim) { bestSim = sw + sh; bestOps = ops; }\n }\n }\n \n sort(candidates.begin(), candidates.end());\n candidates.erase(unique(candidates.begin(), candidates.end()), candidates.end());\n if ((int)candidates.size() > T) candidates.resize(T);\n \n while ((int)candidates.size() < T) {\n auto ops = mutate(bestOps, 2);\n auto [sw, sh] = simulate(ops);\n candidates.push_back({sw + sh, ops});\n }\n \n sort(candidates.begin(), candidates.end());\n \n long long bestObserved = LLONG_MAX;\n int bestIdx = 0;\n \n for (int t = 0; t < T; t++) {\n auto& ops = candidates[min(t, (int)candidates.size()-1)].second;\n \n cout << ops.size() << \"\\n\";\n for (auto& [p, r, d, b] : ops) cout << p << \" \" << r << \" \" << d << \" \" << b << \"\\n\";\n cout.flush();\n \n long long W, H; cin >> W >> H;\n if (W + H < bestObserved) { bestObserved = W + H; bestIdx = t; }\n }\n \n return 0;\n}","ahc041":"#include \nusing namespace std;\n\nint N, M, H;\nvector A;\nvector> adj;\nvector parent_arr;\nvector depth_arr;\n\nlong long compute_score() {\n long long score = 0;\n for (int i = 0; i < N; i++) {\n score += (long long)(depth_arr[i] + 1) * A[i];\n }\n return score;\n}\n\nvoid rebuild_depths() {\n vector> children(N);\n for (int i = 0; i < N; i++) {\n if (parent_arr[i] != -1) {\n children[parent_arr[i]].push_back(i);\n }\n }\n \n fill(depth_arr.begin(), depth_arr.end(), -1);\n queue q;\n for (int i = 0; i < N; i++) {\n if (parent_arr[i] == -1) {\n depth_arr[i] = 0;\n q.push(i);\n }\n }\n while (!q.empty()) {\n int u = q.front(); q.pop();\n for (int c : children[u]) {\n depth_arr[c] = depth_arr[u] + 1;\n q.push(c);\n }\n }\n}\n\nvoid dfs(int u) {\n vector> neighbors;\n for (int v : adj[u]) {\n if (depth_arr[v] == -1) {\n neighbors.push_back({-A[v], v});\n }\n }\n sort(neighbors.begin(), neighbors.end());\n \n for (auto& [neg_beauty, v] : neighbors) {\n if (depth_arr[v] == -1 && depth_arr[u] < H) {\n parent_arr[v] = u;\n depth_arr[v] = depth_arr[u] + 1;\n dfs(v);\n }\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n auto start_time = chrono::steady_clock::now();\n auto elapsed = [&]() {\n return chrono::duration_cast(\n chrono::steady_clock::now() - start_time).count();\n };\n \n cin >> N >> M >> H;\n \n A.resize(N);\n for (int i = 0; i < N; i++) {\n cin >> A[i];\n }\n \n adj.resize(N);\n for (int i = 0; i < M; i++) {\n int u, v;\n cin >> u >> v;\n adj[u].push_back(v);\n adj[v].push_back(u);\n }\n \n for (int i = 0; i < N; i++) {\n int x, y;\n cin >> x >> y;\n }\n \n parent_arr.resize(N, -1);\n depth_arr.resize(N, -1);\n \n vector best_parent(N, -1);\n long long best_score = 0;\n \n mt19937 rng(12345);\n \n // Multiple restarts with different strategies\n for (int trial = 0; trial < 200 && elapsed() < 800; trial++) {\n fill(parent_arr.begin(), parent_arr.end(), -1);\n fill(depth_arr.begin(), depth_arr.end(), -1);\n \n vector order(N);\n iota(order.begin(), order.end(), 0);\n \n if (trial == 0) {\n // Sort by beauty ascending\n sort(order.begin(), order.end(), [&](int a, int b) {\n return A[a] < A[b];\n });\n } else if (trial == 1) {\n // Sort by degree ascending (low degree = likely leaf = good root)\n sort(order.begin(), order.end(), [&](int a, int b) {\n return adj[a].size() < adj[b].size();\n });\n } else {\n // Random with bias toward low beauty\n vector keys(N);\n for (int i = 0; i < N; i++) {\n keys[i] = A[i] + (rng() % 60);\n }\n sort(order.begin(), order.end(), [&](int a, int b) {\n return keys[a] < keys[b];\n });\n }\n \n for (int start : order) {\n if (depth_arr[start] != -1) continue;\n depth_arr[start] = 0;\n parent_arr[start] = -1;\n dfs(start);\n }\n \n long long score = compute_score();\n if (score > best_score) {\n best_score = score;\n best_parent = parent_arr;\n }\n }\n \n parent_arr = best_parent;\n rebuild_depths();\n \n // Local search\n function>&)> calc_height = [&](int v, const vector>& ch) -> int {\n int h = 0;\n for (int c : ch[v]) {\n h = max(h, 1 + calc_height(c, ch));\n }\n return h;\n };\n \n for (int iter = 0; iter < 100 && elapsed() < 1900; iter++) {\n bool improved = false;\n \n vector> children(N);\n for (int i = 0; i < N; i++) {\n if (parent_arr[i] != -1) {\n children[parent_arr[i]].push_back(i);\n }\n }\n \n vector sub_h(N, 0);\n for (int i = 0; i < N; i++) {\n sub_h[i] = calc_height(i, children);\n }\n \n vector vorder(N);\n iota(vorder.begin(), vorder.end(), 0);\n sort(vorder.begin(), vorder.end(), [&](int a, int b) {\n return A[a] > A[b];\n });\n \n for (int v : vorder) {\n if (elapsed() > 1900) break;\n \n int cur_depth = depth_arr[v];\n int best_new_parent = -1;\n int best_new_depth = cur_depth;\n \n for (int u : adj[v]) {\n if (u == parent_arr[v]) continue;\n \n // Check if u is in subtree of v\n bool in_subtree = false;\n int p = u;\n while (p != -1) {\n if (p == v) { in_subtree = true; break; }\n p = parent_arr[p];\n }\n if (in_subtree) continue;\n \n int new_depth = depth_arr[u] + 1;\n if (new_depth > best_new_depth && new_depth + sub_h[v] <= H) {\n best_new_depth = new_depth;\n best_new_parent = u;\n }\n }\n \n if (best_new_parent != -1) {\n parent_arr[v] = best_new_parent;\n rebuild_depths();\n \n // Rebuild children and heights\n for (int i = 0; i < N; i++) children[i].clear();\n for (int i = 0; i < N; i++) {\n if (parent_arr[i] != -1) {\n children[parent_arr[i]].push_back(i);\n }\n }\n for (int i = 0; i < N; i++) {\n sub_h[i] = calc_height(i, children);\n }\n improved = true;\n }\n }\n \n if (!improved) break;\n }\n \n // Final output\n for (int i = 0; i < N; i++) {\n cout << parent_arr[i];\n if (i < N - 1) cout << \" \";\n }\n cout << \"\\n\";\n \n return 0;\n}","ahc042":"#include \nusing namespace std;\n\nint N, M;\nvector> onis;\nvector> valid_dirs;\nvector> dists;\n\ninline int get_key(int k, int dir) {\n return dir * N + ((dir <= 1) ? onis[k].second : onis[k].first);\n}\n\nint compute_cost(const vector& assignment) {\n int batch_max[80] = {};\n for (int k = 0; k < M; k++) {\n int key = get_key(k, assignment[k]);\n batch_max[key] = max(batch_max[key], dists[k][assignment[k]]);\n }\n int total = 0;\n for (int i = 0; i < 80; i++) total += 2 * batch_max[i];\n return total;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n vector board(N);\n for (int i = 0; i < N; i++) cin >> board[i];\n \n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (board[i][j] == 'x') onis.push_back({i, j});\n \n M = onis.size();\n valid_dirs.resize(M);\n dists.resize(M);\n \n for (int k = 0; k < M; k++) {\n int r = onis[k].first, c = onis[k].second;\n bool ok = true;\n for (int i = 0; i < r && ok; i++) if (board[i][c] == 'o') ok = false;\n if (ok) { valid_dirs[k].push_back(0); dists[k][0] = r + 1; }\n ok = true;\n for (int i = r+1; i < N && ok; i++) if (board[i][c] == 'o') ok = false;\n if (ok) { valid_dirs[k].push_back(1); dists[k][1] = N - r; }\n ok = true;\n for (int j = 0; j < c && ok; j++) if (board[r][j] == 'o') ok = false;\n if (ok) { valid_dirs[k].push_back(2); dists[k][2] = c + 1; }\n ok = true;\n for (int j = c+1; j < N && ok; j++) if (board[r][j] == 'o') ok = false;\n if (ok) { valid_dirs[k].push_back(3); dists[k][3] = N - c; }\n }\n \n mt19937 rng(42);\n vector best_assignment(M);\n int best_cost = INT_MAX;\n \n auto local_search = [&](vector& asgn) {\n int cur_cost = compute_cost(asgn);\n for (int iter = 0; iter < 100; iter++) {\n bool improved = false;\n for (int k = 0; k < M; k++) {\n int orig = asgn[k];\n for (int dir : valid_dirs[k]) {\n if (dir == orig) continue;\n asgn[k] = dir;\n int nc = compute_cost(asgn);\n if (nc < cur_cost) { cur_cost = nc; improved = true; }\n else asgn[k] = orig;\n }\n }\n if (!improved) break;\n }\n return cur_cost;\n };\n \n for (int trial = 0; trial < 2000; trial++) {\n vector asgn(M);\n \n if (trial == 0) {\n for (int k = 0; k < M; k++) {\n int bd = valid_dirs[k][0];\n for (int d : valid_dirs[k]) if (dists[k][d] < dists[k][bd]) bd = d;\n asgn[k] = bd;\n }\n } else if (trial <= 4) {\n int pref = trial - 1;\n for (int k = 0; k < M; k++) {\n asgn[k] = valid_dirs[k][0];\n for (int d : valid_dirs[k]) if (d == pref) { asgn[k] = d; break; }\n }\n } else if (trial <= 8) {\n int pref = trial - 5;\n for (int k = 0; k < M; k++) {\n asgn[k] = valid_dirs[k][0];\n int bd = dists[k][asgn[k]];\n for (int d : valid_dirs[k]) {\n if (d == pref && dists[k][d] <= bd + 3) { asgn[k] = d; break; }\n }\n }\n } else {\n for (int k = 0; k < M; k++)\n asgn[k] = valid_dirs[k][rng() % valid_dirs[k].size()];\n }\n \n int cost = local_search(asgn);\n if (cost < best_cost) { best_cost = cost; best_assignment = asgn; }\n }\n \n // Simulated annealing from best\n {\n vector asgn = best_assignment;\n int cur_cost = best_cost;\n double temp = 10.0;\n for (int iter = 0; iter < 50000; iter++) {\n int k = rng() % M;\n if (valid_dirs[k].size() <= 1) continue;\n int orig = asgn[k];\n int nd = valid_dirs[k][rng() % valid_dirs[k].size()];\n if (nd == orig) continue;\n asgn[k] = nd;\n int nc = compute_cost(asgn);\n if (nc < cur_cost || (rng() % 1000) < 1000 * exp((cur_cost - nc) / temp)) {\n cur_cost = nc;\n if (cur_cost < best_cost) { best_cost = cur_cost; best_assignment = asgn; }\n } else {\n asgn[k] = orig;\n }\n temp *= 0.99995;\n }\n }\n \n map> batches;\n for (int k = 0; k < M; k++) batches[get_key(k, best_assignment[k])].push_back(k);\n \n vector> ops;\n auto L = [&](int r) { ops.push_back({'L', r}); };\n auto R = [&](int r) { ops.push_back({'R', r}); };\n auto U = [&](int c) { ops.push_back({'U', c}); };\n auto D = [&](int c) { ops.push_back({'D', c}); };\n \n for (auto& [key, lst] : batches) {\n int dir = key / N, idx = key % N;\n int mx = 0;\n for (int k : lst) mx = max(mx, dists[k][dir]);\n if (dir == 0) { for (int t = 0; t < mx; t++) U(idx); for (int t = 0; t < mx; t++) D(idx); }\n else if (dir == 1) { for (int t = 0; t < mx; t++) D(idx); for (int t = 0; t < mx; t++) U(idx); }\n else if (dir == 2) { for (int t = 0; t < mx; t++) L(idx); for (int t = 0; t < mx; t++) R(idx); }\n else { for (int t = 0; t < mx; t++) R(idx); for (int t = 0; t < mx; t++) L(idx); }\n }\n \n for (auto& [d, p] : ops) cout << d << \" \" << p << \"\\n\";\n return 0;\n}","ahc044":"#include \nusing namespace std;\n\nint N, L;\nvector T;\n\nlong long simulate(const vector& a, const vector& b, vector& t) {\n fill(t.begin(), t.end(), 0);\n int x = 0;\n for (int week = 0; week < L; week++) {\n t[x]++;\n x = (t[x] & 1) ? a[x] : b[x];\n }\n long long error = 0;\n for (int i = 0; i < N; i++) error += abs(t[i] - T[i]);\n return error;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> L;\n T.resize(N);\n for (int i = 0; i < N; i++) cin >> T[i];\n \n mt19937 rng(12345);\n \n vector weighted;\n for (int i = 0; i < N; i++) {\n int cnt = max(1, T[i] / 100);\n for (int j = 0; j < cnt; j++) weighted.push_back(i);\n }\n \n vector sorted_idx(N);\n iota(sorted_idx.begin(), sorted_idx.end(), 0);\n sort(sorted_idx.begin(), sorted_idx.end(), [](int x, int y) { return T[x] > T[y]; });\n \n vector best_a(N), best_b(N), t(N);\n long long global_best = LLONG_MAX;\n \n auto start = chrono::steady_clock::now();\n double time_limit = 1.85;\n \n for (int restart = 0; ; restart++) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > time_limit) break;\n \n vector a(N), b(N);\n \n if (restart == 0) {\n for (int i = 0; i < N; i++) {\n a[sorted_idx[i]] = sorted_idx[(i + 1) % N];\n b[sorted_idx[i]] = sorted_idx[(i + 1) % N];\n }\n } else if (restart == 1) {\n for (int i = 0; i < N; i++) {\n a[sorted_idx[i]] = sorted_idx[(i + 1) % N];\n b[sorted_idx[i]] = sorted_idx[(i + 2) % N];\n }\n } else if (restart % 3 == 0 && global_best < LLONG_MAX) {\n a = best_a; b = best_b;\n for (int k = 0; k < N/4; k++) {\n int idx = rng() % N;\n a[idx] = weighted[rng() % weighted.size()];\n b[idx] = weighted[rng() % weighted.size()];\n }\n } else {\n for (int i = 0; i < N; i++) {\n a[i] = weighted[rng() % weighted.size()];\n b[i] = weighted[rng() % weighted.size()];\n }\n }\n \n long long cur_error = simulate(a, b, t);\n long long local_best = cur_error;\n vector local_a = a, local_b = b;\n \n double restart_budget = min(0.25, (time_limit - elapsed) * 0.6);\n double restart_start = elapsed;\n \n while (true) {\n now = chrono::steady_clock::now();\n elapsed = chrono::duration(now - start).count();\n if (elapsed > time_limit || elapsed - restart_start > restart_budget) break;\n \n double progress = (elapsed - restart_start) / restart_budget;\n double temp = 2500.0 * pow(0.0001, progress);\n \n int i = rng() % N;\n int old_a = a[i], old_b = b[i];\n \n int choice = rng() % 4;\n if (choice == 0) a[i] = weighted[rng() % weighted.size()];\n else if (choice == 1) b[i] = weighted[rng() % weighted.size()];\n else if (choice == 2) a[i] = rng() % N;\n else b[i] = rng() % N;\n \n long long new_error = simulate(a, b, t);\n double delta = new_error - cur_error;\n \n if (delta <= 0 || exp(-delta / temp) > (rng() % 1000000) / 1000000.0) {\n cur_error = new_error;\n if (new_error < local_best) {\n local_best = new_error;\n local_a = a; local_b = b;\n }\n } else {\n a[i] = old_a; b[i] = old_b;\n }\n }\n \n if (local_best < global_best) {\n global_best = local_best;\n best_a = local_a; best_b = local_b;\n }\n }\n \n for (int i = 0; i < N; i++) cout << best_a[i] << \" \" << best_b[i] << \"\\n\";\n return 0;\n}","ahc045":"#include \nusing namespace std;\n\nint queries_used = 0;\nint Q_limit;\n\nvector> query(vector& cities) {\n if (queries_used >= Q_limit || cities.size() < 2) return {};\n cout << \"? \" << cities.size();\n for (int c : cities) cout << \" \" << c;\n cout << endl;\n \n vector> edges;\n for (size_t i = 0; i + 1 < cities.size(); i++) {\n int a, b;\n cin >> a >> b;\n edges.emplace_back(a, b);\n }\n queries_used++;\n return edges;\n}\n\ndouble estDist(double x1, double y1, double x2, double y2) {\n double dx = x1 - x2, dy = y1 - y2;\n return sqrt(dx*dx + dy*dy);\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, Q, L, W;\n cin >> N >> M >> Q >> L >> W;\n Q_limit = Q;\n \n vector G(M);\n for (int i = 0; i < M; i++) cin >> G[i];\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) {\n int lx, rx, ly, ry;\n cin >> lx >> rx >> ly >> ry;\n x[i] = (lx + rx) / 2.0;\n y[i] = (ly + ry) / 2.0;\n }\n \n // Greedy nearest-neighbor grouping\n vector used(N, false);\n vector> groups(M);\n \n // Sort groups by size descending to handle large groups first\n vector groupOrder(M);\n iota(groupOrder.begin(), groupOrder.end(), 0);\n sort(groupOrder.begin(), groupOrder.end(), [&](int a, int b) {\n return G[a] > G[b];\n });\n \n for (int gi : groupOrder) {\n int g = G[gi];\n \n // Find starting city (unused city closest to center of remaining unused cities)\n double cx = 0, cy = 0;\n int cnt = 0;\n for (int i = 0; i < N; i++) {\n if (!used[i]) { cx += x[i]; cy += y[i]; cnt++; }\n }\n if (cnt > 0) { cx /= cnt; cy /= cnt; }\n \n int start = -1;\n double minD = 1e18;\n for (int i = 0; i < N; i++) {\n if (!used[i]) {\n double d = estDist(x[i], y[i], cx, cy);\n if (d < minD) { minD = d; start = i; }\n }\n }\n \n groups[gi].push_back(start);\n used[start] = true;\n \n // Greedily add nearest city\n while ((int)groups[gi].size() < g) {\n int best = -1;\n double bestD = 1e18;\n for (int i = 0; i < N; i++) {\n if (used[i]) continue;\n double minDistToGroup = 1e18;\n for (int c : groups[gi]) {\n minDistToGroup = min(minDistToGroup, estDist(x[i], y[i], x[c], y[c]));\n }\n if (minDistToGroup < bestD) {\n bestD = minDistToGroup;\n best = i;\n }\n }\n groups[gi].push_back(best);\n used[best] = true;\n }\n }\n \n vector>> edges(M);\n \n for (int k = 0; k < M; k++) {\n int g = groups[k].size();\n if (g == 1) continue;\n \n // Sort within group for better query locality\n sort(groups[k].begin(), groups[k].end(), [&](int a, int b) {\n return x[a] + y[a] < x[b] + y[b];\n });\n \n vector> all_edges;\n \n if (g <= L && queries_used < Q) {\n edges[k] = query(groups[k]);\n } else {\n // Estimate queries needed and adjust step\n int queriesNeeded = (g - 1 + L - 2) / (L - 1);\n int queriesAvailable = Q - queries_used;\n int step = max(1, (L - 1));\n \n // If we have budget, use smaller step for more overlap\n if (queriesNeeded * 2 <= queriesAvailable) {\n step = max(1, (L - 1) / 2);\n }\n \n for (int i = 0; i < g && queries_used < Q; i += step) {\n int end = min(i + L, g);\n if (end - i >= 2) {\n vector subset(groups[k].begin() + i, groups[k].begin() + end);\n auto e = query(subset);\n all_edges.insert(all_edges.end(), e.begin(), e.end());\n }\n if (end >= g) break;\n }\n \n map city_to_local;\n for (int i = 0; i < g; i++) city_to_local[groups[k][i]] = i;\n \n vector parent(g);\n iota(parent.begin(), parent.end(), 0);\n function find = [&](int u) -> int {\n return parent[u] == u ? u : parent[u] = find(parent[u]);\n };\n \n sort(all_edges.begin(), all_edges.end(), [&](auto& a, auto& b) {\n double da = estDist(x[a.first], y[a.first], x[a.second], y[a.second]);\n double db = estDist(x[b.first], y[b.first], x[b.second], y[b.second]);\n return da < db;\n });\n \n for (auto& e : all_edges) {\n int u = city_to_local[e.first];\n int v = city_to_local[e.second];\n if (find(u) != find(v)) {\n parent[find(u)] = find(v);\n edges[k].push_back(e);\n }\n }\n \n // Fallback: connect components using shortest estimated edges\n while ((int)edges[k].size() < g - 1) {\n double best_dist = 1e18;\n int best_u = -1, best_v = -1;\n for (int i = 0; i < g; i++) {\n for (int j = i + 1; j < g; j++) {\n if (find(i) != find(j)) {\n double d = estDist(x[groups[k][i]], y[groups[k][i]], \n x[groups[k][j]], y[groups[k][j]]);\n if (d < best_dist) {\n best_dist = d;\n best_u = i;\n best_v = j;\n }\n }\n }\n }\n if (best_u >= 0) {\n parent[find(best_u)] = find(best_v);\n edges[k].push_back({groups[k][best_u], groups[k][best_v]});\n } else break;\n }\n }\n }\n \n cout << \"!\" << endl;\n for (int k = 0; k < M; k++) {\n for (int c : groups[k]) cout << c << \" \";\n cout << \"\\n\";\n for (auto& e : edges[k]) {\n cout << e.first << \" \" << e.second << \"\\n\";\n }\n }\n \n return 0;\n}","ahc046":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M;\n cin >> N >> M;\n \n vector> targets(M);\n for (int i = 0; i < M; i++) {\n cin >> targets[i].first >> targets[i].second;\n }\n \n vector actions;\n int curR = targets[0].first, curC = targets[0].second;\n \n for (int i = 1; i < M; i++) {\n int tR = targets[i].first, tC = targets[i].second;\n \n int moveCost = abs(tR - curR) + abs(tC - curC);\n int bestCost = moveCost;\n int bestStrategy = 0;\n \n // Edge target strategies (1-4)\n if (tR == 0 && curR > 0) {\n int cost = abs(tC - curC) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 1; }\n }\n if (tR == N - 1 && curR < N - 1) {\n int cost = abs(tC - curC) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 2; }\n }\n if (tC == 0 && curC > 0) {\n int cost = abs(tR - curR) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 3; }\n }\n if (tC == N - 1 && curC < N - 1) {\n int cost = abs(tR - curR) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 4; }\n }\n \n // Slide-first strategies (5-8)\n if (curR > 0) {\n int cost = 1 + tR + abs(tC - curC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 5; }\n }\n if (curR < N - 1) {\n int cost = 1 + (N - 1 - tR) + abs(tC - curC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 6; }\n }\n if (curC > 0) {\n int cost = 1 + tC + abs(tR - curR);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 7; }\n }\n if (curC < N - 1) {\n int cost = 1 + (N - 1 - tC) + abs(tR - curR);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 8; }\n }\n \n // Double-slide to corners (9-12)\n if (curR > 0 && curC > 0) { // to (0,0)\n int cost = 2 + tR + tC;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 9; }\n }\n if (curR > 0 && curC < N - 1) { // to (0, N-1)\n int cost = 2 + tR + (N - 1 - tC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 10; }\n }\n if (curR < N - 1 && curC > 0) { // to (N-1, 0)\n int cost = 2 + (N - 1 - tR) + tC;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 11; }\n }\n if (curR < N - 1 && curC < N - 1) { // to (N-1, N-1)\n int cost = 2 + (N - 1 - tR) + (N - 1 - tC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 12; }\n }\n \n switch (bestStrategy) {\n case 0:\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n break;\n case 1: case 2: case 3: case 4:\n if (bestStrategy <= 2) {\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n actions.push_back(bestStrategy == 1 ? \"S U\" : \"S D\");\n curR = (bestStrategy == 1) ? 0 : N - 1;\n } else {\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n actions.push_back(bestStrategy == 3 ? \"S L\" : \"S R\");\n curC = (bestStrategy == 3) ? 0 : N - 1;\n }\n break;\n case 5: actions.push_back(\"S U\"); curR = 0; goto moveToTarget;\n case 6: actions.push_back(\"S D\"); curR = N - 1; goto moveToTarget;\n case 7: actions.push_back(\"S L\"); curC = 0; goto moveToTarget;\n case 8: actions.push_back(\"S R\"); curC = N - 1; goto moveToTarget;\n case 9: actions.push_back(\"S U\"); curR = 0; actions.push_back(\"S L\"); curC = 0; goto moveToTarget;\n case 10: actions.push_back(\"S U\"); curR = 0; actions.push_back(\"S R\"); curC = N - 1; goto moveToTarget;\n case 11: actions.push_back(\"S D\"); curR = N - 1; actions.push_back(\"S L\"); curC = 0; goto moveToTarget;\n case 12: actions.push_back(\"S D\"); curR = N - 1; actions.push_back(\"S R\"); curC = N - 1; goto moveToTarget;\n moveToTarget:\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n break;\n }\n }\n \n for (const string& action : actions) {\n cout << action << \"\\n\";\n }\n \n return 0;\n}"},"8":{"ahc001":"#include \nusing namespace std;\n\nconst int W = 10000;\nint n;\nvector px, py, rr;\nint a[201], b[201], c[201], d[201];\n\nbool canExpand(int i, int dir) {\n int na = a[i], nb = b[i], nc = c[i], nd = d[i];\n if (dir == 0) na--; else if (dir == 1) nc++; else if (dir == 2) nb--; else nd++;\n if (na < 0 || nc > W || nb < 0 || nd > W) return false;\n for (int j = 0; j < n; j++) {\n if (i != j && !(nc <= a[j] || c[j] <= na || nd <= b[j] || d[j] <= nb)) return false;\n }\n return true;\n}\n\nvoid doExpand(int i, int dir) {\n if (dir == 0) a[i]--; else if (dir == 1) c[i]++; else if (dir == 2) b[i]--; else d[i]++;\n}\n\nlong long area(int i) { return (long long)(c[i] - a[i]) * (d[i] - b[i]); }\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> n;\n px.resize(n); py.resize(n); rr.resize(n);\n for (int i = 0; i < n; i++) {\n cin >> px[i] >> py[i] >> rr[i];\n a[i] = px[i]; b[i] = py[i]; c[i] = px[i]+1; d[i] = py[i]+1;\n }\n \n auto start = chrono::high_resolution_clock::now();\n auto timeOk = [&]() {\n return chrono::duration(chrono::high_resolution_clock::now() - start).count() < 4.7;\n };\n \n // Phase 1: Expand only up to target, prioritize by relative deficit\n while (timeOk()) {\n bool changed = false;\n vector order(n);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int i, int j) {\n double di = (double)(rr[i] - area(i)) / rr[i];\n double dj = (double)(rr[j] - area(j)) / rr[j];\n return di > dj;\n });\n \n for (int i : order) {\n if (area(i) >= rr[i]) continue;\n for (int dir = 0; dir < 4; dir++) {\n if (area(i) >= rr[i]) break;\n if (canExpand(i, dir)) {\n doExpand(i, dir);\n changed = true;\n }\n }\n }\n if (!changed) break;\n }\n \n // Phase 2: Fill remaining space (some rectangles couldn't reach target)\n while (timeOk()) {\n bool changed = false;\n vector order(n);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int i, int j) {\n return rr[i] - area(i) > rr[j] - area(j);\n });\n \n for (int i : order) {\n for (int dir = 0; dir < 4; dir++) {\n if (canExpand(i, dir)) {\n doExpand(i, dir);\n changed = true;\n }\n }\n }\n if (!changed) break;\n }\n \n // Phase 3: Multiple shrink-expand cycles\n for (int cycle = 0; cycle < 10 && timeOk(); cycle++) {\n // Shrink oversized (prioritize most oversized)\n for (int iter = 0; iter < 1000 && timeOk(); iter++) {\n bool changed = false;\n vector order(n);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int i, int j) {\n return area(i) - rr[i] > area(j) - rr[j];\n });\n \n for (int i : order) {\n if (area(i) <= rr[i]) continue;\n for (int dir = 0; dir < 4; dir++) {\n int na = a[i], nb = b[i], nc = c[i], nd = d[i];\n if (dir == 0) na++; else if (dir == 1) nc--; else if (dir == 2) nb++; else nd--;\n if (na >= nc || nb >= nd) continue;\n if (!(na <= px[i] && px[i] < nc && nb <= py[i] && py[i] < nd)) continue;\n if ((long long)(nc - na) * (nd - nb) >= rr[i]) {\n a[i] = na; b[i] = nb; c[i] = nc; d[i] = nd;\n changed = true;\n }\n }\n }\n if (!changed) break;\n }\n \n // Expand undersized\n for (int iter = 0; iter < 1000 && timeOk(); iter++) {\n bool changed = false;\n vector order(n);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int i, int j) {\n return rr[i] - area(i) > rr[j] - area(j);\n });\n \n for (int i : order) {\n if (area(i) >= rr[i]) continue;\n for (int dir = 0; dir < 4; dir++) {\n if (canExpand(i, dir)) {\n doExpand(i, dir);\n changed = true;\n }\n }\n }\n if (!changed) break;\n }\n }\n \n for (int i = 0; i < n; i++) {\n cout << a[i] << \" \" << b[i] << \" \" << c[i] << \" \" << d[i] << \"\\n\";\n }\n return 0;\n}","ahc002":"#include \nusing namespace std;\n\nconst int N = 50;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nconst char dc[] = {'U', 'D', 'L', 'R'};\n\nint t[N][N], p[N][N];\nint si, sj;\nmt19937 rng;\n\ninline int countMoves(int x, int y, const bitset<2500>& used, int curTile) {\n int cnt = 0;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < N && ny >= 0 && ny < N && !used[t[nx][ny]] && t[nx][ny] != curTile) cnt++;\n }\n return cnt;\n}\n\nvoid runBeamSearch(int beamWidth, int moveWeight, int timeLimit,\n string& bestPath, int& bestScore, chrono::steady_clock::time_point startTime,\n int randRange = 0) {\n struct State {\n int x, y, score, priority;\n bitset<2500> usedTiles;\n string path;\n };\n \n vector beam;\n State init;\n init.x = si; init.y = sj;\n init.score = p[si][sj];\n init.usedTiles.set(t[si][sj]);\n init.path = \"\";\n init.priority = init.score + countMoves(si, sj, init.usedTiles, -1) * moveWeight;\n beam.push_back(init);\n \n while (!beam.empty()) {\n if (chrono::duration_cast(chrono::steady_clock::now() - startTime).count() > timeLimit) {\n for (const auto& state : beam) {\n if (state.score > bestScore) {\n bestScore = state.score;\n bestPath = state.path;\n }\n }\n break;\n }\n \n vector nextBeam;\n nextBeam.reserve(beam.size() * 4);\n \n for (const auto& state : beam) {\n bool canExtend = false;\n for (int d = 0; d < 4; d++) {\n int nx = state.x + dx[d];\n int ny = state.y + dy[d];\n if (nx < 0 || nx >= N || ny < 0 || ny >= N) continue;\n if (state.usedTiles[t[nx][ny]]) continue;\n \n canExtend = true;\n State newState;\n newState.x = nx; newState.y = ny;\n newState.score = state.score + p[nx][ny];\n newState.usedTiles = state.usedTiles;\n newState.usedTiles.set(t[nx][ny]);\n newState.path = state.path + dc[d];\n \n int fm = countMoves(nx, ny, newState.usedTiles, -1);\n newState.priority = newState.score + fm * moveWeight;\n if (randRange > 0) newState.priority += rng() % randRange;\n nextBeam.push_back(move(newState));\n }\n if (!canExtend && state.score > bestScore) {\n bestScore = state.score;\n bestPath = state.path;\n }\n }\n \n if ((int)nextBeam.size() > beamWidth) {\n nth_element(nextBeam.begin(), nextBeam.begin() + beamWidth, nextBeam.end(),\n [](const State& a, const State& b) { return a.priority > b.priority; });\n nextBeam.resize(beamWidth);\n }\n \n beam = move(nextBeam);\n }\n}\n\nvoid randomGreedy(string& bestPath, int& bestScore, int moveWeight, int randPercent) {\n int x = si, y = sj;\n int score = p[si][sj];\n string path = \"\";\n bitset<2500> usedTiles;\n usedTiles.set(t[si][sj]);\n \n while (true) {\n vector> moves;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx < 0 || nx >= N || ny < 0 || ny >= N) continue;\n if (usedTiles[t[nx][ny]]) continue;\n int fm = countMoves(nx, ny, usedTiles, t[nx][ny]);\n moves.push_back({p[nx][ny] + fm * moveWeight, d});\n }\n if (moves.empty()) break;\n sort(moves.begin(), moves.end(), greater>());\n \n int choice = 0;\n if (moves.size() > 1 && (int)(rng() % 100) < randPercent) {\n choice = rng() % min((int)moves.size(), 3);\n }\n \n int d = moves[choice].second;\n x += dx[d]; y += dy[d];\n score += p[x][y];\n usedTiles.set(t[x][y]);\n path += dc[d];\n }\n if (score > bestScore) {\n bestScore = score;\n bestPath = path;\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n auto startTime = chrono::steady_clock::now();\n rng.seed(chrono::steady_clock::now().time_since_epoch().count());\n \n cin >> si >> sj;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> t[i][j];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> p[i][j];\n \n string bestPath = \"\";\n int bestScore = p[si][sj];\n \n // Diverse beam searches - balanced parameters\n runBeamSearch(700, 0, 200, bestPath, bestScore, startTime); // Pure score\n runBeamSearch(700, 40, 400, bestPath, bestScore, startTime); // Light move\n runBeamSearch(700, 80, 600, bestPath, bestScore, startTime); // Moderate\n runBeamSearch(700, 120, 800, bestPath, bestScore, startTime); // Move heavy\n runBeamSearch(700, 150, 1000, bestPath, bestScore, startTime); // Very move heavy\n runBeamSearch(600, 60, 1150, bestPath, bestScore, startTime, 25); // With randomness\n runBeamSearch(600, 100, 1300, bestPath, bestScore, startTime, 30); // Random + moves\n \n // Extended random greedy with varied strategies\n while (chrono::duration_cast(chrono::steady_clock::now() - startTime).count() < 1950) {\n int moveW = 10 + rng() % 40; // 10-50\n int randP = 20 + rng() % 30; // 20-50\n randomGreedy(bestPath, bestScore, moveW, randP);\n }\n \n cout << bestPath << endl;\n return 0;\n}","ahc003":"#include \nusing namespace std;\n\nconst int N = 30;\ndouble h[N][N-1], v[N-1][N];\nint h_cnt[N][N-1], v_cnt[N-1][N];\ndouble g_sum = 0;\nint g_cnt = 0;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n fill(&h[0][0], &h[0][0] + N*(N-1), 5000.0);\n fill(&v[0][0], &v[0][0] + (N-1)*N, 5000.0);\n fill(&h_cnt[0][0], &h_cnt[0][0] + N*(N-1), 0);\n fill(&v_cnt[0][0], &v_cnt[0][0] + (N-1)*N, 0);\n \n auto getH = [&](int i, int j) -> double {\n if (h_cnt[i][j] > 0) return h[i][j];\n // Distance-weighted row average\n double sum = 0, wgt = 0;\n for (int k = 0; k < N-1; k++) {\n if (h_cnt[i][k] > 0) {\n double w = 1.0 / (1.0 + abs(j - k));\n sum += h[i][k] * w;\n wgt += w;\n }\n }\n if (wgt > 0) return sum / wgt;\n if (g_cnt > 0) return g_sum / g_cnt;\n return 5000.0;\n };\n \n auto getV = [&](int i, int j) -> double {\n if (v_cnt[i][j] > 0) return v[i][j];\n // Distance-weighted column average\n double sum = 0, wgt = 0;\n for (int k = 0; k < N-1; k++) {\n if (v_cnt[k][j] > 0) {\n double w = 1.0 / (1.0 + abs(i - k));\n sum += v[k][j] * w;\n wgt += w;\n }\n }\n if (wgt > 0) return sum / wgt;\n if (g_cnt > 0) return g_sum / g_cnt;\n return 5000.0;\n };\n \n for (int q = 0; q < 1000; q++) {\n int si, sj, ti, tj;\n cin >> si >> sj >> ti >> tj;\n \n auto idx = [](int i, int j) { return i * N + j; };\n vector dist(N*N, 1e18);\n vector prv(N*N, -1);\n \n priority_queue, vector>, greater<>> pq;\n dist[idx(si, sj)] = 0;\n pq.push({0, idx(si, sj)});\n \n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > dist[u]) continue;\n int i = u / N, j = u % N;\n \n auto relax = [&](int ni, int nj, double w) {\n int nu = idx(ni, nj);\n if (dist[u] + w < dist[nu]) {\n dist[nu] = dist[u] + w;\n prv[nu] = u;\n pq.push({dist[nu], nu});\n }\n };\n \n if (i > 0) relax(i-1, j, getV(i-1, j));\n if (i < N-1) relax(i+1, j, getV(i, j));\n if (j > 0) relax(i, j-1, getH(i, j-1));\n if (j < N-1) relax(i, j+1, getH(i, j));\n }\n \n string path = \"\";\n vector> edges;\n \n int cur = idx(ti, tj);\n while (prv[cur] != -1) {\n int ci = cur / N, cj = cur % N;\n int pi = prv[cur] / N, pj = prv[cur] % N;\n \n if (ci < pi) { path += 'U'; edges.emplace_back(1, ci, cj); }\n else if (ci > pi) { path += 'D'; edges.emplace_back(1, pi, pj); }\n else if (cj < pj) { path += 'L'; edges.emplace_back(0, ci, cj); }\n else { path += 'R'; edges.emplace_back(0, pi, pj); }\n \n cur = prv[cur];\n }\n \n reverse(path.begin(), path.end());\n cout << path << \"\\n\" << flush;\n \n int feedback;\n cin >> feedback;\n \n double est = 0;\n for (auto& [t, ei, ej] : edges) {\n est += (t == 0) ? getH(ei, ej) : getV(ei, ej);\n }\n \n double ratio = feedback / est;\n \n for (auto& [t, ei, ej] : edges) {\n double implied = (t == 0) ? getH(ei, ej) * ratio : getV(ei, ej) * ratio;\n \n if (t == 0) {\n int cnt = ++h_cnt[ei][ej];\n double alpha = 1.0 / (1.0 + cnt);\n h[ei][ej] = h[ei][ej] * (1 - alpha) + implied * alpha;\n } else {\n int cnt = ++v_cnt[ei][ej];\n double alpha = 1.0 / (1.0 + cnt);\n v[ei][ej] = v[ei][ej] * (1 - alpha) + implied * alpha;\n }\n }\n \n // Update global average\n g_sum = 0; g_cnt = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N-1; j++) {\n if (h_cnt[i][j] > 0) { g_sum += h[i][j]; g_cnt++; }\n }\n }\n for (int i = 0; i < N-1; i++) {\n for (int j = 0; j < N; j++) {\n if (v_cnt[i][j] > 0) { g_sum += v[i][j]; g_cnt++; }\n }\n }\n }\n \n return 0;\n}","ahc004":"#include \nusing namespace std;\n\nconst int N = 20;\nint m;\nvector strs;\n\nbool matchAt(const char grid[N][N], int idx, int r, int c, int d) {\n const string& s = strs[idx];\n for(int p = 0; p < (int)s.size(); p++) {\n int ni = d ? (r+p)%N : r, nj = d ? c : (c+p)%N;\n if(grid[ni][nj] != s[p]) return false;\n }\n return true;\n}\n\ntuple findMatch(const char grid[N][N], int idx) {\n for(int r = 0; r < N; r++)\n for(int c = 0; c < N; c++) {\n if(matchAt(grid, idx, r, c, 0)) return {r, c, 0};\n if(matchAt(grid, idx, r, c, 1)) return {r, c, 1};\n }\n return {-1, -1, -1};\n}\n\nbool posContains(int r, int c, int d, int len, int i, int j) {\n for(int p = 0; p < len; p++) {\n int ni = d ? (r+p)%N : r, nj = d ? c : (c+p)%N;\n if(ni == i && nj == j) return true;\n }\n return false;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n; cin >> n >> m;\n strs.resize(m);\n for(int i = 0; i < m; i++) cin >> strs[i];\n \n mt19937 rng(12345);\n char bestGrid[N][N];\n int bestScore = 0;\n auto start = chrono::high_resolution_clock::now();\n \n for(int trial = 0; ; trial++) {\n if(chrono::duration(chrono::high_resolution_clock::now() - start).count() > 2.0) break;\n \n char grid[N][N]; fill(&grid[0][0], &grid[N][0], '.');\n vector order(m); iota(order.begin(), order.end(), 0);\n if(trial % 3 == 0) sort(order.begin(), order.end(), [&](int a, int b) { return strs[a].size() > strs[b].size(); });\n else { shuffle(order.begin(), order.end(), rng); if(trial % 3 == 1) stable_sort(order.begin(), order.end(), [&](int a, int b) { return strs[a].size() > strs[b].size(); }); }\n \n for(int idx : order) {\n const string& s = strs[idx];\n vector> cands; int bestOv = -1;\n for(int r = 0; r < N; r++) for(int c = 0; c < N; c++) for(int d = 0; d < 2; d++) {\n bool can = true; int ov = 0;\n for(int p = 0; p < (int)s.size(); p++) {\n int ni = d?(r+p)%N:r, nj = d?c:(c+p)%N;\n if(grid[ni][nj] != '.' && grid[ni][nj] != s[p]) { can = false; break; }\n if(grid[ni][nj] != '.') ov++;\n }\n if(can && ov >= bestOv) { if(ov > bestOv) { bestOv = ov; cands.clear(); } cands.push_back({r,c,d}); }\n }\n if(!cands.empty()) { auto [r,c,d] = cands[rng()%cands.size()]; for(int p = 0; p < (int)s.size(); p++) { int ni = d?(r+p)%N:r, nj = d?c:(c+p)%N; grid[ni][nj] = s[p]; } }\n }\n for(int i = 0; i < N; i++) for(int j = 0; j < N; j++) if(grid[i][j] == '.') grid[i][j] = 'A' + rng()%8;\n int score = 0; for(int i = 0; i < m; i++) if(get<0>(findMatch(grid, i)) >= 0) score++;\n if(score > bestScore) { bestScore = score; memcpy(bestGrid, grid, sizeof(grid)); }\n }\n \n char grid[N][N]; memcpy(grid, bestGrid, sizeof(grid));\n vector> matchPos(m);\n for(int i = 0; i < m; i++) matchPos[i] = findMatch(grid, i);\n int curScore = bestScore;\n \n while(true) {\n double elapsed = chrono::duration(chrono::high_resolution_clock::now() - start).count();\n if(elapsed > 2.95) break;\n double T = 1.5 * max(0.01, 1.0 - elapsed / 3.0);\n \n int ci = rng()%N, cj = rng()%N;\n char old = grid[ci][cj], newc = 'A' + rng()%8;\n if(newc == old) continue;\n \n grid[ci][cj] = newc;\n int delta = 0;\n vector>> changes;\n \n for(int idx = 0; idx < m; idx++) {\n auto [r,c,d] = matchPos[idx];\n int len = strs[idx].size();\n if(r >= 0 && posContains(r, c, d, len, ci, cj)) {\n if(!matchAt(grid, idx, r, c, d)) {\n auto nm = findMatch(grid, idx);\n changes.push_back({idx, nm});\n if(get<0>(nm) < 0) delta--;\n }\n } else if(r < 0) {\n for(int p = 0; p < len; p++) {\n int sc = (cj - p + N) % N;\n if(matchAt(grid, idx, ci, sc, 0)) { delta++; changes.push_back({idx, {ci,sc,0}}); goto nxt; }\n }\n for(int p = 0; p < len; p++) {\n int sr = (ci - p + N) % N;\n if(matchAt(grid, idx, sr, cj, 1)) { delta++; changes.push_back({idx, {sr,cj,1}}); goto nxt; }\n }\n nxt:;\n }\n }\n \n if(delta >= 0 || (rng()&0xFFFF) < 65536.0 * exp(delta / T)) {\n curScore += delta;\n for(auto& [idx, pos] : changes) matchPos[idx] = pos;\n if(curScore > bestScore) { bestScore = curScore; memcpy(bestGrid, grid, sizeof(grid)); }\n } else grid[ci][cj] = old;\n }\n \n for(int i = 0; i < N; i++) cout << string(bestGrid[i], bestGrid[i]+N) << '\\n';\n}","ahc005":"#include \nusing namespace std;\n\nint N, si, sj;\nvector grid;\n\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nconst char dir_char[] = {'U', 'D', 'L', 'R'};\n\ninline bool is_road(int i, int j) {\n return i >= 0 && i < N && j >= 0 && j < N && grid[i][j] != '#';\n}\n\npair>, vector>>> dijkstra(int si, int sj) {\n vector> dist(N, vector(N, INT_MAX));\n vector>> parent(N, vector>(N, {-1,-1}));\n priority_queue, vector>, greater<>> pq;\n dist[si][sj] = 0; pq.push({0, si, sj});\n while (!pq.empty()) {\n auto [d, i, j] = pq.top(); pq.pop();\n if (d > dist[i][j]) continue;\n for (int k = 0; k < 4; k++) {\n int ni = i + dx[k], nj = j + dy[k];\n if (is_road(ni, nj)) {\n int c = grid[ni][nj] - '0';\n if (dist[i][j] + c < dist[ni][nj]) {\n dist[ni][nj] = dist[i][j] + c;\n parent[ni][nj] = {i, j};\n pq.push({dist[ni][nj], ni, nj});\n }\n }\n }\n }\n return {dist, parent};\n}\n\nstring get_path(int i1, int j1, int i2, int j2, vector>>& parent) {\n if (i1 == i2 && j1 == j2) return \"\";\n string path;\n int ci = i2, cj = j2;\n while (ci != i1 || cj != j1) {\n auto [pi, pj] = parent[ci][cj];\n for (int k = 0; k < 4; k++) if (pi + dx[k] == ci && pj + dy[k] == cj) { path += dir_char[k]; break; }\n ci = pi; cj = pj;\n }\n reverse(path.begin(), path.end());\n return path;\n}\n\nint calc_path_time(const string& path) {\n int time = 0, ci = si, cj = sj;\n for (char c : path) {\n if (c == 'U') ci--; else if (c == 'D') ci++; else if (c == 'L') cj--; else cj++;\n time += grid[ci][cj] - '0';\n }\n return time;\n}\n\nstring solve(double alpha, int check_limit) {\n vector> visible(N, vector(N, false));\n int visible_count = 0, total_roads = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (is_road(i, j)) total_roads++;\n \n auto mark_visible = [&](int i, int j) {\n if (!visible[i][j]) { visible[i][j] = true; visible_count++; }\n for (int jj = j - 1; jj >= 0 && is_road(i, jj); jj--) if (!visible[i][jj]) { visible[i][jj] = true; visible_count++; }\n for (int jj = j + 1; jj < N && is_road(i, jj); jj++) if (!visible[i][jj]) { visible[i][jj] = true; visible_count++; }\n for (int ii = i - 1; ii >= 0 && is_road(ii, j); ii--) if (!visible[ii][j]) { visible[ii][j] = true; visible_count++; }\n for (int ii = i + 1; ii < N && is_road(ii, j); ii++) if (!visible[ii][j]) { visible[ii][j] = true; visible_count++; }\n };\n \n auto count_new_visible = [&](int i, int j) {\n int cnt = !visible[i][j];\n for (int jj = j - 1; jj >= 0 && is_road(i, jj); jj--) cnt += !visible[i][jj];\n for (int jj = j + 1; jj < N && is_road(i, jj); jj++) cnt += !visible[i][jj];\n for (int ii = i - 1; ii >= 0 && is_road(ii, j); ii--) cnt += !visible[ii][j];\n for (int ii = i + 1; ii < N && is_road(ii, j); ii++) cnt += !visible[ii][j];\n return cnt;\n };\n \n auto calc_path_visibility = [&](int si, int sj, const string& path) {\n auto vis = visible;\n int cnt = 0, ci = si, cj = sj;\n for (char c : path) {\n if (c == 'U') ci--; else if (c == 'D') ci++; else if (c == 'L') cj--; else cj++;\n if (!vis[ci][cj]) { vis[ci][cj] = true; cnt++; }\n for (int jj = cj - 1; jj >= 0 && is_road(ci, jj); jj--) if (!vis[ci][jj]) { vis[ci][jj] = true; cnt++; }\n for (int jj = cj + 1; jj < N && is_road(ci, jj); jj++) if (!vis[ci][jj]) { vis[ci][jj] = true; cnt++; }\n for (int ii = ci - 1; ii >= 0 && is_road(ii, cj); ii--) if (!vis[ii][cj]) { vis[ii][cj] = true; cnt++; }\n for (int ii = ci + 1; ii < N && is_road(ii, cj); ii++) if (!vis[ii][cj]) { vis[ii][cj] = true; cnt++; }\n }\n return cnt;\n };\n \n auto [dist_from_start, parent_from_start] = dijkstra(si, sj);\n int cur_i = si, cur_j = sj;\n string result;\n mark_visible(cur_i, cur_j);\n \n while (visible_count < total_roads) {\n auto [dist, parent] = dijkstra(cur_i, cur_j);\n \n vector> candidates;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (dist[i][j] == INT_MAX || dist[i][j] == 0) continue;\n int nv = count_new_visible(i, j);\n if (nv == 0) continue;\n double cost = dist[i][j] + alpha * dist_from_start[i][j];\n candidates.push_back({-(double)nv / cost, i, j});\n }\n }\n \n if (candidates.empty()) break;\n sort(candidates.begin(), candidates.end());\n \n int best_i = -1, best_j = -1;\n double best_score = -1e18;\n string best_path;\n \n int check_count = min((int)candidates.size(), check_limit);\n for (int c = 0; c < check_count; c++) {\n auto [_, i, j] = candidates[c];\n string path = get_path(cur_i, cur_j, i, j, parent);\n double nv = (check_limit > 1) ? calc_path_visibility(cur_i, cur_j, path) : count_new_visible(i, j);\n if (nv == 0) continue;\n double cost = dist[i][j] + alpha * dist_from_start[i][j];\n double score = nv / cost;\n if (score > best_score) { best_score = score; best_i = i; best_j = j; best_path = path; }\n }\n \n if (best_i == -1) break;\n result += best_path;\n int ti = cur_i, tj = cur_j;\n for (char c : best_path) {\n if (c == 'U') ti--; else if (c == 'D') ti++; else if (c == 'L') tj--; else tj++;\n mark_visible(ti, tj);\n }\n cur_i = best_i; cur_j = best_j;\n }\n \n if (cur_i != si || cur_j != sj) {\n auto [dist, parent] = dijkstra(cur_i, cur_j);\n result += get_path(cur_i, cur_j, si, sj, parent);\n }\n return result;\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> si >> sj;\n grid.resize(N);\n for (int i = 0; i < N; i++) cin >> grid[i];\n \n string best_result;\n int best_time = INT_MAX;\n \n vector alphas;\n for (int i = 0; i <= 20; i++) alphas.push_back(i * 0.02); // 0.0 to 0.4 step 0.02\n alphas.push_back(0.45);\n alphas.push_back(0.5);\n \n vector check_limits = {1, 12, 20, 30};\n \n for (double alpha : alphas) {\n for (int cl : check_limits) {\n string result = solve(alpha, cl);\n int time = calc_path_time(result);\n if (time < best_time) { best_time = time; best_result = result; }\n }\n }\n \n cout << best_result << endl;\n return 0;\n}","future-contest-2022-qual":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K, R;\n cin >> N >> M >> K >> R;\n \n vector> d(N, vector(K));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < K; j++)\n cin >> d[i][j];\n \n vector> deps(N), rdeps(N);\n for (int i = 0; i < R; i++) {\n int u, v;\n cin >> u >> v;\n u--; v--;\n deps[v].push_back(u);\n rdeps[u].push_back(v);\n }\n \n vector taskStatus(N, -1);\n vector memberTask(M, -1), memberStartDay(M, 0);\n \n double initSkill = 40.0 / sqrt(K);\n vector> skillEst(M, vector(K, initSkill));\n vector> skillLo(M, vector(K, 0.0));\n \n auto estimateTime = [&](int task, int member) -> double {\n double w = 0;\n for (int k = 0; k < K; k++)\n w += max(0.0, (double)d[task][k] - skillEst[member][k]);\n return max(1.0, w);\n };\n \n auto avgTime = [&](int task) -> double {\n double sum = 0;\n for (int j = 0; j < M; j++) sum += estimateTime(task, j);\n return sum / M;\n };\n \n vector downstream(N, 0);\n for (int i = N - 1; i >= 0; i--) {\n downstream[i] = (int)rdeps[i].size();\n for (int v : rdeps[i]) downstream[i] += downstream[v];\n }\n \n vector wdepth(N);\n auto recalcDepth = [&]() {\n for (int i = N - 1; i >= 0; i--) {\n if (taskStatus[i] == 1) { wdepth[i] = 0; continue; }\n wdepth[i] = avgTime(i);\n double maxChild = 0;\n for (int v : rdeps[i]) maxChild = max(maxChild, wdepth[v]);\n wdepth[i] += maxChild;\n }\n };\n recalcDepth();\n \n for (int day = 1; ; day++) {\n if (day % 25 == 1) recalcDepth();\n \n vector availTasks;\n for (int i = 0; i < N; i++) {\n if (taskStatus[i] != -1) continue;\n bool ok = true;\n for (int dep : deps[i])\n if (taskStatus[dep] != 1) { ok = false; break; }\n if (ok) availTasks.push_back(i);\n }\n \n vector freeMembers;\n for (int j = 0; j < M; j++)\n if (memberTask[j] == -1) freeMembers.push_back(j);\n \n vector> candidates;\n for (int task : availTasks) {\n for (int member : freeMembers) {\n double t = estimateTime(task, member);\n double score = wdepth[task] / max(1.0, t) + 0.001 * downstream[task];\n candidates.push_back({-score, task, member});\n }\n }\n sort(candidates.begin(), candidates.end());\n \n vector> assignments;\n vector usedMember(M, false), usedTask(N, false);\n \n for (auto& [score, task, member] : candidates) {\n if (usedMember[member] || usedTask[task]) continue;\n usedMember[member] = true;\n usedTask[task] = true;\n assignments.push_back({member + 1, task + 1});\n taskStatus[task] = 0;\n memberTask[member] = task;\n memberStartDay[member] = day;\n }\n \n cout << assignments.size();\n for (auto& [a, b] : assignments) cout << \" \" << a << \" \" << b;\n cout << \"\\n\";\n cout.flush();\n \n int n; cin >> n;\n if (n == -1) break;\n \n for (int i = 0; i < n; i++) {\n int f; cin >> f; f--;\n int task = memberTask[f];\n int timeTaken = day - memberStartDay[f] + 1;\n taskStatus[task] = 1;\n memberTask[f] = -1;\n \n if (timeTaken == 1) {\n for (int k = 0; k < K; k++) {\n skillLo[f][k] = max(skillLo[f][k], (double)d[task][k]);\n skillEst[f][k] = max(skillEst[f][k], (double)d[task][k]);\n }\n } else {\n double wEst = (double)timeTaken;\n double currW = 0;\n for (int k = 0; k < K; k++)\n currW += max(0.0, (double)d[task][k] - skillEst[f][k]);\n \n if (currW > 0.5) {\n double factor = wEst / currW;\n factor = 0.65 * factor + 0.35;\n factor = max(0.5, min(1.6, factor));\n \n for (int k = 0; k < K; k++) {\n double gap = d[task][k] - skillEst[f][k];\n if (gap > 0) {\n double newSkill = d[task][k] - gap * factor;\n skillEst[f][k] = max(skillLo[f][k], newSkill);\n }\n }\n } else if (wEst > 4) {\n double totalReq = 0;\n for (int k = 0; k < K; k++) totalReq += d[task][k];\n if (totalReq > 0.5) {\n for (int k = 0; k < K; k++) {\n double reduction = (wEst - 2) * d[task][k] / totalReq;\n skillEst[f][k] = max(skillLo[f][k], skillEst[f][k] - reduction);\n }\n }\n }\n }\n }\n }\n return 0;\n}","ahc006":"#include \nusing namespace std;\n\nconst int N = 1000, M = 50, CX = 400, CY = 400;\nint ordA[N], ordB[N], ordC[N], ordD[N];\nmt19937 rng(chrono::steady_clock::now().time_since_epoch().count());\n\ninline int dist(int x1, int y1, int x2, int y2) {\n return abs(x1 - x2) + abs(y1 - y2);\n}\n\nint buildRoute(const vector& sel, vector>& ev) {\n ev.clear();\n ev.reserve(2 * M);\n bool picked[N] = {}, done[N] = {};\n int cx = CX, cy = CY, cost = 0;\n \n for (int i = 0; i < 2*M; i++) {\n int best = -1, bd = 1e9;\n bool isDel = false;\n for (int j : sel) {\n if (!picked[j]) {\n int d = dist(cx, cy, ordA[j], ordB[j]);\n if (d < bd) { bd = d; best = j; isDel = false; }\n } else if (!done[j]) {\n int d = dist(cx, cy, ordC[j], ordD[j]);\n if (d < bd) { bd = d; best = j; isDel = true; }\n }\n }\n cost += bd;\n if (isDel) { cx = ordC[best]; cy = ordD[best]; done[best] = true; }\n else { cx = ordA[best]; cy = ordB[best]; picked[best] = true; }\n ev.push_back({best, isDel});\n }\n return cost + dist(cx, cy, CX, CY);\n}\n\nint calcCost(const vector>& ev) {\n int cx = CX, cy = CY, cost = 0;\n for (auto& [idx, isDel] : ev) {\n int nx = isDel ? ordC[idx] : ordA[idx];\n int ny = isDel ? ordD[idx] : ordB[idx];\n cost += dist(cx, cy, nx, ny);\n cx = nx; cy = ny;\n }\n return cost + dist(cx, cy, CX, CY);\n}\n\nbool validSwap(vector>& ev, int i, int j) {\n swap(ev[i], ev[j]);\n int pickPos[N];\n memset(pickPos, -1, sizeof(pickPos));\n for (int k = 0; k < (int)ev.size(); k++) {\n if (!ev[k].second) pickPos[ev[k].first] = k;\n else if (pickPos[ev[k].first] < 0 || pickPos[ev[k].first] > k) {\n swap(ev[i], ev[j]);\n return false;\n }\n }\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n auto st = chrono::steady_clock::now();\n for (int i = 0; i < N; i++) cin >> ordA[i] >> ordB[i] >> ordC[i] >> ordD[i];\n \n auto elapsed = [&]() {\n return chrono::duration(chrono::steady_clock::now() - st).count();\n };\n \n vector> byDist(N);\n for (int i = 0; i < N; i++) {\n byDist[i] = {dist(CX, CY, ordA[i], ordB[i]) + dist(CX, CY, ordC[i], ordD[i]), i};\n }\n sort(byDist.begin(), byDist.end());\n \n vector sel(M), unsel(N-M);\n for (int i = 0; i < M; i++) sel[i] = byDist[i].second;\n for (int i = 0; i < N-M; i++) unsel[i] = byDist[M+i].second;\n \n vector> ev, bestEv;\n int cost = buildRoute(sel, ev);\n int bestCost = cost;\n vector bestSel = sel;\n bestEv = ev;\n \n double temp = 3000.0;\n \n while (elapsed() < 1.8) {\n int si = rng() % M;\n int ui = rng() % (N-M);\n swap(sel[si], unsel[ui]);\n \n int nc = buildRoute(sel, ev);\n int delta = nc - cost;\n \n if (delta < 0 || (rng() % 10000) < 10000 * exp(-delta / temp)) {\n cost = nc;\n if (nc < bestCost) {\n bestCost = nc;\n bestSel = sel;\n bestEv = ev;\n }\n } else {\n swap(sel[si], unsel[ui]);\n }\n temp *= 0.99995;\n }\n \n // Improved 2-opt: complete full passes, don't break early\n bool improved = true;\n while (improved && elapsed() < 1.95) {\n improved = false;\n for (int i = 0; i < 2*M - 1; i++) {\n for (int j = i + 1; j < 2*M; j++) {\n if (elapsed() > 1.95) break;\n if (bestEv[i].first == bestEv[j].first) continue;\n if (validSwap(bestEv, i, j)) {\n int nc = calcCost(bestEv);\n if (nc < bestCost) {\n bestCost = nc;\n improved = true;\n } else {\n swap(bestEv[i], bestEv[j]);\n }\n }\n }\n }\n }\n \n cout << M;\n for (int x : bestSel) cout << \" \" << (x+1);\n cout << \"\\n\" << (2*M+2) << \" \" << CX << \" \" << CY;\n for (auto& [idx, isDel] : bestEv) {\n if (isDel) cout << \" \" << ordC[idx] << \" \" << ordD[idx];\n else cout << \" \" << ordA[idx] << \" \" << ordB[idx];\n }\n cout << \" \" << CX << \" \" << CY << \"\\n\";\n \n return 0;\n}","ahc007":"#include \nusing namespace std;\n\nclass UnionFind {\n vector parent, rank_;\npublic:\n UnionFind(int n) : parent(n), rank_(n, 0) {\n iota(parent.begin(), parent.end(), 0);\n }\n int find(int x) {\n if (parent[x] != x) parent[x] = find(parent[x]);\n return parent[x];\n }\n bool unite(int x, int y) {\n int px = find(x), py = find(y);\n if (px == py) return false;\n if (rank_[px] < rank_[py]) swap(px, py);\n parent[py] = px;\n if (rank_[px] == rank_[py]) rank_[px]++;\n return true;\n }\n};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n const int N = 400, M = 1995;\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) {\n cin >> x[i] >> y[i];\n }\n \n vector u(M), v(M), d(M);\n for (int i = 0; i < M; i++) {\n cin >> u[i] >> v[i];\n double dx = x[u[i]] - x[v[i]];\n double dy = y[u[i]] - y[v[i]];\n d[i] = (int)round(sqrt(dx * dx + dy * dy));\n }\n \n UnionFind uf(N);\n int components = N;\n \n for (int i = 0; i < M; i++) {\n int l;\n cin >> l;\n \n int pu = uf.find(u[i]);\n int pv = uf.find(v[i]);\n \n bool already_connected = (pu == pv);\n double ratio = (double)l / d[i];\n \n bool adopt = false;\n \n if (!already_connected) {\n // Always accept excellent deals\n if (ratio <= 1.5) {\n adopt = true;\n }\n else {\n int useful_remaining = 0;\n int same_pair_remaining = 0;\n \n for (int j = i + 1; j < M; j++) {\n int uj = uf.find(u[j]);\n int vj = uf.find(v[j]);\n if (uj != vj) {\n useful_remaining++;\n if ((uj == pu && vj == pv) || (uj == pv && vj == pu)) {\n same_pair_remaining++;\n }\n }\n }\n \n int needed = components - 1;\n \n if (same_pair_remaining == 0) {\n adopt = true;\n }\n else if (useful_remaining < needed * 2) {\n adopt = true;\n }\n else {\n // Expected minimum of (k+1) samples from [1,3] is 1 + 2/(k+2)\n double k = same_pair_remaining;\n double expected_min = 1.0 + 2.0 / (k + 2.0);\n double threshold = expected_min + 0.28;\n \n if (ratio <= threshold) {\n adopt = true;\n }\n }\n }\n }\n \n if (adopt) {\n uf.unite(u[i], v[i]);\n components--;\n }\n \n cout << (adopt ? 1 : 0) << \"\\n\" << flush;\n }\n \n return 0;\n}","ahc008":"#include \nusing namespace std;\n\nint N, M;\nvector> pets;\nvector> humans;\nbool blocked[32][32];\n\nint dx[] = {-1, 1, 0, 0}, dy[] = {0, 0, -1, 1};\nchar wc[] = {'u', 'd', 'l', 'r'}, mc[] = {'U', 'D', 'L', 'R'};\n\nbool pet_at(int x, int y) {\n for (auto& p : pets) if (p[0] == x && p[1] == y) return true;\n return false;\n}\n\nbool pet_adjacent(int x, int y) {\n for (int d = 0; d < 4; d++) if (pet_at(x+dx[d], y+dy[d])) return true;\n return pet_at(x, y);\n}\n\nbool can_place(int x, int y) {\n if (x < 1 || x > 30 || y < 1 || y > 30 || blocked[x][y]) return false;\n for (auto& h : humans) if (h[0] == x && h[1] == y) return false;\n return !pet_adjacent(x, y);\n}\n\nbool passable(int x, int y) {\n return x >= 1 && x <= 30 && y >= 1 && y <= 30 && !blocked[x][y];\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N; pets.resize(N);\n for (int i = 0; i < N; i++) cin >> pets[i][0] >> pets[i][1] >> pets[i][2];\n cin >> M; humans.resize(M);\n for (int i = 0; i < M; i++) cin >> humans[i][0] >> humans[i][1];\n \n set> target;\n for (int i = 1; i <= 30; i++) {\n for (int c : {7, 14, 21, 28}) {\n target.insert({i, c});\n target.insert({c, i});\n }\n }\n \n for (int turn = 0; turn < 300; turn++) {\n string action(M, '.');\n set> will_block;\n \n for (int i = 0; i < M; i++) {\n int hx = humans[i][0], hy = humans[i][1];\n \n // Try to build a target wall only\n int bestd = -1;\n for (int d = 0; d < 4; d++) {\n int nx = hx + dx[d], ny = hy + dy[d];\n if (target.count({nx, ny}) && can_place(nx, ny) && !will_block.count({nx, ny})) {\n bestd = d;\n break;\n }\n }\n \n if (bestd >= 0) {\n action[i] = wc[bestd];\n will_block.insert({hx + dx[bestd], hy + dy[bestd]});\n } else {\n // Check if we're adjacent to an unbuilt target (might be blocked by pet)\n bool near_unbuilt_target = false;\n for (int d = 0; d < 4; d++) {\n int nx = hx + dx[d], ny = hy + dy[d];\n if (nx >= 1 && nx <= 30 && ny >= 1 && ny <= 30 &&\n target.count({nx, ny}) && !blocked[nx][ny]) {\n near_unbuilt_target = true;\n break;\n }\n }\n \n if (near_unbuilt_target) {\n // Wait for opportunity to build\n action[i] = '.';\n } else {\n // Move toward closest unbuilt target\n int minD = INT_MAX;\n int moveD = -1;\n \n for (auto& [tx, ty] : target) {\n if (blocked[tx][ty]) continue;\n int dist = abs(hx-tx) + abs(hy-ty);\n if (dist > 0 && dist < minD) {\n minD = dist;\n }\n }\n \n for (int d = 0; d < 4; d++) {\n int nx = hx + dx[d], ny = hy + dy[d];\n if (!passable(nx, ny) || pet_at(nx, ny) || will_block.count({nx, ny})) continue;\n \n for (auto& [tx, ty] : target) {\n if (blocked[tx][ty]) continue;\n int newDist = abs(nx-tx) + abs(ny-ty);\n if (newDist < minD) {\n minD = newDist;\n moveD = d;\n }\n }\n }\n if (moveD >= 0) action[i] = mc[moveD];\n }\n }\n }\n \n cout << action << \"\\n\" << flush;\n \n for (int i = 0; i < M; i++) {\n char a = action[i];\n for (int d = 0; d < 4; d++) {\n if (a == wc[d]) blocked[humans[i][0]+dx[d]][humans[i][1]+dy[d]] = true;\n if (a == mc[d]) { humans[i][0] += dx[d]; humans[i][1] += dy[d]; }\n }\n }\n \n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (char c : s) {\n if (c == 'U') pets[i][0]--;\n else if (c == 'D') pets[i][0]++;\n else if (c == 'L') pets[i][1]--;\n else if (c == 'R') pets[i][1]++;\n }\n }\n }\n return 0;\n}","ahc009":"#include \nusing namespace std;\n\nint N = 20;\nint si, sj, ti, tj;\ndouble p;\nbool hwall[20][19];\nbool vwall[19][20];\n\nbool canMove(int i, int j, char dir) {\n if (dir == 'U') return i > 0 && !vwall[i-1][j];\n if (dir == 'D') return i < 19 && !vwall[i][j];\n if (dir == 'L') return j > 0 && !hwall[i][j-1];\n if (dir == 'R') return j < 19 && !hwall[i][j];\n return false;\n}\n\npair doMove(int i, int j, char dir) {\n if (!canMove(i, j, dir)) return {i, j};\n if (dir == 'U') return {i-1, j};\n if (dir == 'D') return {i+1, j};\n if (dir == 'L') return {i, j-1};\n if (dir == 'R') return {i, j+1};\n return {i, j};\n}\n\ndouble prob[20][20], newProb[20][20];\n\ndouble evaluate(const string& s) {\n if (s.empty() || s.size() > 200) return -1;\n memset(prob, 0, sizeof(prob));\n prob[si][sj] = 1.0;\n double expectedScore = 0;\n for (int t = 1; t <= (int)s.size(); t++) {\n char dir = s[t-1];\n memset(newProb, 0, sizeof(newProb));\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (prob[i][j] < 1e-15) continue;\n auto [ni, nj] = doMove(i, j, dir);\n if (ni == ti && nj == tj) {\n expectedScore += (1-p) * prob[i][j] * (401 - t);\n } else {\n newProb[ni][nj] += (1-p) * prob[i][j];\n }\n newProb[i][j] += p * prob[i][j];\n }\n }\n memcpy(prob, newProb, sizeof(prob));\n }\n return expectedScore;\n}\n\nstring bfsWithOrder(vector& order) {\n vector> dist(N, vector(N, -1));\n vector>> parent(N, vector>(N, {-1,-1}));\n vector> fromDir(N, vector(N, ' '));\n queue> q;\n q.push({si, sj});\n dist[si][sj] = 0;\n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (char d : order) {\n auto [ni, nj] = doMove(i, j, d);\n if (ni == i && nj == j) continue;\n if (dist[ni][nj] == -1) {\n dist[ni][nj] = dist[i][j] + 1;\n parent[ni][nj] = {i, j};\n fromDir[ni][nj] = d;\n q.push({ni, nj});\n }\n }\n }\n string path;\n int ci = ti, cj = tj;\n while (ci != si || cj != sj) {\n path += fromDir[ci][cj];\n auto [pi, pj] = parent[ci][cj];\n ci = pi; cj = pj;\n }\n reverse(path.begin(), path.end());\n return path;\n}\n\nmt19937 rng(42);\nstring best;\ndouble bestScore = -1;\nconst char dirs[] = {'U', 'D', 'L', 'R'};\nchrono::steady_clock::time_point startTime;\n\nbool timeUp(int ms) {\n return chrono::duration_cast(chrono::steady_clock::now() - startTime).count() > ms;\n}\n\nvoid updateBest(const string& s, double score) {\n if (score > bestScore) { bestScore = score; best = s; }\n}\n\nvoid localSearch(string& cur, double& curScore, int maxMs) {\n while (!timeUp(maxMs)) {\n bool improved = false;\n \n for (size_t i = 0; i < cur.size() && !improved; i++) {\n string trial = cur.substr(0, i) + cur.substr(i + 1);\n if (!trial.empty()) {\n double score = evaluate(trial);\n if (score > curScore) { cur = trial; curScore = score; improved = true; updateBest(cur, curScore); }\n }\n }\n \n for (size_t i = 0; i < cur.size() && !improved; i++) {\n for (char d : dirs) {\n if (d == cur[i]) continue;\n string trial = cur; trial[i] = d;\n double score = evaluate(trial);\n if (score > curScore) { cur = trial; curScore = score; improved = true; updateBest(cur, curScore); break; }\n }\n }\n \n if (cur.size() < 200 && !improved) {\n for (size_t i = 0; i <= cur.size() && !improved; i++) {\n for (char d : dirs) {\n string trial = cur.substr(0, i) + d + cur.substr(i);\n double score = evaluate(trial);\n if (score > curScore) { cur = trial; curScore = score; improved = true; updateBest(cur, curScore); break; }\n }\n }\n }\n \n if (cur.size() < 200 && !improved) {\n for (size_t i = 0; i < cur.size() && !improved; i++) {\n string trial = cur.substr(0, i+1) + cur[i] + cur.substr(i+1);\n double score = evaluate(trial);\n if (score > curScore) { cur = trial; curScore = score; improved = true; updateBest(cur, curScore); }\n }\n }\n \n for (int len = 2; len <= 5 && !improved; len++) {\n for (size_t i = 0; i + len <= cur.size() && !improved; i++) {\n string trial = cur.substr(0, i) + cur.substr(i + len);\n if (!trial.empty()) {\n double score = evaluate(trial);\n if (score > curScore) { cur = trial; curScore = score; improved = true; updateBest(cur, curScore); }\n }\n }\n }\n \n if (cur.size() < 195 && !improved) {\n for (int len = 2; len <= 5 && !improved; len++) {\n for (size_t i = 0; i + len <= cur.size() && !improved; i++) {\n string trial = cur.substr(0, i + len) + cur.substr(i, len) + cur.substr(i + len);\n if (trial.size() <= 200) {\n double score = evaluate(trial);\n if (score > curScore) { cur = trial; curScore = score; improved = true; updateBest(cur, curScore); }\n }\n }\n }\n }\n \n if (!improved) break;\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n startTime = chrono::steady_clock::now();\n \n cin >> si >> sj >> ti >> tj >> p;\n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < 19; j++) hwall[i][j] = (s[j] == '1');\n }\n for (int i = 0; i < 19; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) vwall[i][j] = (s[j] == '1');\n }\n \n vector order = {'U', 'D', 'L', 'R'};\n set pathSet;\n for (int iter = 0; iter < 100; iter++) {\n shuffle(order.begin(), order.end(), rng);\n pathSet.insert(bfsWithOrder(order));\n }\n vector paths(pathSet.begin(), pathSet.end());\n sort(paths.begin(), paths.end(), [](const string& a, const string& b) { return a.size() < b.size(); });\n \n for (const string& path : paths) {\n if (timeUp(700)) break;\n int L = path.size();\n \n auto tryAdd = [&](const string& s) {\n if (s.size() > 200 || s.empty()) return;\n double score = evaluate(s);\n updateBest(s, score);\n };\n \n for (int rep = 1; rep * L <= 200; rep++) {\n string r; for (char c : path) for (int i = 0; i < rep; i++) r += c;\n tryAdd(r);\n }\n for (int rep = 1; rep * L <= 200; rep++) {\n string r; for (int i = 0; i < rep; i++) r += path;\n tryAdd(r);\n }\n for (int bonus = 1; bonus <= 12; bonus++) {\n for (int base = 1; base * L <= 200; base++) {\n string r; int ci = si, cj = sj;\n for (char c : path) {\n auto [ni, nj] = doMove(ci, cj, c);\n int reps = !canMove(ni, nj, c) ? base + bonus : base;\n for (int i = 0; i < reps && r.size() < 200; i++) r += c;\n ci = ni; cj = nj;\n }\n tryAdd(r);\n }\n }\n for (int pr = 1; pr <= 12; pr++) {\n for (int mr = 1; mr * L * pr <= 200 && mr <= 12; mr++) {\n string r;\n for (int i = 0; i < pr; i++) for (char c : path) for (int j = 0; j < mr; j++) r += c;\n tryAdd(r);\n }\n }\n for (int sr = 1; sr <= 6; sr++) {\n for (int er = sr; er <= 15; er++) {\n string r;\n for (int i = 0; i < L && r.size() < 200; i++) {\n int rep = sr + (er - sr) * i / max(1, L - 1);\n for (int j = 0; j < rep && r.size() < 200; j++) r += path[i];\n }\n tryAdd(r);\n }\n }\n }\n \n string cur = best;\n double curScore = bestScore;\n localSearch(cur, curScore, 1400);\n \n while (!timeUp(1850)) {\n cur = best;\n curScore = bestScore;\n \n int ops = 1 + rng() % 4;\n for (int i = 0; i < ops && cur.size() > 1; i++) {\n int t = rng() % 5;\n if (t == 0 && cur.size() > 1) cur.erase(rng() % cur.size(), 1);\n else if (t == 1 && cur.size() < 200) cur.insert(rng() % (cur.size() + 1), 1, dirs[rng() % 4]);\n else if (t == 2) cur[rng() % cur.size()] = dirs[rng() % 4];\n else if (t == 3 && cur.size() < 200) { int pos = rng() % cur.size(); cur.insert(pos, 1, cur[pos]); }\n else if (t == 4 && cur.size() >= 3) { int pos = rng() % (cur.size() - 2); cur.erase(pos, 2); }\n }\n \n if (!cur.empty() && cur.size() <= 200) {\n curScore = evaluate(cur);\n if (curScore > bestScore * 0.95) localSearch(cur, curScore, 1850);\n }\n }\n \n cout << best << endl;\n return 0;\n}","ahc010":"#include \nusing namespace std;\n\nconst int N = 30;\nint tiles[N][N];\nint rotation[N][N];\n\nconst int di[] = {0, -1, 0, 1};\nconst int dj[] = {-1, 0, 1, 0};\n\nconst int to_arr[8][4] = {\n {1, 0, -1, -1}, {3, -1, -1, 0}, {-1, -1, 3, 2}, {-1, 2, 1, -1},\n {1, 0, 3, 2}, {3, 2, 1, 0}, {2, -1, 0, -1}, {-1, 3, -1, 1},\n};\n\ninline int getState(int i, int j) {\n int t = tiles[i][j], r = rotation[i][j];\n if (t < 4) return (t + r) % 4;\n if (t < 6) return 4 + (t - 4 + r) % 2;\n return 6 + (t - 6 + r) % 2;\n}\n\nint traceLoop(int si, int sj, int sd) {\n int i = si, j = sj, d = sd, length = 0;\n do {\n int state = getState(i, j);\n int d2 = to_arr[state][d];\n if (d2 == -1) return 0;\n length++;\n if (length > 4 * N * N) return 0;\n i += di[d2]; j += dj[d2];\n if ((unsigned)i >= N || (unsigned)j >= N) return 0;\n d = (d2 + 2) % 4;\n } while (i != si || j != sj || d != sd);\n return length;\n}\n\npair computeTopTwoLoops() {\n static bool visited[N][N][4];\n memset(visited, 0, sizeof(visited));\n int top1 = 0, top2 = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n int state = getState(i, j);\n for (int d = 0; d < 4; d++) {\n if (to_arr[state][d] == -1 || visited[i][j][d]) continue;\n int len = traceLoop(i, j, d);\n if (len > 0) {\n if (len > top1) { top2 = top1; top1 = len; }\n else if (len > top2) { top2 = len; }\n int ci = i, cj = j, cd = d;\n do {\n visited[ci][cj][cd] = true;\n int st = getState(ci, cj);\n int d2 = to_arr[st][cd];\n ci += di[d2]; cj += dj[d2];\n cd = (d2 + 2) % 4;\n } while (ci != i || cj != j || cd != d);\n }\n }\n }\n }\n return {top1, top2};\n}\n\nint best_rotation[N][N];\nlong long best_score;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) {\n tiles[i][j] = s[j] - '0';\n rotation[i][j] = 0;\n }\n }\n \n mt19937 rng(42);\n auto start_time = chrono::steady_clock::now();\n \n auto [l1, l2] = computeTopTwoLoops();\n best_score = (long long)l1 * l2;\n memcpy(best_rotation, rotation, sizeof(rotation));\n long long current_score = best_score;\n \n const double TIME_LIMIT = 1.9;\n \n while (true) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start_time).count();\n if (elapsed > TIME_LIMIT) break;\n \n double T = 1000.0 * pow(0.0001, elapsed / TIME_LIMIT);\n \n int i = rng() % N, j = rng() % N;\n int old_rot = rotation[i][j];\n int new_rot = (old_rot + 1 + rng() % 3) % 4;\n \n rotation[i][j] = new_rot;\n auto [nl1, nl2] = computeTopTwoLoops();\n long long new_score = (long long)nl1 * nl2;\n \n double delta = (double)(new_score - current_score);\n if (delta >= 0 || uniform_real_distribution(0, 1)(rng) < exp(delta / T)) {\n current_score = new_score;\n if (new_score > best_score) {\n best_score = new_score;\n memcpy(best_rotation, rotation, sizeof(rotation));\n }\n } else {\n rotation[i][j] = old_rot;\n }\n }\n \n string result;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n result += ('0' + best_rotation[i][j]);\n cout << result << endl;\n \n return 0;\n}","ahc011":"#include \nusing namespace std;\n\nint N, T;\nint dr[] = {-1, 1, 0, 0};\nint dc[] = {0, 0, -1, 1};\nchar dc_char[] = {'U', 'D', 'L', 'R'};\n\nint hexChar(char c) {\n return (c >= '0' && c <= '9') ? c - '0' : c - 'a' + 10;\n}\n\nint calcScore(const vector>& board) {\n vector> adj(N * N);\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (board[i][j] == 0) continue;\n if (i + 1 < N && board[i+1][j] != 0 && (board[i][j] & 8) && (board[i+1][j] & 2)) {\n adj[i*N+j].push_back((i+1)*N+j);\n adj[(i+1)*N+j].push_back(i*N+j);\n }\n if (j + 1 < N && board[i][j+1] != 0 && (board[i][j] & 4) && (board[i][j+1] & 1)) {\n adj[i*N+j].push_back(i*N+j+1);\n adj[i*N+j+1].push_back(i*N+j);\n }\n }\n }\n vector vis(N * N, false);\n int maxTree = 0;\n for (int s = 0; s < N * N; s++) {\n if (vis[s] || board[s/N][s%N] == 0) continue;\n int cnt = 0, edges = 0;\n queue q; q.push(s); vis[s] = true;\n while (!q.empty()) {\n int u = q.front(); q.pop(); cnt++;\n edges += adj[u].size();\n for (int v : adj[u]) if (!vis[v]) { vis[v] = true; q.push(v); }\n }\n if (edges / 2 == cnt - 1) maxTree = max(maxTree, cnt);\n }\n return maxTree;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> T;\n vector> board(N, vector(N));\n int er, ec;\n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) {\n board[i][j] = hexChar(s[j]);\n if (board[i][j] == 0) { er = i; ec = j; }\n }\n }\n \n string best, cur;\n int bestScore = calcScore(board), curScore = bestScore;\n auto bestBoard = board; int bestEr = er, bestEc = ec;\n \n mt19937 rng(42);\n auto start = chrono::steady_clock::now();\n \n while (chrono::duration_cast(chrono::steady_clock::now() - start).count() < 2800) {\n if (cur.size() >= (size_t)T || bestScore >= N * N - 1) break;\n \n vector valid;\n for (int d = 0; d < 4; d++) {\n int nr = er + dr[d], nc = ec + dc[d];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N) valid.push_back(d);\n }\n int d = valid[rng() % valid.size()];\n int nr = er + dr[d], nc = ec + dc[d];\n \n swap(board[er][ec], board[nr][nc]);\n cur += dc_char[d];\n int newScore = calcScore(board);\n \n double temp = 1.0 - (double)cur.size() / T;\n bool accept = newScore > curScore || (rng() % 1000 < 100 * temp);\n \n if (accept) {\n er = nr; ec = nc; curScore = newScore;\n if (curScore > bestScore || (curScore == bestScore && cur.size() < best.size())) {\n bestScore = curScore; best = cur;\n bestBoard = board; bestEr = er; bestEc = ec;\n }\n } else {\n cur.pop_back();\n swap(board[er][ec], board[nr][nc]);\n }\n \n if (cur.size() > T / 2 && rng() % 100 < 5) {\n board = bestBoard; er = bestEr; ec = bestEc;\n cur = best; curScore = bestScore;\n }\n }\n \n cout << best << endl;\n return 0;\n}","ahc012":"#include \nusing namespace std;\n\ntypedef long long ll;\n\nint N, K;\nvector a(10);\nvector> berries;\nvector> cuts;\nvector> sides;\n\ninline int side(ll x1, ll y1, ll x2, ll y2, ll px, ll py) {\n __int128 cross = (__int128)(x2 - x1) * (py - y1) - (__int128)(y2 - y1) * (px - x1);\n if (cross > 0) return 1;\n if (cross < 0) return -1;\n return 0;\n}\n\nint calcScore() {\n int numCuts = cuts.size();\n unordered_map pieceCount;\n pieceCount.reserve(N);\n \n for (int j = 0; j < N; j++) {\n bool onLine = false;\n uint64_t h = 0;\n for (int i = 0; i < numCuts; i++) {\n if (sides[i][j] == 0) { onLine = true; break; }\n h = h * 3ULL + (uint64_t)(sides[i][j] + 1);\n }\n if (!onLine) pieceCount[h]++;\n }\n \n vector b(11, 0);\n for (auto& [sig, cnt] : pieceCount) {\n if (cnt >= 1 && cnt <= 10) b[cnt]++;\n }\n \n int total = 0;\n for (int d = 1; d <= 10; d++) total += min(a[d-1], b[d]);\n return total;\n}\n\nvoid updateSides(int idx) {\n while ((int)sides.size() <= idx) sides.push_back(vector(N));\n for (int j = 0; j < N; j++) {\n sides[idx][j] = side(cuts[idx][0], cuts[idx][1], cuts[idx][2], cuts[idx][3],\n berries[j].first, berries[j].second);\n }\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> K;\n for (int i = 0; i < 10; i++) cin >> a[i];\n \n berries.resize(N);\n for (int i = 0; i < N; i++) cin >> berries[i].first >> berries[i].second;\n \n mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());\n \n auto randLine = [&]() -> array {\n ll px = (ll)(rng() % 20001) - 10000;\n ll py = (ll)(rng() % 20001) - 10000;\n ll qx = (ll)(rng() % 20001) - 10000;\n ll qy = (ll)(rng() % 20001) - 10000;\n while (px == qx && py == qy) { qx = (ll)(rng() % 20001) - 10000; qy = (ll)(rng() % 20001) - 10000; }\n return {px, py, qx, qy};\n };\n \n auto perpBisector = [&](int i, int j) -> array {\n if (i == j) return randLine();\n ll dx = berries[j].first - berries[i].first;\n ll dy = berries[j].second - berries[i].second;\n ll mx = berries[i].first + berries[j].first;\n ll my = berries[i].second + berries[j].second;\n return {mx - dy * 1000, my + dx * 1000, mx + dy * 1000, my - dx * 1000};\n };\n \n auto radialLine = [&](double angle) -> array {\n ll px = (ll)(cos(angle) * 15000);\n ll py = (ll)(sin(angle) * 15000);\n if (px == 0 && py == 0) px = 1;\n return {px, py, -px, -py};\n };\n \n auto genLine = [&]() -> array {\n int strat = rng() % 5;\n if (strat == 0) return randLine();\n else if (strat <= 2) return perpBisector(rng() % N, rng() % N);\n else if (strat == 3) return radialLine((double)(rng() % 10000) / 10000.0 * M_PI * 2);\n else {\n int b1 = rng() % N, b2 = rng() % N;\n if (b1 != b2) return {berries[b1].first, berries[b1].second, berries[b2].first, berries[b2].second};\n return randLine();\n }\n };\n \n int bestScore = 0;\n vector> bestCuts;\n \n auto start = chrono::steady_clock::now();\n \n for (int restart = 0; ; restart++) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration_cast(now - start).count();\n if (elapsed > 2850) break;\n \n cuts.clear();\n sides.clear();\n int numCuts = 25 + rng() % 35;\n \n for (int i = 0; i < numCuts; i++) {\n cuts.push_back(genLine());\n updateSides(i);\n }\n \n int curScore = calcScore();\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n \n for (int iter = 0; ; iter++) {\n now = chrono::steady_clock::now();\n elapsed = chrono::duration_cast(now - start).count();\n if (elapsed > 2850) break;\n \n double progress = elapsed / 2850.0;\n double temp = 3.0 * (1.0 - progress) + 0.1;\n int moveType = rng() % 100;\n \n if (moveType < 75 && !cuts.empty()) {\n int idx = rng() % cuts.size();\n auto oldCut = cuts[idx];\n auto oldSide = sides[idx];\n \n cuts[idx] = genLine();\n updateSides(idx);\n \n int newScore = calcScore();\n if (newScore > curScore || (double)(rng() % 1000000) / 1000000.0 < exp((newScore - curScore) / temp)) {\n curScore = newScore;\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n } else {\n cuts[idx] = oldCut;\n sides[idx] = oldSide;\n }\n } else if (moveType < 90 && cuts.size() < (size_t)min(K, 80)) {\n cuts.push_back(genLine());\n updateSides(cuts.size() - 1);\n \n int newScore = calcScore();\n if (newScore >= curScore) {\n curScore = newScore;\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n } else {\n cuts.pop_back();\n sides.pop_back();\n }\n } else if (cuts.size() > 10) {\n int idx = rng() % cuts.size();\n auto oldCut = cuts[idx];\n auto oldSide = sides[idx];\n cuts.erase(cuts.begin() + idx);\n sides.erase(sides.begin() + idx);\n \n int newScore = calcScore();\n if (newScore >= curScore) {\n curScore = newScore;\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n } else {\n cuts.insert(cuts.begin() + idx, oldCut);\n sides.insert(sides.begin() + idx, oldSide);\n }\n }\n }\n }\n \n cout << bestCuts.size() << \"\\n\";\n for (auto& c : bestCuts) cout << c[0] << \" \" << c[1] << \" \" << c[2] << \" \" << c[3] << \"\\n\";\n \n return 0;\n}","ahc014":"#include \nusing namespace std;\n\nint N, M, c;\nset> dots;\nset> usedSegs;\nvector> ops;\n\nbool inGrid(int x, int y) { return x >= 0 && x < N && y >= 0 && y < N; }\nlong long wt(int x, int y) { return (long long)(x-c)*(x-c) + (long long)(y-c)*(y-c) + 1; }\n\nvoid addSeg(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g == 0) return;\n dx /= g; dy /= g;\n for (int i = 0; i < g; i++) {\n int a = x1+i*dx, b = y1+i*dy, e = a+dx, f = b+dy;\n if (a > e || (a == e && b > f)) { swap(a,e); swap(b,f); }\n usedSegs.insert({a,b,e,f});\n }\n}\n\nbool segUsed(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g == 0) return true;\n dx /= g; dy /= g;\n for (int i = 0; i < g; i++) {\n int a = x1+i*dx, b = y1+i*dy, e = a+dx, f = b+dy;\n if (a > e || (a == e && b > f)) { swap(a,e); swap(b,f); }\n if (usedSegs.count({a,b,e,f})) return true;\n }\n return false;\n}\n\nbool dotOnSeg(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g <= 1) return false;\n dx /= g; dy /= g;\n for (int i = 1; i < g; i++)\n if (dots.count({x1+i*dx, y1+i*dy})) return true;\n return false;\n}\n\nbool isValidRect(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4) {\n int v1x = x2-x1, v1y = y2-y1;\n int v2x = x3-x2, v2y = y3-y2;\n if (v1x == 0 && v1y == 0) return false;\n if (v2x == 0 && v2y == 0) return false;\n if (v1x*v2x + v1y*v2y != 0) return false;\n bool axis1 = (v1x == 0 || v1y == 0);\n bool diag1 = (abs(v1x) == abs(v1y));\n if (!axis1 && !diag1) return false;\n bool axis2 = (v2x == 0 || v2y == 0);\n bool diag2 = (abs(v2x) == abs(v2y));\n if (!axis2 && !diag2) return false;\n if (x4 != x1 + v2x || y4 != y1 + v2y) return false;\n return true;\n}\n\nbool tryAdd(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4) {\n if (!inGrid(x1,y1) || dots.count({x1,y1})) return false;\n if (!dots.count({x2,y2}) || !dots.count({x3,y3}) || !dots.count({x4,y4})) return false;\n set> pts = {{x1,y1},{x2,y2},{x3,y3},{x4,y4}};\n if (pts.size() != 4) return false;\n if (!isValidRect(x1,y1,x2,y2,x3,y3,x4,y4)) return false;\n if (dotOnSeg(x1,y1,x2,y2) || dotOnSeg(x2,y2,x3,y3) || \n dotOnSeg(x3,y3,x4,y4) || dotOnSeg(x4,y4,x1,y1)) return false;\n if (segUsed(x1,y1,x2,y2) || segUsed(x2,y2,x3,y3) || \n segUsed(x3,y3,x4,y4) || segUsed(x4,y4,x1,y1)) return false;\n \n dots.insert({x1,y1});\n addSeg(x1,y1,x2,y2); addSeg(x2,y2,x3,y3);\n addSeg(x3,y3,x4,y4); addSeg(x4,y4,x1,y1);\n ops.push_back({x1,y1,x2,y2,x3,y3,x4,y4});\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M;\n c = (N-1) / 2;\n for (int i = 0; i < M; i++) { int x, y; cin >> x >> y; dots.insert({x, y}); }\n \n auto tstart = chrono::steady_clock::now();\n mt19937 rng(42);\n \n int fails = 0;\n while (chrono::duration(chrono::steady_clock::now() - tstart).count() < 4.5) {\n vector> dl(dots.begin(), dots.end());\n shuffle(dl.begin(), dl.end(), rng);\n int sz = min((int)dl.size(), 100);\n \n vector>> candidates;\n \n for (int i = 0; i < sz; i++) {\n for (int j = 0; j < sz; j++) {\n if (i == j) continue;\n for (int k = 0; k < sz; k++) {\n if (k == i || k == j) continue;\n auto [ax, ay] = dl[i];\n auto [bx, by] = dl[j];\n auto [cx, cy] = dl[k];\n \n // Try: new point D, with corners D-A-B-C (A opposite to C, B opposite to D)\n // D = A + C - B\n int dx = ax + cx - bx, dy = ay + cy - by;\n if (inGrid(dx, dy) && !dots.count({dx, dy})) {\n long long w = wt(dx, dy);\n candidates.push_back({w, {dx, dy, ax, ay, bx, by, cx, cy}});\n }\n }\n }\n }\n \n sort(candidates.begin(), candidates.end(), greater<>());\n \n bool found = false;\n for (auto& [w, arr] : candidates) {\n if (tryAdd(arr[0],arr[1],arr[2],arr[3],arr[4],arr[5],arr[6],arr[7])) {\n found = true;\n break;\n }\n }\n \n if (!found) {\n if (++fails > 200) break;\n } else {\n fails = 0;\n }\n }\n \n cout << ops.size() << \"\\n\";\n for (auto& op : ops) {\n for (int i = 0; i < 8; i++) cout << op[i] << \" \\n\"[i==7];\n }\n return 0;\n}","ahc015":"#include \nusing namespace std;\n\nconst int N = 10;\n\nstruct State {\n int grid[N][N];\n \n State() { memset(grid, 0, sizeof(grid)); }\n \n int countEmpty() const {\n int cnt = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (grid[i][j] == 0) cnt++;\n return cnt;\n }\n \n void place(int p, int flavor) {\n int cnt = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (grid[i][j] == 0 && ++cnt == p) { grid[i][j] = flavor; return; }\n }\n \n void tilt(int dir) {\n if (dir == 0) {\n for (int j = 0; j < N; j++) {\n int w = 0;\n for (int i = 0; i < N; i++) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[w++][j] = v; }\n }\n } else if (dir == 1) {\n for (int j = 0; j < N; j++) {\n int w = N - 1;\n for (int i = N - 1; i >= 0; i--) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[w--][j] = v; }\n }\n } else if (dir == 2) {\n for (int i = 0; i < N; i++) {\n int w = 0;\n for (int j = 0; j < N; j++) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[i][w++] = v; }\n }\n } else {\n for (int i = 0; i < N; i++) {\n int w = N - 1;\n for (int j = N - 1; j >= 0; j--) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[i][w--] = v; }\n }\n }\n }\n \n long long calcScore() const {\n bool vis[N][N] = {};\n long long sum = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (grid[i][j] && !vis[i][j]) {\n int f = grid[i][j], sz = 0;\n int stk[100], top = 0;\n stk[top++] = i * N + j;\n vis[i][j] = true;\n while (top > 0) {\n int pos = stk[--top];\n int x = pos / N, y = pos % N;\n sz++;\n if (x > 0 && !vis[x-1][y] && grid[x-1][y] == f) { vis[x-1][y] = true; stk[top++] = (x-1)*N+y; }\n if (x < N-1 && !vis[x+1][y] && grid[x+1][y] == f) { vis[x+1][y] = true; stk[top++] = (x+1)*N+y; }\n if (y > 0 && !vis[x][y-1] && grid[x][y-1] == f) { vis[x][y-1] = true; stk[top++] = x*N+y-1; }\n if (y < N-1 && !vis[x][y+1] && grid[x][y+1] == f) { vis[x][y+1] = true; stk[top++] = x*N+y+1; }\n }\n sum += (long long)sz * sz;\n }\n }\n }\n return sum;\n }\n};\n\nmt19937 rng(12345);\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int f[101];\n for (int t = 1; t <= 100; t++) cin >> f[t];\n \n State state;\n \n for (int t = 1; t <= 100; t++) {\n int p; cin >> p;\n state.place(p, f[t]);\n \n int remaining = 100 - t;\n int depth = min(13, remaining);\n int numSims;\n if (t <= 40) numSims = 32;\n else if (t <= 80) numSims = 28;\n else numSims = 20;\n \n int bestDir = 0;\n long long bestScore = -1;\n \n for (int dir = 0; dir < 4; dir++) {\n long long totalScore = 0;\n \n for (int sim = 0; sim < numSims; sim++) {\n State s = state;\n s.tilt(dir);\n \n for (int step = 1; step <= depth && t + step <= 100; step++) {\n int empty = s.countEmpty();\n if (empty == 0) break;\n int randPos = (rng() % empty) + 1;\n s.place(randPos, f[t + step]);\n \n int simBest = 0;\n long long simBestScore = -1;\n for (int d = 0; d < 4; d++) {\n State tmp = s;\n tmp.tilt(d);\n long long sc = tmp.calcScore();\n if (sc > simBestScore) { simBestScore = sc; simBest = d; }\n }\n s.tilt(simBest);\n }\n totalScore += s.calcScore();\n }\n \n if (totalScore > bestScore) {\n bestScore = totalScore;\n bestDir = dir;\n }\n }\n \n state.tilt(bestDir);\n const char dirChar[] = {'F', 'B', 'L', 'R'};\n cout << dirChar[bestDir] << '\\n' << flush;\n }\n \n return 0;\n}","ahc016":"#include \nusing namespace std;\n\nint N, M;\ndouble eps;\n\nvector get_sorted_degrees(const string& s) {\n vector deg(N, 0);\n int idx = 0;\n for (int i = 0; i < N; i++) {\n for (int j = i + 1; j < N; j++) {\n if (s[idx++] == '1') {\n deg[i]++;\n deg[j]++;\n }\n }\n }\n sort(deg.begin(), deg.end());\n return deg;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(0);\n \n cin >> M >> eps;\n \n // Better N selection based on theoretical analysis\n // Need larger N for higher noise to maintain distinguishability\n double noise_factor = (eps < 0.001) ? 1.0 : 1.0 / max(0.2, 1.0 - 2.0 * eps);\n \n // Base N on M and noise\n if (eps < 0.01) {\n N = (int)ceil(sqrt(2.0 * M)) + 2;\n } else if (eps < 0.05) {\n N = (int)ceil(sqrt(2.5 * M)) + 4;\n } else if (eps < 0.15) {\n N = (int)ceil(sqrt(3.0 * M * noise_factor)) + 8;\n } else if (eps < 0.25) {\n N = (int)ceil(sqrt(4.0 * M * noise_factor)) + 15;\n } else if (eps < 0.35) {\n N = (int)ceil(sqrt(5.0 * M * noise_factor)) + 25;\n } else {\n N = (int)ceil(sqrt(6.0 * M * noise_factor)) + 35;\n }\n \n N = max(N, (int)(2.0 * sqrt(M)));\n N = max(N, 8);\n N = min(N, 100);\n \n cout << N << \"\\n\";\n \n int total = N * (N - 1) / 2;\n \n vector G(M);\n vector> expected_deg(M);\n \n // Create M graphs with linearly spaced edge counts\n for (int i = 0; i < M; i++) {\n string s(total, '0');\n long long edges = (M > 1) ? ((long long)i * total / (M - 1)) : 0;\n \n // Fill edges in a pattern that creates varied degree distribution\n int idx = 0;\n int filled = 0;\n for (int a = 0; a < N && filled < edges; a++) {\n for (int b = a + 1; b < N && filled < edges; b++) {\n int pos = a * (2 * N - a - 1) / 2 + (b - a - 1);\n s[pos] = '1';\n filled++;\n }\n }\n \n G[i] = s;\n \n // Compute expected degree sequence after noise\n vector deg = get_sorted_degrees(s);\n expected_deg[i].resize(N);\n double transform = 1.0 - 2.0 * eps;\n double base = (N - 1) * eps;\n for (int j = 0; j < N; j++) {\n expected_deg[i][j] = deg[j] * transform + base;\n }\n \n cout << s << \"\\n\";\n }\n cout.flush();\n \n for (int q = 0; q < 100; q++) {\n string H;\n cin >> H;\n \n vector deg_h = get_sorted_degrees(H);\n \n int best = 0;\n double best_score = 1e18;\n \n for (int i = 0; i < M; i++) {\n // Weighted L2 distance - weight more heavily at extremes\n double score = 0;\n for (int j = 0; j < N; j++) {\n double diff = deg_h[j] - expected_deg[i][j];\n // Weight endpoints more (more informative)\n double weight = 1.0 + 0.5 * (abs(j - N/2.0) / (N/2.0));\n score += weight * diff * diff;\n }\n \n if (score < best_score) {\n best_score = score;\n best = i;\n }\n }\n \n cout << best << \"\\n\";\n cout.flush();\n }\n \n return 0;\n}","ahc017":"#include \nusing namespace std;\n\nint N, M, D, K;\nvector> edges;\nvector>> adj;\nvector> adjEdge;\nmt19937 rng(42);\nconst long long INF = 1e9;\n\nvector dijkstraMask(int src, const vector& excl) {\n vector dist(N, INF);\n priority_queue, vector>, greater<>> pq;\n dist[src] = 0;\n pq.push({0, src});\n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > dist[u]) continue;\n for (size_t i = 0; i < adj[u].size(); i++) {\n if (excl[adjEdge[u][i]]) continue;\n auto [v, w] = adj[u][i];\n if (dist[u] + w < dist[v]) {\n dist[v] = dist[u] + w;\n pq.push({dist[v], v});\n }\n }\n }\n return dist;\n}\n\nint numSamples;\nvector samples;\nvector> origDist;\nvector assign_;\nvector cnt;\n\ndouble evalDay(int d) {\n vector excl(M, false);\n for (int e = 0; e < M; e++) if (assign_[e] == d) excl[e] = true;\n double tot = 0;\n for (int i = 0; i < numSamples; i++) {\n auto dist = dijkstraMask(samples[i], excl);\n for (int v = 0; v < N; v++) if (v != samples[i])\n tot += min(dist[v], INF) - origDist[i][v];\n }\n return tot;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n auto start = chrono::steady_clock::now();\n \n cin >> N >> M >> D >> K;\n edges.resize(M); adj.resize(N); adjEdge.resize(N);\n \n for (int i = 0; i < M; i++) {\n int u, v, w; cin >> u >> v >> w; u--; v--;\n edges[i] = {u, v, w};\n adj[u].push_back({v, w}); adj[v].push_back({u, w});\n adjEdge[u].push_back(i); adjEdge[v].push_back(i);\n }\n for (int i = 0; i < N; i++) { int x, y; cin >> x >> y; }\n \n vector noEdge(M, false);\n vector crit(M);\n for (int e = 0; e < M; e++) {\n noEdge[e] = true;\n auto dist = dijkstraMask(edges[e][0], noEdge);\n crit[e] = dist[edges[e][1]] - edges[e][2];\n noEdge[e] = false;\n }\n \n numSamples = min(55, N);\n samples.resize(N); iota(samples.begin(), samples.end(), 0);\n shuffle(samples.begin(), samples.end(), rng);\n samples.resize(numSamples);\n \n origDist.resize(numSamples);\n for (int i = 0; i < numSamples; i++) origDist[i] = dijkstraMask(samples[i], noEdge);\n \n double globalBest = 1e18;\n vector globalBestAssign;\n \n for (int restart = 0; restart < 3; restart++) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > 5.0) break;\n \n vector order(M); iota(order.begin(), order.end(), 0);\n if (restart == 0) {\n sort(order.begin(), order.end(), [&](int a, int b) { return crit[a] > crit[b]; });\n } else {\n shuffle(order.begin(), order.end(), rng);\n sort(order.begin(), order.end(), [&](int a, int b) { return crit[a] > crit[b]; });\n }\n \n assign_.assign(M, 0);\n cnt.assign(D + 1, 0);\n vector> dayVertices(D + 1);\n \n for (int e : order) {\n int u = edges[e][0], v = edges[e][1];\n int best = 1, bestScore = INT_MAX;\n for (int d = 1; d <= D; d++) {\n if (cnt[d] >= K) continue;\n int conflict = (dayVertices[d].count(u) ? 1 : 0) + (dayVertices[d].count(v) ? 1 : 0);\n int score = conflict * 10000 + cnt[d] + (restart > 0 ? (int)(rng() % 100) : 0);\n if (score < bestScore) { bestScore = score; best = d; }\n }\n assign_[e] = best; cnt[best]++;\n dayVertices[best].insert(u); dayVertices[best].insert(v);\n }\n \n vector dayCost(D + 1);\n double cur = 0;\n for (int d = 1; d <= D; d++) { dayCost[d] = evalDay(d); cur += dayCost[d]; }\n \n double bestScore = cur;\n vector bestAssign = assign_;\n double temp = max(1.0, cur / D / 3);\n int noImprove = 0;\n \n while (true) {\n now = chrono::steady_clock::now();\n elapsed = chrono::duration(now - start).count();\n double timePerRestart = 5.3 / 3;\n if (elapsed > (restart + 1) * timePerRestart || elapsed > 5.3) break;\n \n if (noImprove > 500) {\n temp = max(temp, bestScore / D / 10);\n noImprove = 0;\n }\n \n int worstDay = 1;\n for (int d = 2; d <= D; d++) if (dayCost[d] > dayCost[worstDay]) worstDay = d;\n \n int moveType = rng() % 5;\n \n if (moveType < 2) {\n int e1 = rng() % M, e2 = rng() % M;\n if (assign_[e1] == assign_[e2]) continue;\n int d1 = assign_[e1], d2 = assign_[e2];\n \n swap(assign_[e1], assign_[e2]);\n double nc1 = evalDay(d1), nc2 = evalDay(d2);\n double delta = (nc1 + nc2) - (dayCost[d1] + dayCost[d2]);\n \n if (delta < 0 || (double)(rng() % 1000000) / 1000000 < exp(-delta / temp)) {\n dayCost[d1] = nc1; dayCost[d2] = nc2; cur += delta;\n if (cur < bestScore) { bestScore = cur; bestAssign = assign_; noImprove = 0; }\n else noImprove++;\n } else { swap(assign_[e1], assign_[e2]); noImprove++; }\n } else if (moveType == 2) {\n int e = rng() % M;\n int oldD = assign_[e], newD = rng() % D + 1;\n if (newD == oldD || cnt[newD] >= K) continue;\n \n assign_[e] = newD; cnt[oldD]--; cnt[newD]++;\n double nc1 = evalDay(oldD), nc2 = evalDay(newD);\n double delta = (nc1 + nc2) - (dayCost[oldD] + dayCost[newD]);\n \n if (delta < 0 || (double)(rng() % 1000000) / 1000000 < exp(-delta / temp)) {\n dayCost[oldD] = nc1; dayCost[newD] = nc2; cur += delta;\n if (cur < bestScore) { bestScore = cur; bestAssign = assign_; noImprove = 0; }\n else noImprove++;\n } else { assign_[e] = oldD; cnt[oldD]++; cnt[newD]--; noImprove++; }\n } else {\n vector worstEdges;\n for (int e = 0; e < M; e++) if (assign_[e] == worstDay) worstEdges.push_back(e);\n if (worstEdges.empty()) continue;\n int e = worstEdges[rng() % worstEdges.size()];\n int newD = rng() % D + 1;\n if (newD == worstDay || cnt[newD] >= K) continue;\n \n assign_[e] = newD; cnt[worstDay]--; cnt[newD]++;\n double nc1 = evalDay(worstDay), nc2 = evalDay(newD);\n double delta = (nc1 + nc2) - (dayCost[worstDay] + dayCost[newD]);\n \n if (delta < 0 || (double)(rng() % 1000000) / 1000000 < exp(-delta / temp)) {\n dayCost[worstDay] = nc1; dayCost[newD] = nc2; cur += delta;\n if (cur < bestScore) { bestScore = cur; bestAssign = assign_; noImprove = 0; }\n else noImprove++;\n } else { assign_[e] = worstDay; cnt[worstDay]++; cnt[newD]--; noImprove++; }\n }\n temp *= 0.999995;\n if (temp < 0.1) temp = 0.1;\n }\n \n if (bestScore < globalBest) {\n globalBest = bestScore;\n globalBestAssign = bestAssign;\n }\n }\n \n for (int i = 0; i < M; i++) cout << globalBestAssign[i] << \" \\n\"[i == M-1];\n return 0;\n}","ahc019":"#include \nusing namespace std;\n\nint D;\nstring f[2][15], r[2][15];\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> D;\n for (int i = 0; i < 2; i++) {\n for (int k = 0; k < D; k++) cin >> f[i][k];\n for (int k = 0; k < D; k++) cin >> r[i][k];\n }\n \n vector b[2];\n for (int i = 0; i < 2; i++) b[i].assign(D * D * D, 0);\n \n auto idx = [&](int x, int y, int z) { return x * D * D + y * D + z; };\n int dx[] = {1, -1, 0, 0, 0, 0};\n int dy[] = {0, 0, 1, -1, 0, 0};\n int dz[] = {0, 0, 0, 0, 1, -1};\n \n int n = 0;\n \n // Step 1: Create large shared blocks from cells valid in both at same position\n for (int x = 0; x < D; x++) {\n for (int y = 0; y < D; y++) {\n for (int z = 0; z < D; z++) {\n bool v0 = (f[0][z][x] == '1' && r[0][z][y] == '1');\n bool v1 = (f[1][z][x] == '1' && r[1][z][y] == '1');\n if (v0 && v1 && b[0][idx(x,y,z)] == 0) {\n n++;\n queue> q;\n q.push({x, y, z});\n b[0][idx(x,y,z)] = b[1][idx(x,y,z)] = n;\n while (!q.empty()) {\n auto [cx, cy, cz] = q.front(); q.pop();\n for (int d = 0; d < 6; d++) {\n int nx = cx + dx[d], ny = cy + dy[d], nz = cz + dz[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && nz >= 0 && nz < D) {\n bool nv0 = (f[0][nz][nx] == '1' && r[0][nz][ny] == '1');\n bool nv1 = (f[1][nz][nx] == '1' && r[1][nz][ny] == '1');\n if (nv0 && nv1 && b[0][idx(nx,ny,nz)] == 0) {\n b[0][idx(nx,ny,nz)] = b[1][idx(nx,ny,nz)] = n;\n q.push({nx, ny, nz});\n }\n }\n }\n }\n }\n }\n }\n }\n \n // Step 2: Find remaining constraints for each arrangement\n vector> extra[2];\n for (int arr = 0; arr < 2; arr++) {\n set needFront, needRight;\n for (int z = 0; z < D; z++) {\n for (int x = 0; x < D; x++) if (f[arr][z][x] == '1') needFront.insert(z * D + x);\n for (int y = 0; y < D; y++) if (r[arr][z][y] == '1') needRight.insert(z * D + y);\n }\n \n // Remove constraints already satisfied by shared blocks\n for (int x = 0; x < D; x++) {\n for (int y = 0; y < D; y++) {\n for (int z = 0; z < D; z++) {\n if (b[arr][idx(x,y,z)] > 0) {\n needFront.erase(z * D + x);\n needRight.erase(z * D + y);\n }\n }\n }\n }\n \n // Greedily pick unit blocks for remaining constraints\n while (!needFront.empty() || !needRight.empty()) {\n int bestX = -1, bestY = -1, bestZ = -1, bestScore = -1;\n for (int z = 0; z < D; z++) {\n for (int x = 0; x < D; x++) {\n if (f[arr][z][x] != '1') continue;\n for (int y = 0; y < D; y++) {\n if (r[arr][z][y] != '1') continue;\n int score = 0;\n if (needFront.count(z * D + x)) score++;\n if (needRight.count(z * D + y)) score++;\n if (score > bestScore) {\n bestScore = score;\n bestX = x; bestY = y; bestZ = z;\n }\n }\n }\n }\n if (bestScore <= 0) break;\n extra[arr].push_back({bestX, bestY, bestZ});\n needFront.erase(bestZ * D + bestX);\n needRight.erase(bestZ * D + bestY);\n }\n }\n \n // Step 3: Assign unit blocks (shared between arrangements)\n int m1 = extra[0].size(), m2 = extra[1].size();\n int totalExtra = max(m1, m2);\n \n for (int i = 0; i < m1; i++) {\n auto [x, y, z] = extra[0][i];\n b[0][idx(x,y,z)] = n + 1 + i;\n }\n for (int i = 0; i < m2; i++) {\n auto [x, y, z] = extra[1][i];\n b[1][idx(x,y,z)] = n + 1 + i;\n }\n \n n += totalExtra;\n \n cout << n << \"\\n\";\n for (int i = 0; i < 2; i++) {\n for (int j = 0; j < D * D * D; j++) {\n if (j) cout << \" \";\n cout << b[i][j];\n }\n cout << \"\\n\";\n }\n \n return 0;\n}","ahc020":"#include \nusing namespace std;\n\nint N, M, K;\nvector> V, R;\nvector> E;\nvector>> adj;\nvector> distVV;\nvector> parentV;\n\ndouble getDist(int i, int k) {\n double dx = V[i].first - R[k].first, dy = V[i].second - R[k].second;\n return sqrt(dx*dx + dy*dy);\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> K;\n V.resize(N); R.resize(K); E.resize(M); adj.resize(N);\n \n for(int i = 0; i < N; i++) cin >> V[i].first >> V[i].second;\n for(int j = 0; j < M; j++) {\n int u, v; long long w;\n cin >> u >> v >> w; u--; v--;\n E[j] = {u, v, w};\n adj[u].push_back({v, j});\n adj[v].push_back({u, j});\n }\n for(int k = 0; k < K; k++) cin >> R[k].first >> R[k].second;\n \n // Precompute distances\n vector> distVR(N, vector(K));\n for(int i = 0; i < N; i++)\n for(int k = 0; k < K; k++)\n distVR[i][k] = getDist(i, k);\n \n // All-pairs shortest paths\n distVV.assign(N, vector(N, LLONG_MAX/2));\n parentV.assign(N, vector(N, -1));\n \n for(int s = 0; s < N; s++) {\n distVV[s][s] = 0;\n priority_queue, vector>, greater<>> pq;\n pq.push({0, s});\n while(!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if(d > distVV[s][u]) continue;\n for(auto [v, eid] : adj[u]) {\n long long w = get<2>(E[eid]);\n if(distVV[s][u] + w < distVV[s][v]) {\n distVV[s][v] = distVV[s][u] + w;\n parentV[s][v] = u;\n pq.push({distVV[s][v], v});\n }\n }\n }\n }\n \n auto computeP = [&](const vector& asgn) {\n vector P(N, 0);\n for(int k = 0; k < K; k++) {\n int v = asgn[k];\n P[v] = max(P[v], (int)ceil(distVR[v][k] - 1e-9));\n }\n return P;\n };\n \n auto buildTree = [&](const vector& P) {\n vector B(M, 0);\n for(int i = 0; i < N; i++) if(P[i] > 0) {\n int cur = i;\n while(cur != 0 && parentV[0][cur] != -1) {\n int p = parentV[0][cur];\n for(auto& [nxt, eid] : adj[cur]) if(nxt == p) { B[eid] = 1; break; }\n cur = p;\n }\n }\n return B;\n };\n \n auto getReachable = [&](const vector& B) {\n vector reach; vector vis(N, false);\n queue q; q.push(0); vis[0] = true;\n while(!q.empty()) {\n int u = q.front(); q.pop(); reach.push_back(u);\n for(auto& [v, eid] : adj[u]) if(B[eid] && !vis[v]) { vis[v] = true; q.push(v); }\n }\n return reach;\n };\n \n auto calcCost = [&](const vector& P, const vector& B) {\n long long cost = 0;\n for(int i = 0; i < N; i++) cost += (long long)P[i] * P[i];\n for(int j = 0; j < M; j++) if(B[j]) cost += get<2>(E[j]);\n return cost;\n };\n \n vector bestP(N), bestB(M), bestAsgn(K);\n long long bestCost = LLONG_MAX;\n \n for(double factor : {0.0, 0.001, 0.005, 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1.0}) {\n vector asgn(K);\n for(int k = 0; k < K; k++) {\n int best = -1; double bestScore = 1e18;\n for(int i = 0; i < N; i++) {\n if(distVR[i][k] > 5000) continue;\n double score = distVR[i][k] * distVR[i][k] + factor * distVV[0][i];\n if(score < bestScore) { bestScore = score; best = i; }\n }\n asgn[k] = best;\n }\n \n for(int phase = 0; phase < 3; phase++) {\n auto P = computeP(asgn);\n auto B = buildTree(P);\n \n for(int iter = 0; iter < 20; iter++) {\n auto reach = getReachable(B);\n bool improved = false;\n for(int k = 0; k < K; k++) {\n double curD = distVR[asgn[k]][k];\n for(int v : reach) {\n if(distVR[v][k] < curD - 0.01 && distVR[v][k] <= 5000) {\n asgn[k] = v; curD = distVR[v][k]; improved = true;\n }\n }\n }\n if(!improved) break;\n P = computeP(asgn); B = buildTree(P);\n }\n \n // Outlier optimization\n for(int iter = 0; iter < 10; iter++) {\n auto reach = getReachable(B);\n vector> vRes(N);\n for(int k = 0; k < K; k++) vRes[asgn[k]].push_back(k);\n \n bool improved = false;\n for(int v : reach) {\n if(vRes[v].size() <= 1) continue;\n int fk = -1; double maxD = 0;\n for(int k : vRes[v]) if(distVR[v][k] > maxD) { maxD = distVR[v][k]; fk = k; }\n \n for(int nv : reach) {\n if(nv == v || distVR[nv][fk] > 5000) continue;\n double newMaxV = 0;\n for(int k : vRes[v]) if(k != fk) newMaxV = max(newMaxV, distVR[v][k]);\n double oldMaxNV = 0;\n for(int k : vRes[nv]) oldMaxNV = max(oldMaxNV, distVR[nv][k]);\n double newMaxNV = max(oldMaxNV, distVR[nv][fk]);\n double delta = (newMaxV*newMaxV - maxD*maxD) + (newMaxNV*newMaxNV - oldMaxNV*oldMaxNV);\n if(delta < -1) { asgn[fk] = nv; improved = true; break; }\n }\n }\n if(!improved) break;\n P = computeP(asgn); B = buildTree(P);\n }\n }\n \n auto P = computeP(asgn);\n auto B = buildTree(P);\n long long cost = calcCost(P, B);\n if(cost < bestCost) { bestCost = cost; bestP = P; bestB = B; bestAsgn = asgn; }\n }\n \n for(int i = 0; i < N; i++) cout << bestP[i] << \" \\n\"[i==N-1];\n for(int j = 0; j < M; j++) cout << bestB[j] << \" \\n\"[j==M-1];\n}","ahc021":"#include \nusing namespace std;\n\nconst int N = 30;\nint b[N][N];\nvector> ops;\n\nvoid do_swap(int x1, int y1, int x2, int y2) {\n ops.push_back({x1, y1, x2, y2});\n swap(b[x1][y1], b[x2][y2]);\n}\n\nvoid sift_down(int x, int y) {\n while (x < N - 1) {\n int min_child_y = (b[x + 1][y + 1] < b[x + 1][y]) ? (y + 1) : y;\n if (b[x][y] > b[x + 1][min_child_y]) {\n do_swap(x, y, x + 1, min_child_y);\n x = x + 1;\n y = min_child_y;\n } else {\n break;\n }\n }\n}\n\nbool has_violation(int x, int y) {\n if (x >= N - 1) return false;\n return b[x][y] > b[x + 1][y] || b[x][y] > b[x + 1][y + 1];\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int x = 0; x < N; x++) {\n for (int y = 0; y <= x; y++) {\n cin >> b[x][y];\n }\n }\n \n // Process violations iteratively - prioritize by value (larger values first)\n bool changed = true;\n while (changed) {\n changed = false;\n // Collect all violations with their values\n vector> violations; // (value, x, y)\n for (int x = N - 2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) {\n if (has_violation(x, y)) {\n violations.push_back({b[x][y], x, y});\n }\n }\n }\n \n // Sort by value descending (fix larger values first)\n sort(violations.rbegin(), violations.rend());\n \n for (auto& [val, x, y] : violations) {\n if (has_violation(x, y)) {\n sift_down(x, y);\n changed = true;\n }\n }\n }\n \n cout << ops.size() << \"\\n\";\n for (auto& [x1, y1, x2, y2] : ops) {\n cout << x1 << \" \" << y1 << \" \" << x2 << \" \" << y2 << \"\\n\";\n }\n \n return 0;\n}","toyota2023summer-final":"#include \nusing namespace std;\n\nint D, N;\nint ex, ey;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nvector> grid;\n\nvector> findReachableEmpty() {\n vector> result;\n vector> vis(D, vector(D, false));\n queue> q;\n q.push({ex, ey});\n vis[ex][ey] = true;\n \n while (!q.empty()) {\n int x = q.front().first, y = q.front().second;\n q.pop();\n \n // This is an empty square (entrance or regular empty)\n if (!(x == ex && y == ey)) {\n result.push_back({x, y});\n }\n \n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && !vis[nx][ny] && grid[nx][ny] == -1) {\n vis[nx][ny] = true;\n q.push({nx, ny});\n }\n }\n }\n return result;\n}\n\nvector> findReachableContainers() {\n vector> result;\n vector> vis(D, vector(D, false));\n queue> q;\n q.push({ex, ey});\n vis[ex][ey] = true;\n \n while (!q.empty()) {\n int x = q.front().first, y = q.front().second;\n q.pop();\n \n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && !vis[nx][ny] && grid[nx][ny] != -2) {\n vis[nx][ny] = true;\n if (grid[nx][ny] >= 0) {\n // This is a container adjacent to reachable empty square\n result.push_back({nx, ny});\n } else {\n // This is an empty square, continue searching\n q.push({nx, ny});\n }\n }\n }\n }\n return result;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> D >> N;\n ex = 0;\n ey = (D - 1) / 2;\n \n grid.assign(D, vector(D, -1));\n \n for (int i = 0; i < N; i++) {\n int x, y;\n cin >> x >> y;\n grid[x][y] = -2;\n }\n \n int total = D * D - 1 - N;\n \n // Placement phase\n for (int iter = 0; iter < total; iter++) {\n int t;\n cin >> t;\n \n vector> reach = findReachableEmpty();\n \n // Simple strategy: place at the last reachable position (furthest from entrance in BFS order)\n pair best = reach.back();\n \n grid[best.first][best.second] = t;\n cout << best.first << \" \" << best.second << endl;\n }\n \n // Transport phase\n for (int iter = 0; iter < total; iter++) {\n vector> reachable = findReachableContainers();\n \n // Find container with smallest number\n pair best = reachable[0];\n for (auto& pos : reachable) {\n if (grid[pos.first][pos.second] < grid[best.first][best.second]) {\n best = pos;\n }\n }\n \n cout << best.first << \" \" << best.second << \"\\n\";\n grid[best.first][best.second] = -1;\n }\n \n return 0;\n}","ahc024":"#include \nusing namespace std;\n\nint n, m;\nint dx[] = {0, 0, 1, -1};\nint dy[] = {1, -1, 0, 0};\n\nset adjToZero;\nset> required;\n\nbool quickConnectivityCheck(vector>& grid, int i, int j) {\n int c = grid[i][j];\n vector> neighbors;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n && grid[ni][nj] == c) {\n neighbors.push_back({ni, nj});\n }\n }\n if (neighbors.size() <= 1) return false; // Might disconnect\n if (neighbors.size() >= 3) return true; // Likely safe\n // For 2 neighbors, check if they're adjacent to each other\n int di = abs(neighbors[0].first - neighbors[1].first);\n int dj = abs(neighbors[0].second - neighbors[1].second);\n return (di + dj == 1); // Adjacent = safe\n}\n\nbool fullConnectivityCheck(vector>& grid, int c) {\n int si = -1, sj = -1, total = 0;\n for (int x = 0; x < n; x++) for (int y = 0; y < n; y++) {\n if (grid[x][y] == c) { if (si < 0) { si = x; sj = y; } total++; }\n }\n if (total == 0) return true;\n vector> vis(n, vector(n));\n queue> q; q.push({si, sj}); vis[si][sj] = true;\n int found = 1;\n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < n && ny >= 0 && ny < n && !vis[nx][ny] && grid[nx][ny] == c) {\n vis[nx][ny] = true; found++; q.push({nx, ny});\n }\n }\n }\n return found == total;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> n >> m;\n vector> orig(n, vector(n));\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) cin >> orig[i][j];\n \n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++)\n if (i == 0 || i == n-1 || j == 0 || j == n-1) adjToZero.insert(orig[i][j]);\n \n map, int> initEdge;\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) {\n int c = orig[i][j];\n if (i == 0 || i == n-1 || j == 0 || j == n-1) initEdge[{0,c}]++;\n if (j+1 < n && orig[i][j+1] != c) initEdge[{min(c,orig[i][j+1]), max(c,orig[i][j+1])}]++;\n if (i+1 < n && orig[i+1][j] != c) initEdge[{min(c,orig[i+1][j]), max(c,orig[i+1][j])}]++;\n }\n for (auto& [p, cnt] : initEdge) if (cnt > 0) required.insert(p);\n \n vector initCount(m+1);\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) initCount[orig[i][j]]++;\n \n auto start = chrono::steady_clock::now();\n vector> best = orig;\n int bestScore = 0;\n \n auto output = [&](vector>& g) {\n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) { cout << g[i][j]; if (j < n-1) cout << \" \"; }\n cout << \"\\n\";\n }\n cout.flush();\n };\n \n output(best);\n \n for (int seed = 0; seed < 200; seed++) {\n auto elapsed = chrono::steady_clock::now() - start;\n if (chrono::duration_cast(elapsed).count() > 1900) break;\n \n auto grid = orig;\n auto edgeCount = initEdge;\n auto colorCount = initCount;\n \n mt19937 rng(seed * 7919 + 42);\n \n for (int iter = 0; iter < 200; iter++) {\n vector> cands; // priority, random, i, j\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) {\n if (grid[i][j] == 0) continue;\n bool adj0 = (i == 0 || i == n-1 || j == 0 || j == n-1);\n for (int d = 0; d < 4 && !adj0; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n && grid[ni][nj] == 0) adj0 = true;\n }\n if (adj0) {\n int pri = colorCount[grid[i][j]] * 100 + (quickConnectivityCheck(grid, i, j) ? 50 : 0);\n cands.push_back({pri, (int)(rng() % 1000), i, j});\n }\n }\n if (cands.empty()) break;\n \n sort(cands.rbegin(), cands.rend());\n \n int removed = 0;\n for (auto [pri, r, i, j] : cands) {\n int c = grid[i][j];\n if (c == 0 || colorCount[c] <= 1) continue;\n \n bool canRemove = true;\n for (int d = 0; d < 4 && canRemove; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n) {\n int nc = grid[ni][nj];\n if (nc != 0 && adjToZero.find(nc) == adjToZero.end()) canRemove = false;\n }\n }\n if (!canRemove) continue;\n \n bool touchesZero = (i == 0 || i == n-1 || j == 0 || j == n-1);\n for (int d = 0; d < 4 && !touchesZero; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n && grid[ni][nj] == 0) touchesZero = true;\n }\n if (!touchesZero) continue;\n \n map, int> delta;\n if (i == 0 || i == n-1 || j == 0 || j == n-1) delta[{0, c}]--;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n) {\n int nc = grid[ni][nj];\n if (nc != c && nc != 0) { delta[{min(c,nc), max(c,nc)}]--; delta[{0, nc}]++; }\n }\n }\n \n bool wouldBreak = false;\n for (auto& [e, d] : delta)\n if (required.count(e) && edgeCount[e] + d <= 0) { wouldBreak = true; break; }\n if (wouldBreak) continue;\n \n grid[i][j] = 0;\n if (!fullConnectivityCheck(grid, c)) { grid[i][j] = c; continue; }\n \n for (auto& [e, d] : delta) edgeCount[e] += d;\n colorCount[c]--;\n removed++;\n }\n if (removed == 0) break;\n }\n \n int sc = 0;\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) if (grid[i][j] == 0) sc++;\n if (sc > bestScore) { bestScore = sc; best = grid; output(best); }\n }\n \n return 0;\n}","ahc025":"#include \nusing namespace std;\n\nint N, D, Q;\nint query_count = 0;\n\nchar query(const vector& L, const vector& R) {\n cout << L.size() << \" \" << R.size();\n for (int x : L) cout << \" \" << x;\n for (int x : R) cout << \" \" << x;\n cout << \"\\n\" << flush;\n char c;\n cin >> c;\n query_count++;\n return c;\n}\n\nvector sorted_items;\n\nvoid merge_sort(int l, int r) {\n if (r - l <= 1 || query_count >= Q) return;\n int m = (l + r) / 2;\n merge_sort(l, m);\n merge_sort(m, r);\n \n vector left(sorted_items.begin() + l, sorted_items.begin() + m);\n vector right(sorted_items.begin() + m, sorted_items.begin() + r);\n \n int i = 0, j = 0, k = l;\n while (i < (int)left.size() && j < (int)right.size()) {\n if (query_count >= Q) {\n while (i < (int)left.size()) sorted_items[k++] = left[i++];\n while (j < (int)right.size()) sorted_items[k++] = right[j++];\n return;\n }\n char c = query({left[i]}, {right[j]});\n if (c != '>') sorted_items[k++] = left[i++];\n else sorted_items[k++] = right[j++];\n }\n while (i < (int)left.size()) sorted_items[k++] = left[i++];\n while (j < (int)right.size()) sorted_items[k++] = right[j++];\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> D >> Q;\n \n sorted_items.resize(N);\n iota(sorted_items.begin(), sorted_items.end(), 0);\n merge_sort(0, N);\n \n vector rank_of(N);\n for (int i = 0; i < N; i++) rank_of[sorted_items[i]] = i;\n \n // Weight estimation\n vector w(N);\n for (int i = 0; i < N; i++) w[i] = i + 1;\n \n int remaining = Q - query_count;\n int est_budget = remaining / 3;\n \n for (int j = N - 1; j >= 1 && est_budget > 0; j--) {\n int lo = 1, hi = j;\n while (lo < hi && est_budget > 0 && query_count < Q) {\n int mid = (lo + hi) / 2;\n vector L, R = {sorted_items[j]};\n for (int t = 0; t < mid; t++) L.push_back(sorted_items[t]);\n char c = query(L, R);\n est_budget--;\n if (c == '>' || c == '=') hi = mid;\n else lo = mid + 1;\n }\n double sum = 0;\n for (int t = 0; t < lo; t++) sum += w[t];\n w[j] = max(w[j], sum);\n }\n \n // Greedy assignment\n vector set_weight(D, 0);\n vector assignment(N);\n vector> sets(D);\n \n for (int i = N - 1; i >= 0; i--) {\n int item = sorted_items[i];\n int best = 0;\n for (int j = 1; j < D; j++)\n if (set_weight[j] < set_weight[best]) best = j;\n assignment[item] = best;\n set_weight[best] += w[i];\n sets[best].push_back(item);\n }\n \n // Local search on all pairs - move lightest item from heavy to light\n bool improved = true;\n while (improved && query_count + 3 < Q) {\n improved = false;\n \n for (int a = 0; a < D && query_count + 3 < Q; a++) {\n for (int b = a + 1; b < D && query_count + 3 < Q; b++) {\n if (sets[a].empty() || sets[b].empty()) continue;\n \n char cmp = query(sets[a], sets[b]);\n if (cmp == '=') continue;\n \n int heavy = (cmp == '>') ? a : b;\n int light = (cmp == '>') ? b : a;\n \n if (sets[heavy].size() <= 1) continue;\n \n // Find lightest item in heavy set\n int min_item = sets[heavy][0];\n int min_rank = rank_of[min_item];\n for (int item : sets[heavy]) {\n if (rank_of[item] < min_rank) {\n min_rank = rank_of[item];\n min_item = item;\n }\n }\n \n // Try moving it\n vector new_heavy, new_light = sets[light];\n for (int item : sets[heavy])\n if (item != min_item) new_heavy.push_back(item);\n new_light.push_back(min_item);\n \n if (new_heavy.empty()) continue;\n \n char new_cmp = query(new_heavy, new_light);\n \n // Accept if balanced or flipped (improvement)\n if (new_cmp == '=' || new_cmp != cmp) {\n sets[heavy] = new_heavy;\n sets[light] = new_light;\n assignment[min_item] = light;\n set_weight[heavy] -= w[min_rank];\n set_weight[light] += w[min_rank];\n improved = true;\n }\n }\n }\n }\n \n while (query_count < Q) query({sorted_items[0]}, {sorted_items[1]});\n \n for (int i = 0; i < N; i++)\n cout << assignment[i] << \" \\n\"[i == N - 1];\n \n return 0;\n}","ahc026":"#include \nusing namespace std;\n\nstruct State {\n vector> stacks;\n vector pos;\n vector stack_min;\n \n void init(const vector>& init_stacks, int n, int m) {\n stacks = init_stacks;\n pos.resize(n + 1);\n stack_min.resize(m, INT_MAX);\n \n for (int i = 0; i < m; i++) {\n for (int j = 0; j < (int)stacks[i].size(); j++) {\n pos[stacks[i][j]] = i;\n stack_min[i] = min(stack_min[i], stacks[i][j]);\n }\n }\n }\n \n void updateMin(int i) {\n stack_min[i] = INT_MAX;\n for (int b : stacks[i]) {\n stack_min[i] = min(stack_min[i], b);\n }\n }\n};\n\nint simulate(const vector>& init_stacks, int n, int m, \n vector>& ops, mt19937& rng, int noise_level, bool random_mode) {\n \n State state;\n state.init(init_stacks, n, m);\n \n ops.clear();\n int total_energy = 0;\n \n uniform_int_distribution noise_dist(0, noise_level);\n uniform_int_distribution random_dest(0, m - 2);\n \n for (int v = 1; v <= n; v++) {\n int stack_id = state.pos[v];\n \n int idx = 0;\n while (state.stacks[stack_id][idx] != v) idx++;\n \n if (idx < (int)state.stacks[stack_id].size() - 1) {\n int move_start = idx + 1;\n int bottom_box = state.stacks[stack_id][move_start];\n \n int max_moving = 0;\n int min_moving = INT_MAX;\n int cnt = (int)state.stacks[stack_id].size() - move_start;\n \n for (int j = move_start; j < (int)state.stacks[stack_id].size(); j++) {\n int b = state.stacks[stack_id][j];\n max_moving = max(max_moving, b);\n min_moving = min(min_moving, b);\n }\n \n int best_dest = -1;\n int best_score = INT_MIN;\n \n if (random_mode && (rng() % 10) == 0) {\n // Occasionally pick random destination\n int r = random_dest(rng);\n best_dest = (r >= stack_id) ? r + 1 : r;\n } else {\n for (int i = 0; i < m; i++) {\n if (i == stack_id) continue;\n \n int score = 0;\n \n if (state.stacks[i].empty()) {\n score = n * 3 + (n - min_moving);\n } else {\n int min_in_dest = state.stack_min[i];\n \n if (min_in_dest > min_moving) {\n score = n * 3;\n if (state.stacks[i].back() > max_moving) {\n score += 50;\n }\n } else {\n score = min_in_dest;\n score -= cnt * 3;\n }\n }\n \n score -= (int)state.stacks[i].size() * 2;\n \n if (noise_level > 0) {\n score += noise_dist(rng);\n }\n \n if (score > best_score) {\n best_score = score;\n best_dest = i;\n }\n }\n }\n \n total_energy += cnt + 1;\n ops.push_back({bottom_box, best_dest + 1});\n \n for (int j = move_start; j < (int)state.stacks[stack_id].size(); j++) {\n int b = state.stacks[stack_id][j];\n state.stacks[best_dest].push_back(b);\n state.pos[b] = best_dest;\n }\n state.stacks[stack_id].resize(move_start);\n \n state.updateMin(stack_id);\n state.updateMin(best_dest);\n }\n \n ops.push_back({v, 0});\n state.stacks[stack_id].pop_back();\n state.updateMin(stack_id);\n }\n \n return total_energy;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n, m;\n cin >> n >> m;\n \n vector> init_stacks(m);\n \n for (int i = 0; i < m; i++) {\n int h = n / m;\n for (int j = 0; j < h; j++) {\n int x;\n cin >> x;\n init_stacks[i].push_back(x);\n }\n }\n \n vector> best_ops;\n int best_energy = INT_MAX;\n \n auto start_time = chrono::steady_clock::now();\n \n // Noise levels to try\n vector noise_levels = {0, 5, 10, 15, 20, 25, 30, 40, 50, 70};\n \n int seed = 0;\n int level_idx = 0;\n \n while (true) {\n auto current_time = chrono::steady_clock::now();\n auto elapsed = chrono::duration_cast(current_time - start_time).count();\n if (elapsed > 1900) break;\n \n int noise_level = noise_levels[level_idx % noise_levels.size()];\n bool random_mode = (seed % 20 == 19); // 5% random mode\n \n mt19937 rng(seed);\n vector> ops;\n int energy = simulate(init_stacks, n, m, ops, rng, noise_level, random_mode);\n \n if (energy < best_energy) {\n best_energy = energy;\n best_ops = ops;\n }\n \n seed++;\n level_idx++;\n }\n \n for (auto& [a, b] : best_ops) {\n cout << a << \" \" << b << \"\\n\";\n }\n \n return 0;\n}","ahc027":"#include \nusing namespace std;\n\nint N;\nvector h, v;\nvector> d;\nlong long totalD;\nmt19937 rng(42);\n\nint di[] = {0, 1, 0, -1};\nint dj[] = {1, 0, -1, 0};\nchar dirChar[] = {'R', 'D', 'L', 'U'};\n\nbool canMove(int i, int j, int dir) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) return false;\n if (dir == 0) return v[i][j] == '0';\n if (dir == 1) return h[i][j] == '0';\n if (dir == 2) return j > 0 && v[i][j-1] == '0';\n return i > 0 && h[i-1][j] == '0';\n}\n\nlong double fastEvaluate(const string& path) {\n int L = path.size();\n vector> contrib(N, vector(N, 0));\n long long contribSum = 0;\n int ci = 0, cj = 0;\n \n auto move = [&](int t, char c) {\n int dir = (c == 'R') ? 0 : (c == 'D') ? 1 : (c == 'L') ? 2 : 3;\n ci += di[dir]; cj += dj[dir];\n contribSum -= contrib[ci][cj];\n contrib[ci][cj] = (long long)d[ci][cj] * t;\n contribSum += contrib[ci][cj];\n };\n \n for (int t = 1; t <= L; t++) move(t, path[t-1]);\n \n long double totalSum = 0;\n for (int t = L + 1; t <= 2 * L; t++) {\n totalSum += (long long)totalD * t - contribSum;\n move(t, path[(t-1) % L]);\n }\n return totalSum / L;\n}\n\nvector> getVisitCounts(const string& path) {\n vector> cnt(N, vector(N, 0));\n int ci = 0, cj = 0;\n cnt[0][0] = 1;\n for (char c : path) {\n int dir = (c == 'R') ? 0 : (c == 'D') ? 1 : (c == 'L') ? 2 : 3;\n ci += di[dir]; cj += dj[dir];\n cnt[ci][cj]++;\n }\n return cnt;\n}\n\nstring generatePath(int mode) {\n vector> visited(N, vector(N, false));\n string path;\n \n function dfs = [&](int i, int j) {\n visited[i][j] = true;\n vector> children;\n for (int dir = 0; dir < 4; dir++) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (ni >= 0 && ni < N && nj >= 0 && nj < N && !visited[ni][nj] && canMove(i, j, dir)) {\n children.push_back({d[ni][nj], dir});\n }\n }\n if (mode == 0) sort(children.begin(), children.end());\n else if (mode == 1) sort(children.rbegin(), children.rend());\n else shuffle(children.begin(), children.end(), rng);\n \n for (auto& [dval, dir] : children) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (!visited[ni][nj]) {\n path += dirChar[dir];\n dfs(ni, nj);\n path += dirChar[(dir + 2) % 4];\n }\n }\n };\n dfs(0, 0);\n return path;\n}\n\nvector> dist0;\nvector> allLoops;\n\nvoid precomputeLoops() {\n dist0.assign(N, vector(N, -1));\n queue> bfs;\n bfs.push({0, 0});\n dist0[0][0] = 0;\n vector> par(N, vector(N, -1));\n par[0][0] = -2;\n \n while (!bfs.empty()) {\n auto [i, j] = bfs.front(); bfs.pop();\n for (int dir = 0; dir < 4; dir++) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (ni >= 0 && ni < N && nj >= 0 && nj < N && dist0[ni][nj] == -1 && canMove(i, j, dir)) {\n dist0[ni][nj] = dist0[i][j] + 1;\n par[ni][nj] = (dir + 2) % 4;\n bfs.push({ni, nj});\n }\n }\n }\n \n for (int ti = 0; ti < N; ti++) {\n for (int tj = 0; tj < N; tj++) {\n if (ti == 0 && tj == 0) continue;\n string toTarget, fromTarget;\n int ci = ti, cj = tj;\n while (ci != 0 || cj != 0) {\n int pdir = par[ci][cj];\n fromTarget += dirChar[pdir];\n toTarget += dirChar[(pdir + 2) % 4];\n ci += di[pdir]; cj += dj[pdir];\n }\n reverse(toTarget.begin(), toTarget.end());\n allLoops.push_back({d[ti][tj], ti, tj, toTarget + fromTarget});\n }\n }\n sort(allLoops.rbegin(), allLoops.rend());\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N - 1);\n v.resize(N);\n d.resize(N, vector(N));\n \n for (int i = 0; i < N - 1; i++) cin >> h[i];\n for (int i = 0; i < N; i++) cin >> v[i];\n totalD = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n cin >> d[i][j];\n totalD += d[i][j];\n }\n \n precomputeLoops();\n \n string bestPath;\n long double bestScore = 1e18;\n vector> topPaths;\n \n auto tryPath = [&](const string& path) -> long double {\n if (path.size() > 100000) return 1e18;\n long double score = fastEvaluate(path);\n if (score < bestScore) {\n bestScore = score;\n bestPath = path;\n }\n return score;\n };\n \n for (int mode = 0; mode < 2; mode++) {\n string p = generatePath(mode);\n long double s = tryPath(p);\n topPaths.push_back({s, p});\n }\n \n auto startTime = chrono::steady_clock::now();\n while (chrono::duration_cast(chrono::steady_clock::now() - startTime).count() < 1200) {\n string p = generatePath(2);\n long double s = tryPath(p);\n topPaths.push_back({s, p});\n }\n \n sort(topPaths.begin(), topPaths.end());\n if (topPaths.size() > 6) topPaths.resize(6);\n \n // Loop addition on top paths\n for (auto& [baseScore, basePath] : topPaths) {\n string current = basePath;\n long double curScore = baseScore;\n \n for (int iter = 0; iter < 20; iter++) {\n bool improved = false;\n auto visits = getVisitCounts(current);\n \n // Sort loops by d/visits ratio for this path\n vector> priorities;\n for (int i = 0; i < (int)allLoops.size(); i++) {\n auto& [dval, ti, tj, loop] = allLoops[i];\n double priority = (double)dval / max(1, visits[ti][tj]);\n priorities.push_back({priority, i});\n }\n sort(priorities.rbegin(), priorities.rend());\n \n for (auto& [pri, idx] : priorities) {\n auto& [dval, ti, tj, loop] = allLoops[idx];\n if (current.size() + loop.size() > 100000) continue;\n string candidate = current + loop;\n long double score = fastEvaluate(candidate);\n if (score < curScore) {\n curScore = score;\n current = candidate;\n improved = true;\n if (score < bestScore) {\n bestScore = score;\n bestPath = current;\n }\n break;\n }\n }\n if (!improved) break;\n }\n }\n \n // Multi-loop to same cell\n for (int c = 0; c < min(8, (int)allLoops.size()); c++) {\n auto& [dval, ti, tj, loop] = allLoops[c];\n string candidate = bestPath;\n for (int rep = 1; rep <= 30 && candidate.size() + loop.size() <= 100000; rep++) {\n candidate += loop;\n long double score = tryPath(candidate);\n }\n }\n \n cout << bestPath << endl;\n return 0;\n}","ahc028":"#include \nusing namespace std;\n\nint N, M, si, sj;\nmap>> charPos;\n\nint overlap(const string& a, const string& b) {\n int maxOv = min(a.length(), b.length());\n for (int ov = maxOv; ov >= 1; ov--) {\n bool match = true;\n int aStart = a.length() - ov;\n for (int k = 0; k < ov && match; k++) {\n if (a[aStart + k] != b[k]) match = false;\n }\n if (match) return ov;\n }\n return 0;\n}\n\nstring buildSuperstring(vector remaining) {\n while (remaining.size() > 1) {\n int bestOv = -1, bestI = -1, bestJ = -1;\n \n for (int i = 0; i < (int)remaining.size(); i++) {\n for (int j = 0; j < (int)remaining.size(); j++) {\n if (i != j) {\n int ov = overlap(remaining[i], remaining[j]);\n if (ov > bestOv) { bestOv = ov; bestI = i; bestJ = j; }\n }\n }\n }\n \n string merged = remaining[bestI] + remaining[bestJ].substr(bestOv);\n \n vector newRemaining;\n newRemaining.reserve(remaining.size() - 1);\n for (int k = 0; k < (int)remaining.size(); k++) {\n if (k != bestI && k != bestJ) {\n newRemaining.push_back(move(remaining[k]));\n }\n }\n newRemaining.push_back(move(merged));\n remaining = move(newRemaining);\n }\n return remaining[0];\n}\n\npair>> computePath(const string& ss) {\n int n = ss.length();\n if (n == 0) return {0, {}};\n \n vector> dp(n);\n \n for (int pos = n - 1; pos >= 0; pos--) {\n char c = ss[pos];\n const auto& positions = charPos[c];\n int sz = positions.size();\n dp[pos].assign(sz, 0);\n \n if (pos < n - 1) {\n char nc = ss[pos + 1];\n const auto& nextPositions = charPos[nc];\n for (int idx = 0; idx < sz; idx++) {\n int r = positions[idx].first, col = positions[idx].second;\n int best = INT_MAX;\n for (size_t nidx = 0; nidx < nextPositions.size(); nidx++) {\n int nr = nextPositions[nidx].first, ncol = nextPositions[nidx].second;\n best = min(best, abs(nr - r) + abs(ncol - col) + 1 + dp[pos + 1][nidx]);\n }\n dp[pos][idx] = best;\n }\n }\n }\n \n const auto& pos0 = charPos[ss[0]];\n int bestCost = INT_MAX;\n for (size_t idx = 0; idx < pos0.size(); idx++) {\n int dist = abs(pos0[idx].first - si) + abs(pos0[idx].second - sj) + 1;\n bestCost = min(bestCost, dist + dp[0][idx]);\n }\n \n vector> path(n);\n int curI = si, curJ = sj;\n for (int pos = 0; pos < n; pos++) {\n const auto& positions = charPos[ss[pos]];\n int best = INT_MAX, bIdx = 0;\n for (size_t idx = 0; idx < positions.size(); idx++) {\n int r = positions[idx].first, col = positions[idx].second;\n int total = abs(r - curI) + abs(col - curJ) + 1 + dp[pos][idx];\n if (total < best) { best = total; bIdx = idx; }\n }\n path[pos] = positions[bIdx];\n curI = path[pos].first;\n curJ = path[pos].second;\n }\n \n return {bestCost, path};\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> si >> sj;\n for (int i = 0; i < N; i++) {\n string row; cin >> row;\n for (int j = 0; j < N; j++)\n charPos[row[j]].push_back({i, j});\n }\n \n vector t(M);\n for (int i = 0; i < M; i++) cin >> t[i];\n \n mt19937 rng(12345);\n vector> bestPath;\n int bestCost = INT_MAX;\n \n auto startTime = chrono::steady_clock::now();\n \n for (int iter = 0; ; iter++) {\n if (iter > 0) {\n auto elapsed = chrono::duration_cast(\n chrono::steady_clock::now() - startTime).count();\n if (elapsed > 1850) break;\n }\n \n vector input = t;\n if (iter == 1) {\n sort(input.begin(), input.end());\n } else if (iter == 2) {\n sort(input.begin(), input.end(), greater());\n } else if (iter == 3) {\n sort(input.begin(), input.end(), [](const string& a, const string& b) {\n return a.back() < b.back();\n });\n } else if (iter == 4) {\n sort(input.begin(), input.end(), [](const string& a, const string& b) {\n return a[0] < b[0];\n });\n } else if (iter > 4) {\n shuffle(input.begin(), input.end(), rng);\n }\n \n string ss = buildSuperstring(input);\n auto [cost, path] = computePath(ss);\n \n if (cost < bestCost) {\n bestCost = cost;\n bestPath = path;\n }\n }\n \n for (auto& [i, j] : bestPath)\n cout << i << \" \" << j << \"\\n\";\n \n return 0;\n}","ahc030":"#include \nusing namespace std;\n\nint N, M;\ndouble eps;\nvector>> shapes;\nmap, int> drilled;\nset> confirmed_oil, confirmed_no_oil;\nint qcount = 0;\nint maxQ;\n\nint queryDrill(int i, int j) {\n pair key = make_pair(i, j);\n if (drilled.count(key)) return drilled[key];\n cout << \"q 1 \" << i << \" \" << j << \"\\n\" << flush;\n qcount++;\n int v; cin >> v;\n drilled[key] = v;\n if (v > 0) confirmed_oil.insert(key);\n else confirmed_no_oil.insert(key);\n return v;\n}\n\nint queryDivine(const vector>& cells) {\n cout << \"q \" << cells.size();\n for (auto& c : cells) cout << \" \" << c.first << \" \" << c.second;\n cout << \"\\n\" << flush;\n qcount++;\n int v; cin >> v;\n return v;\n}\n\nint submit(set> oil) {\n for (auto& c : confirmed_oil) oil.insert(c);\n cout << \"a \" << oil.size();\n for (auto& c : oil) cout << \" \" << c.first << \" \" << c.second;\n cout << \"\\n\" << flush;\n qcount++;\n int r; cin >> r;\n return r;\n}\n\nvector>>> placements;\n\nvoid filterPlacements() {\n for (int m = 0; m < M; m++) {\n vector>> valid;\n for (auto& p : placements[m]) {\n bool ok = true;\n for (auto& c : confirmed_no_oil)\n if (p.count(c)) { ok = false; break; }\n if (ok) valid.push_back(p);\n }\n if (!valid.empty()) placements[m] = valid;\n }\n}\n\nbool allUnique() {\n for (int m = 0; m < M; m++)\n if (placements[m].size() > 1) return false;\n return true;\n}\n\nset> getAnswer() {\n set> answer;\n for (int m = 0; m < M; m++)\n if (!placements[m].empty())\n for (auto& c : placements[m][0]) answer.insert(c);\n return answer;\n}\n\nset> getPossible() {\n set> possible;\n for (int m = 0; m < M; m++)\n for (auto& p : placements[m])\n for (auto& c : p) possible.insert(c);\n return possible;\n}\n\npair getBestCell(const vector>& prob) {\n map, vector> cellCounts;\n \n for (int m = 0; m < M; m++) {\n for (auto& p : placements[m])\n for (auto& c : p) {\n if (cellCounts.find(c) == cellCounts.end())\n cellCounts[c] = vector(M, 0);\n cellCounts[c][m]++;\n }\n }\n \n pair best = {-1, -1};\n double bestScore = -1e18;\n \n for (auto& kv : cellCounts) {\n pair cell = kv.first;\n vector& counts = kv.second;\n \n if (drilled.count(cell)) continue;\n \n double p = prob[cell.first][cell.second];\n \n bool valid = true;\n for (int m = 0; m < M; m++) {\n if ((int)placements[m].size() - counts[m] <= 0) {\n valid = false; break;\n }\n }\n if (!valid) continue;\n \n // Entropy-based scoring: prefer cells that split placements evenly\n double entropyGain = 0;\n for (int m = 0; m < M; m++) {\n int sz = placements[m].size();\n if (sz <= 1) continue;\n double ratio = (double)counts[m] / sz;\n // Binary entropy approximation\n double h = ratio * (1 - ratio) * 4; // peaks at 0.5\n entropyGain += h * log((double)sz);\n }\n \n // Weight by probability of no oil (since that's when we eliminate)\n double score = (1.0 - p) * entropyGain;\n \n // Tie-breaker: total elimination potential\n double totalElim = 0;\n for (int m = 0; m < M; m++)\n totalElim += counts[m];\n score += totalElim * 0.001;\n \n if (score > bestScore) {\n bestScore = score;\n best = cell;\n }\n }\n return best;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> eps;\n maxQ = 2 * N * N;\n shapes.resize(M);\n \n for (int m = 0; m < M; m++) {\n int d; cin >> d;\n shapes[m].resize(d);\n for (int i = 0; i < d; i++)\n cin >> shapes[m][i].first >> shapes[m][i].second;\n }\n \n placements.resize(M);\n for (int m = 0; m < M; m++) {\n int maxI = 0, maxJ = 0;\n for (auto& c : shapes[m]) {\n maxI = max(maxI, c.first);\n maxJ = max(maxJ, c.second);\n }\n for (int di = 0; di + maxI < N; di++)\n for (int dj = 0; dj + maxJ < N; dj++) {\n set> cells;\n for (auto& c : shapes[m])\n cells.insert({di + c.first, dj + c.second});\n placements[m].push_back(cells);\n }\n }\n \n vector> prob(N, vector(N, 0.3));\n \n // Row divination only if eps is reasonable\n if (eps <= 0.15) {\n for (int i = 0; i < N; i++) {\n vector> row;\n for (int j = 0; j < N; j++) row.push_back({i, j});\n int est = queryDivine(row);\n double denom = max(0.01, 1.0 - 2.0 * eps);\n double trueEst = max(0.0, (est - N * eps) / denom);\n for (int j = 0; j < N; j++)\n prob[i][j] = min(0.9, max(0.1, trueEst / N));\n }\n \n // Column divination only for very low eps\n if (eps <= 0.05) {\n for (int j = 0; j < N; j++) {\n vector> col;\n for (int i = 0; i < N; i++) col.push_back({i, j});\n int est = queryDivine(col);\n double denom = max(0.01, 1.0 - 2.0 * eps);\n double trueEst = max(0.0, (est - N * eps) / denom);\n for (int i = 0; i < N; i++)\n prob[i][j] = (prob[i][j] + min(0.9, max(0.1, trueEst / N))) / 2.0;\n }\n }\n }\n \n while (qcount < maxQ - 5 && !allUnique()) {\n filterPlacements();\n auto cell = getBestCell(prob);\n if (cell.first < 0) break;\n queryDrill(cell.first, cell.second);\n }\n \n filterPlacements();\n set> answer = allUnique() ? getAnswer() : getPossible();\n for (auto& c : confirmed_no_oil) answer.erase(c);\n \n if (!submit(answer)) {\n while (qcount < maxQ - 2) {\n filterPlacements();\n if (allUnique()) break;\n auto cell = getBestCell(prob);\n if (cell.first < 0) {\n auto possible = getPossible();\n for (auto& c : possible)\n if (!drilled.count(c)) { cell = c; break; }\n }\n if (cell.first < 0) break;\n queryDrill(cell.first, cell.second);\n }\n filterPlacements();\n answer = allUnique() ? getAnswer() : getPossible();\n for (auto& c : confirmed_no_oil) answer.erase(c);\n if (!submit(answer)) submit(confirmed_oil);\n }\n \n return 0;\n}","ahc031":"#include \nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int W, D, N;\n cin >> W >> D >> N;\n \n vector> a(D, vector(N));\n for (int d = 0; d < D; d++) {\n for (int k = 0; k < N; k++) {\n cin >> a[d][k];\n }\n }\n \n for (int d = 0; d < D; d++) {\n vector h(N);\n int totalH = 0;\n \n // Calculate minimum height needed for each reservation\n for (int k = 0; k < N; k++) {\n h[k] = (a[d][k] + W - 1) / W; // ceil(a[k] / W)\n if (h[k] == 0) h[k] = 1;\n totalH += h[k];\n }\n \n if (totalH > W) {\n int excess = totalH - W;\n \n // Reduce heights, always picking the one with largest slack (minimum penalty)\n while (excess > 0) {\n int bestK = -1;\n int maxSlack = INT_MIN;\n \n for (int k = 0; k < N; k++) {\n if (h[k] > 1) {\n int slack = h[k] * W - a[d][k];\n if (slack > maxSlack) {\n maxSlack = slack;\n bestK = k;\n }\n }\n }\n \n if (bestK == -1) break;\n h[bestK]--;\n excess--;\n }\n } else if (totalH < W) {\n int extra = W - totalH;\n // Distribute extra space to larger reservations\n while (extra > 0) {\n for (int k = N - 1; k >= 0 && extra > 0; k--) {\n h[k]++;\n extra--;\n }\n }\n }\n \n // Output rectangles\n int y = 0;\n for (int k = 0; k < N; k++) {\n cout << y << \" 0 \" << y + h[k] << \" \" << W << \"\\n\";\n y += h[k];\n }\n }\n \n return 0;\n}","ahc032":"#include \nusing namespace std;\n\nconst long long P = 998244353;\nint N, M, K;\nvector> a_init;\nvector, 3>> stamps;\n\nvoid applyOp(vector>& a, int m, int p, int q) {\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n a[p+i][q+j] = (a[p+i][q+j] + stamps[m][i][j]) % P;\n}\n\nlong long calcGain(const vector>& a, int m, int p, int q) {\n long long gain = 0;\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n gain += (a[p+i][q+j] + stamps[m][i][j]) % P - a[p+i][q+j];\n return gain;\n}\n\nlong long calcScore(const vector>& a) {\n long long s = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n s += a[i][j];\n return s;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(0);\n \n cin >> N >> M >> K;\n a_init.assign(N, vector(N));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n cin >> a_init[i][j];\n a_init[i][j] %= P;\n }\n \n stamps.resize(M);\n for (int m = 0; m < M; m++)\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n cin >> stamps[m][i][j];\n \n auto start = chrono::steady_clock::now();\n auto elapsed = [&]() { return chrono::duration(chrono::steady_clock::now() - start).count(); };\n \n vector> best_ops;\n long long best_score = calcScore(a_init);\n \n mt19937 rng(42);\n \n for (int trial = 0; elapsed() < 1.9; trial++) {\n vector> ops;\n auto a = a_init;\n \n // Randomized greedy\n for (int op = 0; op < K; op++) {\n vector> cands;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N-3; p++)\n for (int q = 0; q <= N-3; q++) {\n long long gain = calcGain(a, m, p, q);\n if (gain > 0) cands.push_back({gain, m, p, q});\n }\n if (cands.empty()) break;\n sort(cands.rbegin(), cands.rend());\n int pick = (trial == 0) ? 0 : rng() % min((int)cands.size(), 2 + trial / 3);\n auto [g, m, p, q] = cands[pick];\n applyOp(a, m, p, q);\n ops.push_back({m, p, q});\n }\n \n long long score = calcScore(a);\n \n // Local optimization passes\n for (int iter = 0; iter < 5 && elapsed() < 1.9; iter++) {\n bool improved = false;\n \n // Try replacing each operation\n for (int idx = 0; idx < (int)ops.size() && elapsed() < 1.9; idx++) {\n auto orig = ops[idx];\n auto a2 = a_init;\n for (int k = 0; k < (int)ops.size(); k++)\n if (k != idx) {\n auto [m,p,q] = ops[k];\n applyOp(a2, m, p, q);\n }\n \n long long bestGain = 0;\n int bm=-1, bp=-1, bq=-1;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N-3; p++)\n for (int q = 0; q <= N-3; q++) {\n long long gain = calcGain(a2, m, p, q);\n if (gain > bestGain) { bestGain = gain; bm=m; bp=p; bq=q; }\n }\n \n if (bm != -1) {\n auto newOp = make_tuple(bm, bp, bq);\n if (newOp != orig) {\n ops[idx] = newOp;\n a = a2;\n applyOp(a, bm, bp, bq);\n long long newScore = calcScore(a);\n if (newScore > score) {\n score = newScore;\n improved = true;\n }\n }\n }\n }\n \n // Try removing operations\n for (int idx = (int)ops.size()-1; idx >= 0 && elapsed() < 1.9; idx--) {\n auto a2 = a_init;\n for (int k = 0; k < (int)ops.size(); k++)\n if (k != idx) {\n auto [m,p,q] = ops[k];\n applyOp(a2, m, p, q);\n }\n long long newScore = calcScore(a2);\n if (newScore >= score) {\n ops.erase(ops.begin() + idx);\n a = a2;\n score = newScore;\n improved = true;\n }\n }\n \n // Try adding more operations\n while (ops.size() < (size_t)K && elapsed() < 1.9) {\n long long bestGain = 0;\n int bm=-1, bp=-1, bq=-1;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N-3; p++)\n for (int q = 0; q <= N-3; q++) {\n long long gain = calcGain(a, m, p, q);\n if (gain > bestGain) { bestGain = gain; bm=m; bp=p; bq=q; }\n }\n if (bm == -1) break;\n applyOp(a, bm, bp, bq);\n ops.push_back({bm, bp, bq});\n score += bestGain;\n improved = true;\n }\n \n if (!improved) break;\n }\n \n if (score > best_score) {\n best_score = score;\n best_ops = ops;\n }\n }\n \n cout << best_ops.size() << \"\\n\";\n for (auto& [m,p,q] : best_ops) cout << m << \" \" << p << \" \" << q << \"\\n\";\n}","ahc033":"#include \nusing namespace std;\n\nconst int N = 5;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n; cin >> n;\n int A[N][N];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n cin >> A[i][j];\n \n string ans[N];\n int grid[N][N]; memset(grid, -1, sizeof(grid));\n int cr = 0, cc = 0, hold = -1;\n int next_in[N] = {0};\n int next_needed[N]; // next container needed for each row\n for (int i = 0; i < N; i++) next_needed[i] = i * N;\n \n for (int t = 0; t < 9000; t++) {\n // Step 1: Bring in containers\n for (int i = 0; i < N; i++) {\n if (next_in[i] < N && grid[i][0] == -1) {\n bool blocked = (cr == i && cc == 0 && hold != -1);\n if (!blocked) grid[i][0] = A[i][next_in[i]++];\n }\n }\n \n char moves[N];\n for (int c = 0; c < N; c++) moves[c] = '.';\n \n if (t == 0) {\n for (int c = 1; c < N; c++) moves[c] = 'B';\n }\n \n if (hold == -1) {\n if (grid[cr][cc] != -1) {\n moves[0] = 'P';\n } else {\n // Find best container to pick up\n // Priority: containers that are \"ready\" (next needed for their row)\n int best_r = -1, best_c = -1;\n int best_score = -1000000;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (grid[i][j] != -1) {\n int cont = grid[i][j];\n int target_row = cont / N;\n int dist = abs(i - cr) + abs(j - cc);\n \n int score = -dist * 10;\n \n // Bonus if this container is next needed for its row\n if (cont == next_needed[target_row]) {\n score += 1000;\n }\n // Small bonus for lower container numbers\n score -= cont;\n \n if (score > best_score) {\n best_score = score;\n best_r = i; best_c = j;\n }\n }\n }\n }\n \n if (best_r != -1) {\n if (best_r > cr) moves[0] = 'D';\n else if (best_r < cr) moves[0] = 'U';\n else if (best_c > cc) moves[0] = 'R';\n else if (best_c < cc) moves[0] = 'L';\n }\n }\n } else {\n int target_row = hold / N;\n if (cr != target_row) {\n if (target_row > cr) moves[0] = 'D';\n else moves[0] = 'U';\n } else if (cc < N-1) {\n moves[0] = 'R';\n } else {\n moves[0] = 'Q';\n }\n }\n \n // Execute\n if (moves[0] == 'P') { hold = grid[cr][cc]; grid[cr][cc] = -1; }\n else if (moves[0] == 'Q') { \n int target_row = hold / N;\n if (cr == target_row && cc == N-1) {\n // Update next_needed when dispatching\n if (hold == next_needed[target_row]) {\n next_needed[target_row]++;\n }\n }\n grid[cr][cc] = hold; \n hold = -1; \n }\n else if (moves[0] == 'R') cc++;\n else if (moves[0] == 'L') cc--;\n else if (moves[0] == 'U') cr--;\n else if (moves[0] == 'D') cr++;\n \n // Step 3: Dispatch\n for (int i = 0; i < N; i++) grid[i][N-1] = -1;\n \n for (int c = 0; c < N; c++) ans[c] += moves[c];\n \n // Check if done\n bool done = true;\n for (int i = 0; i < N; i++) if (next_in[i] < N) done = false;\n if (hold != -1) done = false;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (grid[i][j] != -1) done = false;\n if (done) break;\n }\n \n for (int i = 0; i < N; i++) cout << ans[i] << \"\\n\";\n return 0;\n}","ahc034":"#include \nusing namespace std;\n\nint N;\nvector> h;\nvector ops;\nint cx = 0, cy = 0;\nint load = 0;\n\nvoid do_load(int d) {\n if (d <= 0) return;\n ops.push_back(\"+\" + to_string(d));\n load += d;\n h[cx][cy] -= d;\n}\n\nvoid do_unload(int d) {\n if (d <= 0) return;\n ops.push_back(\"-\" + to_string(d));\n load -= d;\n h[cx][cy] += d;\n}\n\nvoid move_one(char dir) {\n ops.push_back(string(1, dir));\n if (dir == 'U') cx--;\n else if (dir == 'D') cx++;\n else if (dir == 'L') cy--;\n else if (dir == 'R') cy++;\n}\n\nvoid process_cell() {\n if (h[cx][cy] > 0) do_load(h[cx][cy]);\n if (h[cx][cy] < 0 && load > 0) do_unload(min(load, -h[cx][cy]));\n}\n\n// Calculate work done on path considering load state\nint calc_path_work(int fx, int fy, int tx, int ty, int init_load, bool vert_first) {\n int work = 0;\n int sim_load = init_load;\n int x = fx, y = fy;\n \n auto process = [&](int px, int py) {\n if (h[px][py] > 0) {\n work += h[px][py];\n sim_load += h[px][py];\n } else if (h[px][py] < 0 && sim_load > 0) {\n int unload = min(sim_load, -h[px][py]);\n work += unload;\n sim_load -= unload;\n }\n };\n \n if (vert_first) {\n while (x != tx) { x += (tx > x) ? 1 : -1; process(x, y); }\n while (y != ty) { y += (ty > y) ? 1 : -1; process(x, y); }\n } else {\n while (y != ty) { y += (ty > y) ? 1 : -1; process(x, y); }\n while (x != tx) { x += (tx > x) ? 1 : -1; process(x, y); }\n }\n return work;\n}\n\nint best_path_work(int fx, int fy, int tx, int ty, int init_load) {\n return max(calc_path_work(fx, fy, tx, ty, init_load, true),\n calc_path_work(fx, fy, tx, ty, init_load, false));\n}\n\nvoid move_to(int tx, int ty) {\n int vert_work = calc_path_work(cx, cy, tx, ty, load, true);\n int horiz_work = calc_path_work(cx, cy, tx, ty, load, false);\n \n if (vert_work >= horiz_work) {\n while (cx < tx) { move_one('D'); process_cell(); }\n while (cx > tx) { move_one('U'); process_cell(); }\n while (cy < ty) { move_one('R'); process_cell(); }\n while (cy > ty) { move_one('L'); process_cell(); }\n } else {\n while (cy < ty) { move_one('R'); process_cell(); }\n while (cy > ty) { move_one('L'); process_cell(); }\n while (cx < tx) { move_one('D'); process_cell(); }\n while (cx > tx) { move_one('U'); process_cell(); }\n }\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N, vector(N));\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n cin >> h[i][j];\n }\n }\n \n while (true) {\n if (load == 0) {\n int si = -1, sj = -1;\n int best_score = INT_MIN;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (h[i][j] > 0) {\n int dist = abs(i - cx) + abs(j - cy);\n int path_work = best_path_work(cx, cy, i, j, 0);\n int target_amt = h[i][j];\n // Score: path work + target amount - distance penalty\n int score = path_work * 3 + target_amt - dist * 5;\n if (score > best_score) {\n best_score = score;\n si = i; sj = j;\n }\n }\n }\n }\n \n if (si == -1) break;\n \n move_to(si, sj);\n if (h[cx][cy] > 0) do_load(h[cx][cy]);\n } else {\n int ti = -1, tj = -1;\n int best_score = INT_MIN;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (h[i][j] < 0) {\n int dist = abs(i - cx) + abs(j - cy);\n int path_work = best_path_work(cx, cy, i, j, load);\n int target_amt = -h[i][j];\n int score = path_work * 3 + min(target_amt, load) - dist * 5;\n if (score > best_score) {\n best_score = score;\n ti = i; tj = j;\n }\n }\n }\n }\n \n if (ti == -1) break;\n \n move_to(ti, tj);\n if (h[cx][cy] < 0 && load > 0) {\n do_unload(min(load, -h[cx][cy]));\n }\n }\n }\n \n for (const auto& op : ops) {\n cout << op << \"\\n\";\n }\n \n return 0;\n}","ahc035":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, T;\n cin >> N >> M >> T;\n\n int seed_count = 2 * N * (N - 1);\n vector> X(seed_count, vector(M, 0));\n\n for (int i = 0; i < seed_count; i++) {\n for (int j = 0; j < M; j++) {\n cin >> X[i][j];\n }\n }\n\n for (int t = 0; t < T; t++) {\n vector maxVal(M, 0);\n for (int l = 0; l < M; l++) {\n for (int i = 0; i < seed_count; i++) {\n maxVal[l] = max(maxVal[l], X[i][l]);\n }\n }\n \n auto getValue = [&](int idx) {\n int total = 0;\n for (int l = 0; l < M; l++) total += X[idx][l];\n return total;\n };\n \n auto getMaxCount = [&](int idx) {\n int cnt = 0;\n for (int l = 0; l < M; l++) {\n if (X[idx][l] == maxVal[l]) cnt++;\n }\n return cnt;\n };\n \n // Calculate sum of max values that this seed has\n auto getMaxSum = [&](int idx) {\n int sum = 0;\n for (int l = 0; l < M; l++) {\n if (X[idx][l] == maxVal[l]) sum += X[idx][l];\n }\n return sum;\n };\n \n // Selection: value + strong max bonus\n vector> seed_scores(seed_count);\n for (int i = 0; i < seed_count; i++) {\n double score = getValue(i) + getMaxCount(i) * 1000.0;\n seed_scores[i] = {score, i};\n }\n \n sort(seed_scores.begin(), seed_scores.end(), greater>());\n \n vector selected(N * N);\n for (int i = 0; i < N * N; i++) {\n selected[i] = seed_scores[i].second;\n }\n \n // Placement: prioritize seeds with many max values and high maxSum\n sort(selected.begin(), selected.end(), [&](int a, int b) {\n // Primary: weighted score combining value and max importance\n double sa = getValue(a) + getMaxCount(a) * 400.0 + getMaxSum(a) * 2.0;\n double sb = getValue(b) + getMaxCount(b) * 400.0 + getMaxSum(b) * 2.0;\n if (sa != sb) return sa > sb;\n return getValue(a) > getValue(b);\n });\n \n vector> pos_order;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n pos_order.push_back({i, j});\n }\n }\n \n double cx = (N - 1) / 2.0;\n double cy = (N - 1) / 2.0;\n sort(pos_order.begin(), pos_order.end(), [&](auto& a, auto& b) {\n double da = abs(a.first - cx) + abs(a.second - cy);\n double db = abs(b.first - cx) + abs(b.second - cy);\n if (da != db) return da < db;\n if (a.first != b.first) return a.first < b.first;\n return a.second < b.second;\n });\n \n vector> A(N, vector(N, -1));\n for (int i = 0; i < N * N; i++) {\n A[pos_order[i].first][pos_order[i].second] = selected[i];\n }\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n cout << A[i][j];\n if (j < N - 1) cout << \" \";\n else cout << \"\\n\";\n }\n }\n cout.flush();\n\n for (int i = 0; i < seed_count; i++) {\n for (int j = 0; j < M; j++) {\n cin >> X[i][j];\n }\n }\n }\n\n return 0;\n}","ahc038":"#include \nusing namespace std;\n\nint N, M, V;\nconst int DX[] = {0, 1, 0, -1};\nconst int DY[] = {1, 0, -1, 0};\n\nint rx, ry;\nvector dirs;\nvector lens;\nvector holding;\nint numF;\n\npair fingertip(int i) { \n return {rx + DX[dirs[i]] * lens[i], ry + DY[dirs[i]] * lens[i]}; \n}\nbool valid(int x, int y) { return x >= 0 && x < N && y >= 0 && y < N; }\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> V;\n vector grid(N), target(N);\n for (int i = 0; i < N; i++) cin >> grid[i];\n for (int i = 0; i < N; i++) cin >> target[i];\n \n numF = V - 1;\n \n // Use varied edge lengths for better coverage\n lens.resize(numF);\n for (int i = 0; i < numF; i++) {\n lens[i] = min(i + 1, N - 1);\n }\n \n cout << numF + 1 << \"\\n\";\n for (int i = 0; i < numF; i++) cout << \"0 \" << lens[i] << \"\\n\";\n \n // Calculate centroid for better starting position\n set> pickup, dropS;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n if (grid[i][j] == '1' && target[i][j] == '0') pickup.insert({i, j});\n if (target[i][j] == '1' && grid[i][j] == '0') dropS.insert({i, j});\n }\n \n int sumX = 0, sumY = 0, cnt = 0;\n for (auto& p : pickup) { sumX += p.first; sumY += p.second; cnt++; }\n for (auto& p : dropS) { sumX += p.first; sumY += p.second; cnt++; }\n \n rx = cnt > 0 ? sumX / cnt : N / 2;\n ry = cnt > 0 ? sumY / cnt : N / 2;\n rx = max(0, min(N - 1, rx));\n ry = max(0, min(N - 1, ry));\n \n cout << rx << \" \" << ry << \"\\n\";\n \n dirs.assign(numF, 0);\n holding.assign(numF, false);\n \n vector ops;\n \n while (ops.size() < 95000 && (!pickup.empty() || !dropS.empty() || \n any_of(holding.begin(), holding.end(), [](bool h){return h;}))) {\n \n vector rot(numF, '.'), act(numF, '.');\n bool acted = false;\n \n for (int i = 0; i < numF; i++) {\n auto [fx, fy] = fingertip(i);\n if (!valid(fx, fy)) continue;\n if (!holding[i] && pickup.count({fx, fy})) {\n act[i] = 'P'; pickup.erase({fx, fy}); holding[i] = true; acted = true;\n } else if (holding[i] && dropS.count({fx, fy})) {\n act[i] = 'P'; dropS.erase({fx, fy}); holding[i] = false; acted = true;\n }\n }\n if (acted) {\n string s = \".\";\n for (int i = 0; i < numF; i++) s += '.';\n s += '.';\n for (int i = 0; i < numF; i++) s += act[i];\n ops.push_back(s);\n continue;\n }\n \n int bestF = -1, bestDir = 0, bestCost = INT_MAX;\n pair bestTarget;\n \n for (int i = 0; i < numF; i++) {\n auto& targets = holding[i] ? dropS : pickup;\n if (targets.empty()) continue;\n \n for (auto& t : targets) {\n for (int d = 0; d < 4; d++) {\n int nrx = t.first - DX[d] * lens[i];\n int nry = t.second - DY[d] * lens[i];\n if (!valid(nrx, nry)) continue;\n int diff = (d - dirs[i] + 4) % 4;\n int rotCost = min(diff, 4 - diff);\n int cost = abs(nrx - rx) + abs(nry - ry) + rotCost;\n if (cost < bestCost) {\n bestCost = cost; bestF = i;\n bestTarget = t; bestDir = d;\n }\n }\n }\n }\n \n if (bestF == -1) break;\n \n int trx = bestTarget.first - DX[bestDir] * lens[bestF];\n int tr_y = bestTarget.second - DY[bestDir] * lens[bestF];\n char mv = '.';\n \n if (rx < trx && valid(rx + 1, ry)) { mv = 'D'; rx++; }\n else if (rx > trx && valid(rx - 1, ry)) { mv = 'U'; rx--; }\n else if (ry < tr_y && valid(rx, ry + 1)) { mv = 'R'; ry++; }\n else if (ry > tr_y && valid(rx, ry - 1)) { mv = 'L'; ry--; }\n \n if (dirs[bestF] != bestDir) {\n int diff = (bestDir - dirs[bestF] + 4) % 4;\n if (diff == 1) { rot[bestF] = 'R'; dirs[bestF] = (dirs[bestF] + 1) % 4; }\n else if (diff == 3) { rot[bestF] = 'L'; dirs[bestF] = (dirs[bestF] + 3) % 4; }\n else { rot[bestF] = 'R'; dirs[bestF] = (dirs[bestF] + 1) % 4; }\n }\n \n if (mv == '.' && rot[bestF] == '.') {\n if (valid(rx + 1, ry)) { mv = 'D'; rx++; }\n else if (valid(rx - 1, ry)) { mv = 'U'; rx--; }\n else if (valid(rx, ry + 1)) { mv = 'R'; ry++; }\n else if (valid(rx, ry - 1)) { mv = 'L'; ry--; }\n else { rot[bestF] = 'R'; dirs[bestF] = (dirs[bestF] + 1) % 4; }\n }\n \n string s; s += mv;\n for (int i = 0; i < numF; i++) s += rot[i];\n s += '.';\n for (int i = 0; i < numF; i++) s += act[i];\n ops.push_back(s);\n }\n \n for (auto& op : ops) cout << op << \"\\n\";\n return 0;\n}","ahc039":"#include \nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N;\n cin >> N;\n \n vector> mackerel(N), sardine(N);\n for (int i = 0; i < N; i++) cin >> mackerel[i].first >> mackerel[i].second;\n for (int i = 0; i < N; i++) cin >> sardine[i].first >> sardine[i].second;\n \n vector xs, ys;\n for (auto& p : mackerel) { xs.push_back(p.first); ys.push_back(p.second); }\n for (auto& p : sardine) { xs.push_back(p.first); ys.push_back(p.second); }\n \n sort(xs.begin(), xs.end()); xs.erase(unique(xs.begin(), xs.end()), xs.end());\n sort(ys.begin(), ys.end()); ys.erase(unique(ys.begin(), ys.end()), ys.end());\n \n int nx = xs.size(), ny = ys.size();\n map x_idx, y_idx;\n for (int i = 0; i < nx; i++) x_idx[xs[i]] = i;\n for (int i = 0; i < ny; i++) y_idx[ys[i]] = i;\n \n vector> grid(ny + 1, vector(nx + 1, 0));\n for (auto& p : mackerel) grid[y_idx[p.second] + 1][x_idx[p.first] + 1]++;\n for (auto& p : sardine) grid[y_idx[p.second] + 1][x_idx[p.first] + 1]--;\n for (int i = 1; i <= ny; i++)\n for (int j = 1; j <= nx; j++)\n grid[i][j] += grid[i-1][j] + grid[i][j-1] - grid[i-1][j-1];\n \n auto query = [&](int y1, int x1, int y2, int x2) -> int {\n if (x1 > x2 || y1 > y2) return 0;\n return grid[y2+1][x2+1] - grid[y1][x2+1] - grid[y2+1][x1] + grid[y1][x1];\n };\n \n int best_score = 0, bx1 = 0, by1 = 0, bx2 = 0, by2 = 0;\n mt19937 rng(42);\n vector> candidates;\n \n for (int iter = 0; iter < 500000; iter++) {\n int i1 = rng() % N, i2 = rng() % N;\n int x1i = x_idx[mackerel[i1].first], y1i = y_idx[mackerel[i1].second];\n int x2i = x_idx[mackerel[i2].first], y2i = y_idx[mackerel[i2].second];\n if (x1i > x2i) swap(x1i, x2i);\n if (y1i > y2i) swap(y1i, y2i);\n int score = query(y1i, x1i, y2i, x2i);\n if (score > best_score - 100) candidates.push_back({score, x1i, y1i, x2i, y2i});\n if (score > best_score) { best_score = score; bx1 = x1i; by1 = y1i; bx2 = x2i; by2 = y2i; }\n }\n \n sort(candidates.rbegin(), candidates.rend());\n if (candidates.size() > 80) candidates.resize(80);\n \n for (auto& [sc, cx1, cy1, cx2, cy2] : candidates) {\n for (int round = 0; round < 3; round++) {\n for (int x = 0; x <= cx2; x++) if (query(cy1, x, cy2, cx2) > query(cy1, cx1, cy2, cx2)) cx1 = x;\n for (int x = cx1; x < nx; x++) if (query(cy1, cx1, cy2, x) > query(cy1, cx1, cy2, cx2)) cx2 = x;\n for (int y = 0; y <= cy2; y++) if (query(y, cx1, cy2, cx2) > query(cy1, cx1, cy2, cx2)) cy1 = y;\n for (int y = cy1; y < ny; y++) if (query(cy1, cx1, y, cx2) > query(cy1, cx1, cy2, cx2)) cy2 = y;\n }\n if (query(cy1, cx1, cy2, cx2) > best_score) {\n best_score = query(cy1, cx1, cy2, cx2); bx1 = cx1; by1 = cy1; bx2 = cx2; by2 = cy2;\n }\n }\n \n int l_type = 0, lcx = 0, lcy = 0, l_score = best_score;\n \n for (int iter = 0; iter < 100000 && bx2 > bx1 + 1 && by2 > by1 + 1; iter++) {\n int corner = rng() % 4;\n int cx = bx1 + 1 + rng() % (bx2 - bx1 - 1);\n int cy = by1 + 1 + rng() % (by2 - by1 - 1);\n int cut = 0;\n switch (corner) {\n case 0: cut = query(by1, bx1, cy - 1, cx - 1); break;\n case 1: cut = query(by1, cx + 1, cy - 1, bx2); break;\n case 2: cut = query(cy + 1, cx + 1, by2, bx2); break;\n case 3: cut = query(cy + 1, bx1, by2, cx - 1); break;\n }\n if (best_score - cut > l_score) { l_score = best_score - cut; l_type = corner + 1; lcx = cx; lcy = cy; }\n }\n \n if (l_score <= 0) { cout << \"4\\n0 0\\n1 0\\n1 1\\n0 1\\n\"; return 0; }\n \n int ox1 = xs[bx1], oy1 = ys[by1], ox2 = xs[bx2], oy2 = ys[by2];\n \n if (l_type == 0) {\n cout << \"4\\n\" << ox1 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy2 << \"\\n\" << ox1 << \" \" << oy2 << \"\\n\";\n } else {\n int ocx = xs[lcx], ocy = ys[lcy];\n cout << \"6\\n\";\n if (l_type == 1) cout << ocx << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy2 << \"\\n\" << ox1 << \" \" << oy2 << \"\\n\" << ox1 << \" \" << ocy << \"\\n\" << ocx << \" \" << ocy << \"\\n\";\n else if (l_type == 2) cout << ox1 << \" \" << oy1 << \"\\n\" << ocx << \" \" << oy1 << \"\\n\" << ocx << \" \" << ocy << \"\\n\" << ox2 << \" \" << ocy << \"\\n\" << ox2 << \" \" << oy2 << \"\\n\" << ox1 << \" \" << oy2 << \"\\n\";\n else if (l_type == 3) cout << ox1 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << ocy << \"\\n\" << ocx << \" \" << ocy << \"\\n\" << ocx << \" \" << oy2 << \"\\n\" << ox1 << \" \" << oy2 << \"\\n\";\n else cout << ox1 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy2 << \"\\n\" << ocx << \" \" << oy2 << \"\\n\" << ocx << \" \" << ocy << \"\\n\" << ox1 << \" \" << ocy << \"\\n\";\n }\n return 0;\n}","ahc040":"#include \nusing namespace std;\n\nint N, T;\nlong long sigma;\nvector w, h;\n\nstruct PlacedRect { long long x1, y1, x2, y2; int id; };\n\npair simulate(const vector>& ops) {\n vector placed;\n long long W = 0, H = 0;\n for (auto& [p, r, d, b] : ops) {\n long long rw = w[p], rh = h[p];\n if (r) swap(rw, rh);\n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n placed.push_back({x, y, x + rw, y + rh, p});\n W = max(W, x + rw); H = max(H, y + rh);\n }\n return {W, H};\n}\n\nmt19937 rng(42);\n\nvector> genGreedy(double wBias, int maxBase = 15) {\n vector> ops;\n vector placed;\n long long curW = 0, curH = 0;\n \n for (int i = 0; i < N; i++) {\n double best = 1e18; \n tuple bc = {0,'U',-1};\n \n for (int r = 0; r < 2; r++) {\n long long rw = w[i], rh = h[i]; \n if (r) swap(rw, rh);\n \n for (char d : {'U','L'}) {\n for (int b = -1; b < i; b++) {\n if (b >= 0 && i - b > maxBase) continue;\n \n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n double sc = wBias * max(curW, x+rw) + max(curH, y+rh);\n if (sc < best) { best = sc; bc = {r, d, b}; }\n }\n }\n }\n \n auto [r, d, b] = bc;\n long long rw = w[i], rh = h[i]; if (r) swap(rw, rh);\n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n placed.push_back({x, y, x+rw, y+rh, i}); \n curW = max(curW, x+rw); curH = max(curH, y+rh);\n ops.push_back({i, r, d, b});\n }\n return ops;\n}\n\nvector> genShelf(double widthFactor, int rotMode) {\n long long totalArea = 0;\n for (int i = 0; i < N; i++) totalArea += w[i] * h[i];\n long long targetW = max(1LL, (long long)(sqrt((double)totalArea) * widthFactor));\n \n vector> ops;\n long long curX = 0;\n int lastInShelf = -1, shelfStart = -1;\n \n for (int i = 0; i < N; i++) {\n int r = (rotMode == 0) ? 0 : (rotMode == 1) ? 1 : (h[i] > w[i] ? 1 : 0);\n long long rw = w[i], rh = h[i]; if (r) swap(rw, rh);\n \n if (curX + rw > targetW && lastInShelf >= 0) {\n ops.push_back({i, r, 'L', shelfStart});\n shelfStart = i; curX = rw; lastInShelf = i;\n } else {\n if (lastInShelf < 0) {\n ops.push_back({i, r, 'U', -1});\n shelfStart = i;\n } else {\n ops.push_back({i, r, 'U', lastInShelf});\n }\n curX += rw; lastInShelf = i;\n }\n }\n return ops;\n}\n\nvector> genStrip(char dir, int rotMode) {\n vector> ops;\n for (int i = 0; i < N; i++) {\n int r = (rotMode == 0) ? 0 : (rotMode == 1) ? 1 : \n ((dir == 'U') ? (w[i] < h[i] ? 1 : 0) : (h[i] < w[i] ? 1 : 0));\n ops.push_back({i, r, dir, -1});\n }\n return ops;\n}\n\nvector> mutate(vector> ops, int intensity) {\n int numMut = 1 + rng() % (intensity + 1);\n for (int m = 0; m < numMut; m++) {\n int i = rng() % N;\n auto& [p, r, d, b] = ops[i];\n int choice = rng() % 3;\n if (choice == 0) r = 1 - r;\n else if (choice == 1) d = (d == 'U') ? 'L' : 'U';\n else if (i > 0) b = (int)(rng() % (i + 1)) - 1;\n }\n return ops;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> T >> sigma;\n w.resize(N); h.resize(N);\n for (int i = 0; i < N; i++) cin >> w[i] >> h[i];\n \n auto startTime = chrono::steady_clock::now();\n vector>>> candidates;\n \n auto addCandidate = [&](vector> ops) {\n auto [sw, sh] = simulate(ops);\n candidates.push_back({sw + sh, ops});\n };\n \n // Diverse greedy with different biases\n for (double bias : {0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.5, 2.0}) {\n addCandidate(genGreedy(bias));\n }\n \n // Shelf packing with different widths\n for (double wf : {0.6, 0.8, 1.0, 1.2, 1.5, 2.0}) {\n for (int rm = 0; rm < 3; rm++) {\n addCandidate(genShelf(wf, rm));\n }\n }\n \n // Strip packing\n for (char d : {'U', 'L'}) {\n for (int rm = 0; rm < 3; rm++) {\n addCandidate(genStrip(d, rm));\n }\n }\n \n sort(candidates.begin(), candidates.end());\n auto bestOps = candidates[0].second;\n long long bestSim = candidates[0].first;\n \n // Hill climbing with time limit\n while (true) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration_cast(now - startTime).count() > 2500) break;\n if ((int)candidates.size() >= T * 3) break;\n \n int srcIdx = (rng() % 100 < 70) ? 0 : rng() % min((int)candidates.size(), 10);\n int intensity = 1 + (rng() % 3);\n auto ops = mutate(candidates[srcIdx].second, intensity);\n auto [sw, sh] = simulate(ops);\n \n if (sw + sh <= bestSim * 1.05) {\n candidates.push_back({sw + sh, ops});\n if (sw + sh < bestSim) { \n bestSim = sw + sh; \n bestOps = ops;\n }\n }\n }\n \n sort(candidates.begin(), candidates.end());\n \n // Remove duplicates\n vector>>> unique_cands;\n set>> seen;\n for (auto& c : candidates) {\n if (seen.find(c.second) == seen.end()) {\n seen.insert(c.second);\n unique_cands.push_back(c);\n }\n if ((int)unique_cands.size() >= T) break;\n }\n candidates = unique_cands;\n \n // Fill remaining slots\n while ((int)candidates.size() < T) {\n auto ops = mutate(bestOps, 2);\n auto [sw, sh] = simulate(ops);\n candidates.push_back({sw + sh, ops});\n }\n \n sort(candidates.begin(), candidates.end());\n \n for (int t = 0; t < T; t++) {\n auto& ops = candidates[t].second;\n cout << ops.size() << \"\\n\";\n for (auto& [p, r, d, b] : ops) cout << p << \" \" << r << \" \" << d << \" \" << b << \"\\n\";\n cout.flush();\n long long W, H; cin >> W >> H;\n }\n \n return 0;\n}","ahc041":"#include \nusing namespace std;\n\nint N, M, H;\nvector A;\nvector> adj;\nvector parent_arr;\nvector depth_arr;\nvector> children;\nvector sub_h;\n\nlong long compute_score() {\n long long score = 0;\n for (int i = 0; i < N; i++) {\n score += (long long)(depth_arr[i] + 1) * A[i];\n }\n return score;\n}\n\nvoid rebuild_all() {\n for (int i = 0; i < N; i++) children[i].clear();\n for (int i = 0; i < N; i++) {\n if (parent_arr[i] != -1) {\n children[parent_arr[i]].push_back(i);\n }\n }\n \n fill(depth_arr.begin(), depth_arr.end(), -1);\n queue q;\n for (int i = 0; i < N; i++) {\n if (parent_arr[i] == -1) {\n depth_arr[i] = 0;\n q.push(i);\n }\n }\n while (!q.empty()) {\n int u = q.front(); q.pop();\n for (int c : children[u]) {\n depth_arr[c] = depth_arr[u] + 1;\n q.push(c);\n }\n }\n \n function calc = [&](int v) -> int {\n int h = 0;\n for (int c : children[v]) h = max(h, 1 + calc(c));\n return sub_h[v] = h;\n };\n for (int i = 0; i < N; i++) {\n if (parent_arr[i] == -1) calc(i);\n }\n}\n\nvoid dfs(int u) {\n vector> neighbors;\n for (int v : adj[u]) {\n if (depth_arr[v] == -1) {\n neighbors.push_back({-A[v], v});\n }\n }\n sort(neighbors.begin(), neighbors.end());\n \n for (auto& [neg_beauty, v] : neighbors) {\n if (depth_arr[v] == -1 && depth_arr[u] < H) {\n parent_arr[v] = u;\n depth_arr[v] = depth_arr[u] + 1;\n dfs(v);\n }\n }\n}\n\nbool is_ancestor(int anc, int desc) {\n while (desc != -1) {\n if (desc == anc) return true;\n desc = parent_arr[desc];\n }\n return false;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n auto start_time = chrono::steady_clock::now();\n auto elapsed = [&]() {\n return chrono::duration_cast(\n chrono::steady_clock::now() - start_time).count();\n };\n \n cin >> N >> M >> H;\n \n A.resize(N);\n for (int i = 0; i < N; i++) cin >> A[i];\n \n adj.resize(N);\n for (int i = 0; i < M; i++) {\n int u, v;\n cin >> u >> v;\n adj[u].push_back(v);\n adj[v].push_back(u);\n }\n \n for (int i = 0; i < N; i++) {\n int x, y;\n cin >> x >> y;\n }\n \n parent_arr.resize(N);\n depth_arr.resize(N);\n children.resize(N);\n sub_h.resize(N);\n \n vector best_parent(N, -1);\n long long best_score = 0;\n \n mt19937 rng(54321);\n \n // Multiple restarts\n for (int trial = 0; trial < 300 && elapsed() < 600; trial++) {\n fill(parent_arr.begin(), parent_arr.end(), -1);\n fill(depth_arr.begin(), depth_arr.end(), -1);\n \n vector order(N);\n iota(order.begin(), order.end(), 0);\n \n if (trial == 0) {\n sort(order.begin(), order.end(), [&](int a, int b) { return A[a] < A[b]; });\n } else if (trial == 1) {\n sort(order.begin(), order.end(), [&](int a, int b) { return adj[a].size() < adj[b].size(); });\n } else {\n vector keys(N);\n for (int i = 0; i < N; i++) keys[i] = A[i] + (rng() % 80);\n sort(order.begin(), order.end(), [&](int a, int b) { return keys[a] < keys[b]; });\n }\n \n for (int start : order) {\n if (depth_arr[start] != -1) continue;\n depth_arr[start] = 0;\n parent_arr[start] = -1;\n dfs(start);\n }\n \n long long score = compute_score();\n if (score > best_score) {\n best_score = score;\n best_parent = parent_arr;\n }\n }\n \n parent_arr = best_parent;\n rebuild_all();\n best_score = compute_score();\n \n // Local search with multiple strategies\n for (int phase = 0; phase < 10 && elapsed() < 1850; phase++) {\n vector vorder(N);\n iota(vorder.begin(), vorder.end(), 0);\n \n if (phase % 3 == 0) {\n sort(vorder.begin(), vorder.end(), [&](int a, int b) { return A[a] > A[b]; });\n } else if (phase % 3 == 1) {\n sort(vorder.begin(), vorder.end(), [&](int a, int b) { return depth_arr[a] < depth_arr[b]; });\n } else {\n shuffle(vorder.begin(), vorder.end(), rng);\n }\n \n bool improved = true;\n while (improved && elapsed() < 1850) {\n improved = false;\n \n for (int v : vorder) {\n if (elapsed() > 1850) break;\n \n int cur_depth = depth_arr[v];\n int best_new_parent = -1;\n int best_gain = 0;\n \n for (int u : adj[v]) {\n if (u == parent_arr[v]) continue;\n if (is_ancestor(v, u)) continue;\n \n int new_depth = depth_arr[u] + 1;\n if (new_depth + sub_h[v] <= H) {\n int gain = (new_depth - cur_depth) * A[v];\n // Also account for descendants\n function desc_gain = [&](int node, int delta) -> int {\n int g = delta * A[node];\n for (int c : children[node]) g += desc_gain(c, delta);\n return g;\n };\n int total_gain = desc_gain(v, new_depth - cur_depth);\n \n if (total_gain > best_gain) {\n best_gain = total_gain;\n best_new_parent = u;\n }\n }\n }\n \n if (best_new_parent != -1) {\n parent_arr[v] = best_new_parent;\n rebuild_all();\n improved = true;\n }\n }\n }\n \n long long cur_score = compute_score();\n if (cur_score > best_score) {\n best_score = cur_score;\n best_parent = parent_arr;\n }\n }\n \n for (int i = 0; i < N; i++) {\n cout << best_parent[i];\n if (i < N - 1) cout << \" \";\n }\n cout << \"\\n\";\n \n return 0;\n}","ahc042":"#include \nusing namespace std;\n\nint N, M;\nint oni_r[50], oni_c[50];\nint valid_cnt[50], valid[50][4], dist[50][4];\nint asgn[50], batch_max[80];\n\ninline int get_key(int k, int d) { return d * 20 + ((d <= 1) ? oni_c[k] : oni_r[k]); }\n\nint full_cost() {\n memset(batch_max, 0, sizeof(batch_max));\n for (int k = 0; k < M; k++) {\n int key = get_key(k, asgn[k]);\n batch_max[key] = max(batch_max[key], dist[k][asgn[k]]);\n }\n int t = 0; for (int i = 0; i < 80; i++) t += batch_max[i];\n return 2 * t;\n}\n\nint try_change(int k, int new_d) {\n int old_d = asgn[k];\n if (old_d == new_d) return 0;\n int old_key = get_key(k, old_d), new_key = get_key(k, new_d);\n int old_cost = 2 * (batch_max[old_key] + batch_max[new_key]);\n \n int new_old_max = 0;\n for (int i = 0; i < M; i++) if (i != k && get_key(i, asgn[i]) == old_key)\n new_old_max = max(new_old_max, dist[i][asgn[i]]);\n int new_new_max = max(batch_max[new_key], dist[k][new_d]);\n \n return 2 * (new_old_max + new_new_max) - old_cost;\n}\n\nvoid apply_change(int k, int new_d) {\n int old_key = get_key(k, asgn[k]), new_key = get_key(k, new_d);\n asgn[k] = new_d;\n int new_old_max = 0;\n for (int i = 0; i < M; i++) if (get_key(i, asgn[i]) == old_key)\n new_old_max = max(new_old_max, dist[i][asgn[i]]);\n batch_max[old_key] = new_old_max;\n batch_max[new_key] = max(batch_max[new_key], dist[k][new_d]);\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n auto start = chrono::steady_clock::now();\n auto elapsed = [&]() { return chrono::duration(chrono::steady_clock::now() - start).count(); };\n \n cin >> N;\n vector board(N);\n for (int i = 0; i < N; i++) cin >> board[i];\n \n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (board[i][j] == 'x') {\n oni_r[M] = i; oni_c[M] = j; M++;\n }\n \n for (int k = 0; k < M; k++) {\n int r = oni_r[k], c = oni_c[k];\n bool ok = true; for (int i = 0; i < r && ok; i++) if (board[i][c] == 'o') ok = false;\n if (ok) { valid[k][valid_cnt[k]] = 0; dist[k][0] = r + 1; valid_cnt[k]++; }\n ok = true; for (int i = r+1; i < N && ok; i++) if (board[i][c] == 'o') ok = false;\n if (ok) { valid[k][valid_cnt[k]] = 1; dist[k][1] = N - r; valid_cnt[k]++; }\n ok = true; for (int j = 0; j < c && ok; j++) if (board[r][j] == 'o') ok = false;\n if (ok) { valid[k][valid_cnt[k]] = 2; dist[k][2] = c + 1; valid_cnt[k]++; }\n ok = true; for (int j = c+1; j < N && ok; j++) if (board[r][j] == 'o') ok = false;\n if (ok) { valid[k][valid_cnt[k]] = 3; dist[k][3] = N - c; valid_cnt[k]++; }\n }\n \n mt19937 rng(42);\n int best_asgn[50], best_cost = INT_MAX;\n \n auto local_search = [&]() {\n int cur = full_cost();\n for (int it = 0; it < 30; it++) {\n bool imp = false;\n for (int k = 0; k < M; k++) for (int vi = 0; vi < valid_cnt[k]; vi++) {\n int d = valid[k][vi]; if (d == asgn[k]) continue;\n int delta = try_change(k, d);\n if (delta < 0) { apply_change(k, d); cur += delta; imp = true; }\n }\n if (!imp) break;\n }\n if (cur < best_cost) { best_cost = cur; memcpy(best_asgn, asgn, sizeof(asgn)); }\n };\n \n // Initial: minimum individual distance\n for (int k = 0; k < M; k++) {\n int bd = valid[k][0];\n for (int vi = 0; vi < valid_cnt[k]; vi++) if (dist[k][valid[k][vi]] < dist[k][bd]) bd = valid[k][vi];\n asgn[k] = bd;\n }\n local_search();\n \n // Prefer each direction\n for (int p = 0; p < 4; p++) {\n for (int k = 0; k < M; k++) {\n asgn[k] = valid[k][0];\n for (int vi = 0; vi < valid_cnt[k]; vi++) if (valid[k][vi] == p) { asgn[k] = p; break; }\n }\n local_search();\n }\n \n // Greedy incremental\n vector order(M); iota(order.begin(), order.end(), 0);\n for (int t = 0; t < 30 && elapsed() < 0.3; t++) {\n shuffle(order.begin(), order.end(), rng);\n memset(asgn, -1, sizeof(asgn)); memset(batch_max, 0, sizeof(batch_max));\n for (int k : order) {\n int bd = valid[k][0], bc = INT_MAX;\n for (int vi = 0; vi < valid_cnt[k]; vi++) {\n int d = valid[k][vi], key = get_key(k, d);\n int add = max(0, dist[k][d] - batch_max[key]);\n if (add < bc) { bc = add; bd = d; }\n }\n asgn[k] = bd; batch_max[get_key(k, bd)] = max(batch_max[get_key(k, bd)], dist[k][bd]);\n }\n local_search();\n }\n \n // SA with restarts\n memcpy(asgn, best_asgn, sizeof(asgn)); full_cost();\n int cur_cost = best_cost;\n double temp = 10.0;\n int no_improve = 0;\n while (elapsed() < 1.9) {\n int k = rng() % M;\n if (valid_cnt[k] <= 1) continue;\n int new_d = valid[k][rng() % valid_cnt[k]];\n if (new_d == asgn[k]) continue;\n int delta = try_change(k, new_d);\n if (delta < 0 || (rng() % 10000) < 10000 * exp(-delta / temp)) {\n apply_change(k, new_d); cur_cost += delta;\n if (cur_cost < best_cost) { best_cost = cur_cost; memcpy(best_asgn, asgn, sizeof(asgn)); no_improve = 0; }\n else no_improve++;\n } else no_improve++;\n temp *= 0.999995;\n if (no_improve > 50000) { memcpy(asgn, best_asgn, sizeof(asgn)); full_cost(); cur_cost = best_cost; temp = 5.0; no_improve = 0; }\n }\n \n map batches;\n for (int k = 0; k < M; k++) batches[get_key(k, best_asgn[k])] = max(batches[get_key(k, best_asgn[k])], dist[k][best_asgn[k]]);\n \n for (auto& [key, mx] : batches) {\n int dir = key / 20, idx = key % 20;\n char c1 = (dir == 0 ? 'U' : dir == 1 ? 'D' : dir == 2 ? 'L' : 'R');\n char c2 = (dir == 0 ? 'D' : dir == 1 ? 'U' : dir == 2 ? 'R' : 'L');\n for (int t = 0; t < mx; t++) cout << c1 << \" \" << idx << \"\\n\";\n for (int t = 0; t < mx; t++) cout << c2 << \" \" << idx << \"\\n\";\n }\n return 0;\n}","ahc044":"#include \nusing namespace std;\n\nint N, L;\nvector T;\n\nlong long simulate(const vector& a, const vector& b, vector& t) {\n fill(t.begin(), t.end(), 0);\n int x = 0;\n for (int week = 0; week < L; week++) {\n t[x]++;\n x = (t[x] & 1) ? a[x] : b[x];\n }\n long long error = 0;\n for (int i = 0; i < N; i++) error += abs(t[i] - T[i]);\n return error;\n}\n\nvoid runOptimization(mt19937& rng, const vector& weighted, const vector& sorted_idx,\n vector& best_a, vector& best_b, long long& global_best,\n double time_limit, chrono::steady_clock::time_point start) {\n vector t(N);\n \n for (int restart = 0; ; restart++) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > time_limit) break;\n \n vector a(N), b(N);\n \n if (restart == 0) {\n for (int i = 0; i < N; i++) {\n a[sorted_idx[i]] = sorted_idx[(i + 1) % N];\n b[sorted_idx[i]] = sorted_idx[(i + 1) % N];\n }\n } else if (restart == 1) {\n for (int i = 0; i < N; i++) {\n a[sorted_idx[i]] = sorted_idx[(i + 1) % N];\n b[sorted_idx[i]] = sorted_idx[(i + 2) % N];\n }\n } else if (restart % 3 == 0 && global_best < LLONG_MAX) {\n a = best_a; b = best_b;\n for (int k = 0; k < N/4; k++) {\n int idx = rng() % N;\n a[idx] = weighted[rng() % weighted.size()];\n b[idx] = weighted[rng() % weighted.size()];\n }\n } else {\n for (int i = 0; i < N; i++) {\n a[i] = weighted[rng() % weighted.size()];\n b[i] = weighted[rng() % weighted.size()];\n }\n }\n \n long long cur_error = simulate(a, b, t);\n long long local_best = cur_error;\n vector local_a = a, local_b = b;\n \n double restart_budget = min(0.25, (time_limit - elapsed) * 0.6);\n double restart_start = elapsed;\n \n while (true) {\n now = chrono::steady_clock::now();\n elapsed = chrono::duration(now - start).count();\n if (elapsed > time_limit || elapsed - restart_start > restart_budget) break;\n \n double progress = (elapsed - restart_start) / restart_budget;\n double temp = 2500.0 * pow(0.0001, progress);\n \n int i = rng() % N;\n int old_a = a[i], old_b = b[i];\n \n int choice = rng() % 4;\n if (choice == 0) a[i] = weighted[rng() % weighted.size()];\n else if (choice == 1) b[i] = weighted[rng() % weighted.size()];\n else if (choice == 2) a[i] = rng() % N;\n else b[i] = rng() % N;\n \n long long new_error = simulate(a, b, t);\n double delta = new_error - cur_error;\n \n if (delta <= 0 || exp(-delta / temp) > (rng() % 1000000) / 1000000.0) {\n cur_error = new_error;\n if (new_error < local_best) {\n local_best = new_error;\n local_a = a; local_b = b;\n }\n } else {\n a[i] = old_a; b[i] = old_b;\n }\n }\n \n if (local_best < global_best) {\n global_best = local_best;\n best_a = local_a; best_b = local_b;\n }\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> L;\n T.resize(N);\n for (int i = 0; i < N; i++) cin >> T[i];\n \n vector weighted;\n for (int i = 0; i < N; i++) {\n int cnt = max(1, T[i] / 100);\n for (int j = 0; j < cnt; j++) weighted.push_back(i);\n }\n \n vector sorted_idx(N);\n iota(sorted_idx.begin(), sorted_idx.end(), 0);\n sort(sorted_idx.begin(), sorted_idx.end(), [](int x, int y) { return T[x] > T[y]; });\n \n vector best_a(N), best_b(N);\n long long global_best = LLONG_MAX;\n \n auto start = chrono::steady_clock::now();\n \n vector seeds = {12345, 67890, 11111, 99999};\n for (int seed : seeds) {\n mt19937 rng(seed);\n runOptimization(rng, weighted, sorted_idx, best_a, best_b, global_best, 1.9, start);\n }\n \n for (int i = 0; i < N; i++) cout << best_a[i] << \" \" << best_b[i] << \"\\n\";\n return 0;\n}","ahc045":"#include \nusing namespace std;\n\nint queries_used = 0;\nint Q_limit;\n\nvector> query(vector& cities) {\n if (queries_used >= Q_limit || cities.size() < 2) return {};\n cout << \"? \" << cities.size();\n for (int c : cities) cout << \" \" << c;\n cout << endl;\n \n vector> edges;\n for (size_t i = 0; i + 1 < cities.size(); i++) {\n int a, b;\n cin >> a >> b;\n edges.emplace_back(a, b);\n }\n queries_used++;\n return edges;\n}\n\ndouble estDist(double x1, double y1, double x2, double y2) {\n double dx = x1 - x2, dy = y1 - y2;\n return sqrt(dx*dx + dy*dy);\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, Q, L, W;\n cin >> N >> M >> Q >> L >> W;\n Q_limit = Q;\n \n vector G(M);\n for (int i = 0; i < M; i++) cin >> G[i];\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) {\n int lx, rx, ly, ry;\n cin >> lx >> rx >> ly >> ry;\n x[i] = (lx + rx) / 2.0;\n y[i] = (ly + ry) / 2.0;\n }\n \n // Greedy nearest-neighbor grouping\n vector used(N, false);\n vector> groups(M);\n \n vector groupOrder(M);\n iota(groupOrder.begin(), groupOrder.end(), 0);\n sort(groupOrder.begin(), groupOrder.end(), [&](int a, int b) {\n return G[a] > G[b];\n });\n \n for (int gi : groupOrder) {\n int g = G[gi];\n double cx = 0, cy = 0;\n int cnt = 0;\n for (int i = 0; i < N; i++) {\n if (!used[i]) { cx += x[i]; cy += y[i]; cnt++; }\n }\n if (cnt > 0) { cx /= cnt; cy /= cnt; }\n \n int start = -1;\n double minD = 1e18;\n for (int i = 0; i < N; i++) {\n if (!used[i]) {\n double d = estDist(x[i], y[i], cx, cy);\n if (d < minD) { minD = d; start = i; }\n }\n }\n \n groups[gi].push_back(start);\n used[start] = true;\n \n while ((int)groups[gi].size() < g) {\n int best = -1;\n double bestD = 1e18;\n for (int i = 0; i < N; i++) {\n if (used[i]) continue;\n double minDistToGroup = 1e18;\n for (int c : groups[gi]) {\n minDistToGroup = min(minDistToGroup, estDist(x[i], y[i], x[c], y[c]));\n }\n if (minDistToGroup < bestD) {\n bestD = minDistToGroup;\n best = i;\n }\n }\n groups[gi].push_back(best);\n used[best] = true;\n }\n }\n \n // Local TSP-like reordering within each group\n for (int k = 0; k < M; k++) {\n int g = groups[k].size();\n if (g <= 2) continue;\n \n vector ordered;\n vector inOrder(g, false);\n ordered.push_back(0);\n inOrder[0] = true;\n \n while ((int)ordered.size() < g) {\n int last = ordered.back();\n int best = -1;\n double bestD = 1e18;\n for (int i = 0; i < g; i++) {\n if (inOrder[i]) continue;\n double d = estDist(x[groups[k][last]], y[groups[k][last]], \n x[groups[k][i]], y[groups[k][i]]);\n if (d < bestD) { bestD = d; best = i; }\n }\n ordered.push_back(best);\n inOrder[best] = true;\n }\n \n vector newGroup(g);\n for (int i = 0; i < g; i++) newGroup[i] = groups[k][ordered[i]];\n groups[k] = newGroup;\n }\n \n // Calculate total minimum queries needed\n int totalMinQueries = 0;\n for (int k = 0; k < M; k++) {\n int g = groups[k].size();\n if (g <= 1) continue;\n else if (g <= L) totalMinQueries += 1;\n else totalMinQueries += (g - 2) / (L - 1) + 1;\n }\n \n vector>> edges(M);\n vector>> all_edges_per_group(M);\n \n // First pass: ensure connectivity\n for (int k = 0; k < M; k++) {\n int g = groups[k].size();\n if (g == 1) continue;\n \n if (g <= L && queries_used < Q) {\n edges[k] = query(groups[k]);\n } else {\n int remainingBudget = Q - queries_used;\n int remainingGroups = 0;\n for (int j = k; j < M; j++) if (groups[j].size() > (size_t)L) remainingGroups++;\n \n int step = L - 1;\n if (remainingBudget > totalMinQueries * 2 && remainingGroups > 0) {\n step = max(1, (L - 1) / 2);\n }\n \n // Main sliding window\n for (int i = 0; i < g && queries_used < Q; i += step) {\n int end = min(i + L, g);\n if (end - i >= 2) {\n vector subset(groups[k].begin() + i, groups[k].begin() + end);\n auto e = query(subset);\n all_edges_per_group[k].insert(all_edges_per_group[k].end(), e.begin(), e.end());\n }\n if (end >= g) break;\n }\n \n // Second pass with offset\n if (step > 1 && queries_used < Q && g > L) {\n for (int i = step/2; i + 1 < g && queries_used < Q; i += step) {\n int end = min(i + L, g);\n if (end - i >= 2) {\n vector subset(groups[k].begin() + i, groups[k].begin() + end);\n auto e = query(subset);\n all_edges_per_group[k].insert(all_edges_per_group[k].end(), e.begin(), e.end());\n }\n if (end >= g) break;\n }\n }\n \n // Build MST\n map city_to_local;\n for (int i = 0; i < g; i++) city_to_local[groups[k][i]] = i;\n \n vector parent(g);\n iota(parent.begin(), parent.end(), 0);\n function find = [&](int u) -> int {\n return parent[u] == u ? u : parent[u] = find(parent[u]);\n };\n \n auto& ae = all_edges_per_group[k];\n sort(ae.begin(), ae.end(), [&](auto& a, auto& b) {\n double da = estDist(x[a.first], y[a.first], x[a.second], y[a.second]);\n double db = estDist(x[b.first], y[b.first], x[b.second], y[b.second]);\n return da < db;\n });\n \n for (auto& e : ae) {\n int u = city_to_local[e.first];\n int v = city_to_local[e.second];\n if (find(u) != find(v)) {\n parent[find(u)] = find(v);\n edges[k].push_back(e);\n }\n }\n \n // Fallback\n while ((int)edges[k].size() < g - 1) {\n double best_dist = 1e18;\n int best_u = -1, best_v = -1;\n for (int i = 0; i < g; i++) {\n for (int j = i + 1; j < g; j++) {\n if (find(i) != find(j)) {\n double d = estDist(x[groups[k][i]], y[groups[k][i]], \n x[groups[k][j]], y[groups[k][j]]);\n if (d < best_dist) {\n best_dist = d;\n best_u = i; best_v = j;\n }\n }\n }\n }\n if (best_u >= 0) {\n parent[find(best_u)] = find(best_v);\n edges[k].push_back({groups[k][best_u], groups[k][best_v]});\n } else break;\n }\n }\n }\n \n // Use remaining queries for large groups - random sampling\n mt19937 rng(42);\n vector largeGroups;\n for (int k = 0; k < M; k++) {\n if ((int)groups[k].size() > L) largeGroups.push_back(k);\n }\n \n while (queries_used < Q && !largeGroups.empty()) {\n int k = largeGroups[rng() % largeGroups.size()];\n int g = groups[k].size();\n \n // Sample L random cities\n vector indices(g);\n iota(indices.begin(), indices.end(), 0);\n shuffle(indices.begin(), indices.end(), rng);\n \n vector subset;\n for (int i = 0; i < min(L, g); i++) {\n subset.push_back(groups[k][indices[i]]);\n }\n \n auto e = query(subset);\n // Check if any edge improves our MST\n for (auto& edge : e) {\n bool found = false;\n for (auto& existing : edges[k]) {\n if ((existing.first == edge.first && existing.second == edge.second) ||\n (existing.first == edge.second && existing.second == edge.first)) {\n found = true;\n break;\n }\n }\n if (!found) {\n all_edges_per_group[k].push_back(edge);\n }\n }\n }\n \n cout << \"!\" << endl;\n for (int k = 0; k < M; k++) {\n for (int c : groups[k]) cout << c << \" \";\n cout << \"\\n\";\n for (auto& e : edges[k]) {\n cout << e.first << \" \" << e.second << \"\\n\";\n }\n }\n \n return 0;\n}","ahc046":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M;\n cin >> N >> M;\n \n vector> targets(M);\n for (int i = 0; i < M; i++) {\n cin >> targets[i].first >> targets[i].second;\n }\n \n vector actions;\n int curR = targets[0].first, curC = targets[0].second;\n \n for (int i = 1; i < M; i++) {\n int tR = targets[i].first, tC = targets[i].second;\n \n int moveCost = abs(tR - curR) + abs(tC - curC);\n int bestCost = moveCost;\n int bestStrategy = 0;\n \n // Edge target strategies (1-4)\n if (tR == 0 && curR > 0) {\n int cost = abs(tC - curC) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 1; }\n }\n if (tR == N - 1 && curR < N - 1) {\n int cost = abs(tC - curC) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 2; }\n }\n if (tC == 0 && curC > 0) {\n int cost = abs(tR - curR) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 3; }\n }\n if (tC == N - 1 && curC < N - 1) {\n int cost = abs(tR - curR) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 4; }\n }\n \n // Slide-first strategies (5-8)\n if (curR > 0) {\n int cost = 1 + tR + abs(tC - curC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 5; }\n }\n if (curR < N - 1) {\n int cost = 1 + (N - 1 - tR) + abs(tC - curC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 6; }\n }\n if (curC > 0) {\n int cost = 1 + tC + abs(tR - curR);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 7; }\n }\n if (curC < N - 1) {\n int cost = 1 + (N - 1 - tC) + abs(tR - curR);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 8; }\n }\n \n // Double-slide to corners (9-12)\n if (curR > 0 && curC > 0) { // to (0,0)\n int cost = 2 + tR + tC;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 9; }\n }\n if (curR > 0 && curC < N - 1) { // to (0, N-1)\n int cost = 2 + tR + (N - 1 - tC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 10; }\n }\n if (curR < N - 1 && curC > 0) { // to (N-1, 0)\n int cost = 2 + (N - 1 - tR) + tC;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 11; }\n }\n if (curR < N - 1 && curC < N - 1) { // to (N-1, N-1)\n int cost = 2 + (N - 1 - tR) + (N - 1 - tC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 12; }\n }\n \n switch (bestStrategy) {\n case 0:\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n break;\n case 1: case 2: case 3: case 4:\n if (bestStrategy <= 2) {\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n actions.push_back(bestStrategy == 1 ? \"S U\" : \"S D\");\n curR = (bestStrategy == 1) ? 0 : N - 1;\n } else {\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n actions.push_back(bestStrategy == 3 ? \"S L\" : \"S R\");\n curC = (bestStrategy == 3) ? 0 : N - 1;\n }\n break;\n case 5: actions.push_back(\"S U\"); curR = 0; goto moveToTarget;\n case 6: actions.push_back(\"S D\"); curR = N - 1; goto moveToTarget;\n case 7: actions.push_back(\"S L\"); curC = 0; goto moveToTarget;\n case 8: actions.push_back(\"S R\"); curC = N - 1; goto moveToTarget;\n case 9: actions.push_back(\"S U\"); curR = 0; actions.push_back(\"S L\"); curC = 0; goto moveToTarget;\n case 10: actions.push_back(\"S U\"); curR = 0; actions.push_back(\"S R\"); curC = N - 1; goto moveToTarget;\n case 11: actions.push_back(\"S D\"); curR = N - 1; actions.push_back(\"S L\"); curC = 0; goto moveToTarget;\n case 12: actions.push_back(\"S D\"); curR = N - 1; actions.push_back(\"S R\"); curC = N - 1; goto moveToTarget;\n moveToTarget:\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n break;\n }\n }\n \n for (const string& action : actions) {\n cout << action << \"\\n\";\n }\n \n return 0;\n}"},"16":{"ahc001":"#include \nusing namespace std;\n\nconst int W = 10000;\nint n;\nvector px, py, rr;\nint a[201], b[201], c[201], d[201];\n\nbool canExpand(int i, int dir) {\n int na = a[i], nb = b[i], nc = c[i], nd = d[i];\n if (dir == 0) na--; else if (dir == 1) nc++; else if (dir == 2) nb--; else nd++;\n if (na < 0 || nc > W || nb < 0 || nd > W) return false;\n for (int j = 0; j < n; j++) {\n if (i != j && !(nc <= a[j] || c[j] <= na || nd <= b[j] || d[j] <= nb)) return false;\n }\n return true;\n}\n\nvoid doExpand(int i, int dir) {\n if (dir == 0) a[i]--; else if (dir == 1) c[i]++; else if (dir == 2) b[i]--; else d[i]++;\n}\n\nlong long area(int i) { return (long long)(c[i] - a[i]) * (d[i] - b[i]); }\n\ndouble score(int i) {\n long long s = area(i);\n double ratio = (double)min((long long)rr[i], s) / max((long long)rr[i], s);\n return 1.0 - (1.0 - ratio) * (1.0 - ratio);\n}\n\ndouble totalScore() { double s = 0; for (int i = 0; i < n; i++) s += score(i); return s; }\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> n;\n px.resize(n); py.resize(n); rr.resize(n);\n for (int i = 0; i < n; i++) {\n cin >> px[i] >> py[i] >> rr[i];\n a[i] = px[i]; b[i] = py[i]; c[i] = px[i]+1; d[i] = py[i]+1;\n }\n \n auto start = chrono::high_resolution_clock::now();\n auto elapsed = [&]() {\n return chrono::duration(chrono::high_resolution_clock::now() - start).count();\n };\n \n // Phase 1: Quick initial expansion up to target\n while (elapsed() < 0.8) {\n bool changed = false;\n vector order(n);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int i, int j) {\n return (double)(rr[i] - area(i)) / rr[i] > (double)(rr[j] - area(j)) / rr[j];\n });\n for (int i : order) {\n if (area(i) >= rr[i]) continue;\n for (int dir = 0; dir < 4; dir++) {\n if (area(i) >= rr[i]) break;\n if (canExpand(i, dir)) { doExpand(i, dir); changed = true; }\n }\n }\n if (!changed) break;\n }\n \n // Phase 2: Fill remaining space\n while (elapsed() < 1.2) {\n bool changed = false;\n vector order(n);\n iota(order.begin(), order.end(), 0);\n sort(order.begin(), order.end(), [&](int i, int j) { return rr[i] - area(i) > rr[j] - area(j); });\n for (int i : order) {\n for (int dir = 0; dir < 4; dir++)\n if (canExpand(i, dir)) { doExpand(i, dir); changed = true; }\n }\n if (!changed) break;\n }\n \n // Phase 3: Quick shrink-expand\n for (int cycle = 0; cycle < 3 && elapsed() < 1.8; cycle++) {\n for (int iter = 0; iter < 200; iter++) {\n bool changed = false;\n for (int i = 0; i < n; i++) {\n if (area(i) <= rr[i]) continue;\n for (int dir = 0; dir < 4; dir++) {\n int na = a[i], nb = b[i], nc = c[i], nd = d[i];\n if (dir == 0) na++; else if (dir == 1) nc--; else if (dir == 2) nb++; else nd--;\n if (na >= nc || nb >= nd) continue;\n if (!(na <= px[i] && px[i] < nc && nb <= py[i] && py[i] < nd)) continue;\n if ((long long)(nc - na) * (nd - nb) >= rr[i]) {\n a[i] = na; b[i] = nb; c[i] = nc; d[i] = nd; changed = true;\n }\n }\n }\n if (!changed) break;\n }\n for (int iter = 0; iter < 200; iter++) {\n bool changed = false;\n for (int i = 0; i < n; i++) {\n if (area(i) >= rr[i]) continue;\n for (int dir = 0; dir < 4; dir++) if (canExpand(i, dir)) { doExpand(i, dir); changed = true; }\n }\n if (!changed) break;\n }\n }\n \n // Phase 4: Extended simulated annealing\n mt19937 rng(42);\n uniform_real_distribution prob(0.0, 1.0);\n vector sa(n), sb(n), sc(n), sd(n);\n double bestScore = totalScore();\n vector ba(n), bb(n), bc(n), bd(n);\n for (int i = 0; i < n; i++) { ba[i] = a[i]; bb[i] = b[i]; bc[i] = c[i]; bd[i] = d[i]; }\n \n double startT = 0.05, endT = 0.001;\n \n while (elapsed() < 4.7) {\n double progress = (elapsed() - 1.8) / (4.7 - 1.8);\n double T = startT * pow(endT / startT, progress);\n \n for (int i = 0; i < n; i++) { sa[i] = a[i]; sb[i] = b[i]; sc[i] = c[i]; sd[i] = d[i]; }\n double oldScore = totalScore();\n \n // Pick rectangle to shrink - prefer oversized\n vector> candidates;\n for (int i = 0; i < n; i++) {\n long long excess = area(i) - rr[i];\n if (excess > -rr[i]/2) candidates.push_back({-excess, i}); // negative so oversized comes first\n }\n if (candidates.empty()) break;\n sort(candidates.begin(), candidates.end());\n \n int pick = min((int)(prob(rng) * prob(rng) * candidates.size()), (int)candidates.size() - 1);\n int idx = candidates[pick].second;\n int dir = rng() % 4;\n \n int na = a[idx], nb = b[idx], nc = c[idx], nd = d[idx];\n if (dir == 0) na++; else if (dir == 1) nc--; else if (dir == 2) nb++; else nd--;\n if (na >= nc || nb >= nd || !(na <= px[idx] && px[idx] < nc && nb <= py[idx] && py[idx] < nd)) continue;\n \n a[idx] = na; b[idx] = nb; c[idx] = nc; d[idx] = nd;\n \n // Expand undersized neighbors\n for (int it = 0; it < 30; it++) {\n bool ch = false;\n for (int i = 0; i < n; i++) {\n if (area(i) >= rr[i]) continue;\n for (int d = 0; d < 4; d++) if (canExpand(i, d)) { doExpand(i, d); ch = true; }\n }\n if (!ch) break;\n }\n \n double newScore = totalScore();\n if (newScore > oldScore || prob(rng) < exp((newScore - oldScore) / T)) {\n if (newScore > bestScore) {\n bestScore = newScore;\n for (int i = 0; i < n; i++) { ba[i] = a[i]; bb[i] = b[i]; bc[i] = c[i]; bd[i] = d[i]; }\n }\n } else {\n for (int i = 0; i < n; i++) { a[i] = sa[i]; b[i] = sb[i]; c[i] = sc[i]; d[i] = sd[i]; }\n }\n }\n \n for (int i = 0; i < n; i++) { a[i] = ba[i]; b[i] = bb[i]; c[i] = bc[i]; d[i] = bd[i]; }\n \n for (int i = 0; i < n; i++) {\n cout << a[i] << \" \" << b[i] << \" \" << c[i] << \" \" << d[i] << \"\\n\";\n }\n return 0;\n}","ahc002":"#include \nusing namespace std;\n\nconst int N = 50;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nconst char dc[] = {'U', 'D', 'L', 'R'};\n\nint t[N][N], p[N][N];\nint si, sj;\nmt19937 rng;\n\ninline int countMoves(int x, int y, const bitset<2500>& used, int curTile) {\n int cnt = 0;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < N && ny >= 0 && ny < N && !used[t[nx][ny]] && t[nx][ny] != curTile) cnt++;\n }\n return cnt;\n}\n\ninline int countMoves2(int x, int y, const bitset<2500>& used, int curTile) {\n int cnt = 0;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx < 0 || nx >= N || ny < 0 || ny >= N) continue;\n int tile = t[nx][ny];\n if (used[tile] || tile == curTile) continue;\n cnt++;\n for (int d2 = 0; d2 < 4; d2++) {\n int nnx = nx + dx[d2], nny = ny + dy[d2];\n if (nnx >= 0 && nnx < N && nny >= 0 && nny < N && \n !used[t[nnx][nny]] && t[nnx][nny] != tile && t[nnx][nny] != curTile) cnt++;\n }\n }\n return cnt;\n}\n\nstruct State {\n int x, y, score, priority;\n bitset<2500> usedTiles;\n string path;\n bool operator<(const State& o) const { return priority < o.priority; }\n};\n\nvoid chokudaiSearch(int beamWidth, int moveWeight, int timeLimit,\n string& bestPath, int& bestScore, chrono::steady_clock::time_point startTime,\n bool use2Step = false) {\n const int MAX_DEPTH = 2600;\n vector> queues(MAX_DEPTH);\n \n State init;\n init.x = si; init.y = sj;\n init.score = p[si][sj];\n init.usedTiles.set(t[si][sj]);\n init.path = \"\";\n int fm = use2Step ? countMoves2(si, sj, init.usedTiles, -1) : countMoves(si, sj, init.usedTiles, -1);\n init.priority = init.score + fm * moveWeight;\n queues[0].push(init);\n \n while (chrono::duration_cast(chrono::steady_clock::now() - startTime).count() < timeLimit) {\n for (int depth = 0; depth < MAX_DEPTH - 1; depth++) {\n if (queues[depth].empty()) continue;\n \n for (int w = 0; w < beamWidth && !queues[depth].empty(); w++) {\n State state = queues[depth].top();\n queues[depth].pop();\n \n bool canExtend = false;\n for (int d = 0; d < 4; d++) {\n int nx = state.x + dx[d];\n int ny = state.y + dy[d];\n if (nx < 0 || nx >= N || ny < 0 || ny >= N) continue;\n if (state.usedTiles[t[nx][ny]]) continue;\n \n canExtend = true;\n State newState;\n newState.x = nx; newState.y = ny;\n newState.score = state.score + p[nx][ny];\n newState.usedTiles = state.usedTiles;\n newState.usedTiles.set(t[nx][ny]);\n newState.path = state.path + dc[d];\n \n fm = use2Step ? countMoves2(nx, ny, newState.usedTiles, -1) : countMoves(nx, ny, newState.usedTiles, -1);\n newState.priority = newState.score + fm * moveWeight;\n queues[depth + 1].push(newState);\n }\n \n if (!canExtend && state.score > bestScore) {\n bestScore = state.score;\n bestPath = state.path;\n }\n }\n \n while ((int)queues[depth + 1].size() > beamWidth * 2) {\n queues[depth + 1].pop();\n }\n }\n }\n \n for (int d = 0; d < MAX_DEPTH; d++) {\n while (!queues[d].empty()) {\n if (queues[d].top().score > bestScore) {\n bestScore = queues[d].top().score;\n bestPath = queues[d].top().path;\n }\n queues[d].pop();\n }\n }\n}\n\nvoid randomGreedy(string& bestPath, int& bestScore, int moveWeight, int randPercent) {\n int x = si, y = sj;\n int score = p[si][sj];\n string path = \"\";\n bitset<2500> usedTiles;\n usedTiles.set(t[si][sj]);\n \n while (true) {\n vector> moves;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx < 0 || nx >= N || ny < 0 || ny >= N) continue;\n if (usedTiles[t[nx][ny]]) continue;\n int fm = countMoves(nx, ny, usedTiles, t[nx][ny]);\n moves.push_back({p[nx][ny] + fm * moveWeight, d});\n }\n if (moves.empty()) break;\n sort(moves.begin(), moves.end(), greater>());\n \n int choice = 0;\n if (moves.size() > 1 && (int)(rng() % 100) < randPercent) {\n choice = rng() % min((int)moves.size(), 3);\n }\n \n int d = moves[choice].second;\n x += dx[d]; y += dy[d];\n score += p[x][y];\n usedTiles.set(t[x][y]);\n path += dc[d];\n }\n if (score > bestScore) {\n bestScore = score;\n bestPath = path;\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n auto startTime = chrono::steady_clock::now();\n rng.seed(chrono::steady_clock::now().time_since_epoch().count());\n \n cin >> si >> sj;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> t[i][j];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) cin >> p[i][j];\n \n string bestPath = \"\";\n int bestScore = p[si][sj];\n \n // 7 Chokudai configs - added 2-step pure score\n chokudaiSearch(100, 0, 270, bestPath, bestScore, startTime); // Pure score\n chokudaiSearch(100, 50, 540, bestPath, bestScore, startTime); // Light move\n chokudaiSearch(100, 100, 810, bestPath, bestScore, startTime); // Moderate\n chokudaiSearch(80, 0, 1020, bestPath, bestScore, startTime, true); // 2-step pure score (NEW)\n chokudaiSearch(80, 80, 1230, bestPath, bestScore, startTime, true);// 2-step moderate\n chokudaiSearch(100, 150, 1440, bestPath, bestScore, startTime); // Move heavy\n chokudaiSearch(80, 120, 1650, bestPath, bestScore, startTime, true);// 2-step heavy\n \n // Random greedy with remaining time\n while (chrono::duration_cast(chrono::steady_clock::now() - startTime).count() < 1950) {\n int moveW = 15 + rng() % 35;\n int randP = 25 + rng() % 25;\n randomGreedy(bestPath, bestScore, moveW, randP);\n }\n \n cout << bestPath << endl;\n return 0;\n}","ahc003":"#include \nusing namespace std;\n\nconst int N = 30;\ndouble h[N][N-1], v[N-1][N];\nint h_cnt[N][N-1], v_cnt[N-1][N];\ndouble g_sum = 0;\nint g_cnt = 0;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n fill(&h[0][0], &h[0][0] + N*(N-1), 5000.0);\n fill(&v[0][0], &v[0][0] + (N-1)*N, 5000.0);\n fill(&h_cnt[0][0], &h_cnt[0][0] + N*(N-1), 0);\n fill(&v_cnt[0][0], &v_cnt[0][0] + (N-1)*N, 0);\n \n auto getH = [&](int i, int j) -> double {\n if (h_cnt[i][j] > 0) return h[i][j];\n double sum = 0, wgt = 0;\n for (int k = 0; k < N-1; k++) {\n if (h_cnt[i][k] > 0) {\n double w = 1.0 / (1.0 + abs(j - k));\n sum += h[i][k] * w;\n wgt += w;\n }\n }\n if (wgt > 0) return sum / wgt;\n if (g_cnt > 0) return g_sum / g_cnt;\n return 5000.0;\n };\n \n auto getV = [&](int i, int j) -> double {\n if (v_cnt[i][j] > 0) return v[i][j];\n double sum = 0, wgt = 0;\n for (int k = 0; k < N-1; k++) {\n if (v_cnt[k][j] > 0) {\n double w = 1.0 / (1.0 + abs(i - k));\n sum += v[k][j] * w;\n wgt += w;\n }\n }\n if (wgt > 0) return sum / wgt;\n if (g_cnt > 0) return g_sum / g_cnt;\n return 5000.0;\n };\n \n for (int q = 0; q < 1000; q++) {\n int si, sj, ti, tj;\n cin >> si >> sj >> ti >> tj;\n \n auto idx = [](int i, int j) { return i * N + j; };\n vector dist(N*N, 1e18);\n vector prv(N*N, -1);\n \n priority_queue, vector>, greater<>> pq;\n dist[idx(si, sj)] = 0;\n pq.push({0, idx(si, sj)});\n \n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > dist[u]) continue;\n int i = u / N, j = u % N;\n \n auto relax = [&](int ni, int nj, double w) {\n int nu = idx(ni, nj);\n if (dist[u] + w < dist[nu]) {\n dist[nu] = dist[u] + w;\n prv[nu] = u;\n pq.push({dist[nu], nu});\n }\n };\n \n if (i > 0) relax(i-1, j, getV(i-1, j));\n if (i < N-1) relax(i+1, j, getV(i, j));\n if (j > 0) relax(i, j-1, getH(i, j-1));\n if (j < N-1) relax(i, j+1, getH(i, j));\n }\n \n string path = \"\";\n vector> edges;\n \n int cur = idx(ti, tj);\n while (prv[cur] != -1) {\n int ci = cur / N, cj = cur % N;\n int pi = prv[cur] / N, pj = prv[cur] % N;\n \n if (ci < pi) { path += 'U'; edges.emplace_back(1, ci, cj); }\n else if (ci > pi) { path += 'D'; edges.emplace_back(1, pi, pj); }\n else if (cj < pj) { path += 'L'; edges.emplace_back(0, ci, cj); }\n else { path += 'R'; edges.emplace_back(0, pi, pj); }\n \n cur = prv[cur];\n }\n \n reverse(path.begin(), path.end());\n cout << path << \"\\n\" << flush;\n \n int feedback;\n cin >> feedback;\n \n double est = 0;\n for (auto& [t, ei, ej] : edges) {\n est += (t == 0) ? getH(ei, ej) : getV(ei, ej);\n }\n \n double ratio = feedback / est;\n \n for (auto& [t, ei, ej] : edges) {\n double implied = (t == 0) ? getH(ei, ej) * ratio : getV(ei, ej) * ratio;\n \n if (t == 0) {\n int cnt = ++h_cnt[ei][ej];\n double alpha = 3.0 / (3.0 + cnt);\n h[ei][ej] = h[ei][ej] * (1 - alpha) + implied * alpha;\n } else {\n int cnt = ++v_cnt[ei][ej];\n double alpha = 3.0 / (3.0 + cnt);\n v[ei][ej] = v[ei][ej] * (1 - alpha) + implied * alpha;\n }\n }\n \n g_sum = 0; g_cnt = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N-1; j++) {\n if (h_cnt[i][j] > 0) { g_sum += h[i][j]; g_cnt++; }\n }\n }\n for (int i = 0; i < N-1; i++) {\n for (int j = 0; j < N; j++) {\n if (v_cnt[i][j] > 0) { g_sum += v[i][j]; g_cnt++; }\n }\n }\n }\n \n return 0;\n}","ahc004":"#include \nusing namespace std;\n\nconst int N = 20;\nint m;\nvector strs;\n\nbool matchAt(const char grid[N][N], int idx, int r, int c, int d) {\n const string& s = strs[idx];\n for(int p = 0; p < (int)s.size(); p++) {\n int ni = d ? (r+p)%N : r, nj = d ? c : (c+p)%N;\n if(grid[ni][nj] != s[p]) return false;\n }\n return true;\n}\n\ntuple findMatch(const char grid[N][N], int idx) {\n for(int r = 0; r < N; r++)\n for(int c = 0; c < N; c++) {\n if(matchAt(grid, idx, r, c, 0)) return {r, c, 0};\n if(matchAt(grid, idx, r, c, 1)) return {r, c, 1};\n }\n return {-1, -1, -1};\n}\n\nbool posContains(int r, int c, int d, int len, int i, int j) {\n for(int p = 0; p < len; p++) {\n int ni = d ? (r+p)%N : r, nj = d ? c : (c+p)%N;\n if(ni == i && nj == j) return true;\n }\n return false;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n; cin >> n >> m;\n strs.resize(m);\n for(int i = 0; i < m; i++) cin >> strs[i];\n \n mt19937 rng(12345);\n char bestGrid[N][N];\n int bestScore = 0;\n auto start = chrono::high_resolution_clock::now();\n \n for(int trial = 0; ; trial++) {\n if(chrono::duration(chrono::high_resolution_clock::now() - start).count() > 2.0) break;\n \n char grid[N][N]; fill(&grid[0][0], &grid[N][0], '.');\n vector order(m); iota(order.begin(), order.end(), 0);\n if(trial % 3 == 0) sort(order.begin(), order.end(), [&](int a, int b) { return strs[a].size() > strs[b].size(); });\n else { shuffle(order.begin(), order.end(), rng); if(trial % 3 == 1) stable_sort(order.begin(), order.end(), [&](int a, int b) { return strs[a].size() > strs[b].size(); }); }\n \n for(int idx : order) {\n const string& s = strs[idx];\n vector> cands; int bestOv = -1;\n for(int r = 0; r < N; r++) for(int c = 0; c < N; c++) for(int d = 0; d < 2; d++) {\n bool can = true; int ov = 0;\n for(int p = 0; p < (int)s.size(); p++) {\n int ni = d?(r+p)%N:r, nj = d?c:(c+p)%N;\n if(grid[ni][nj] != '.' && grid[ni][nj] != s[p]) { can = false; break; }\n if(grid[ni][nj] != '.') ov++;\n }\n if(can && ov >= bestOv) { if(ov > bestOv) { bestOv = ov; cands.clear(); } cands.push_back({r,c,d}); }\n }\n if(!cands.empty()) { auto [r,c,d] = cands[rng()%cands.size()]; for(int p = 0; p < (int)s.size(); p++) { int ni = d?(r+p)%N:r, nj = d?c:(c+p)%N; grid[ni][nj] = s[p]; } }\n }\n for(int i = 0; i < N; i++) for(int j = 0; j < N; j++) if(grid[i][j] == '.') grid[i][j] = 'A' + rng()%8;\n int score = 0; for(int i = 0; i < m; i++) if(get<0>(findMatch(grid, i)) >= 0) score++;\n if(score > bestScore) { bestScore = score; memcpy(bestGrid, grid, sizeof(grid)); }\n }\n \n char grid[N][N]; memcpy(grid, bestGrid, sizeof(grid));\n vector> matchPos(m);\n for(int i = 0; i < m; i++) matchPos[i] = findMatch(grid, i);\n int curScore = bestScore;\n \n while(true) {\n double elapsed = chrono::duration(chrono::high_resolution_clock::now() - start).count();\n if(elapsed > 2.95) break;\n double T = 1.5 * max(0.01, 1.0 - elapsed / 3.0);\n \n int ci = rng()%N, cj = rng()%N;\n char old = grid[ci][cj];\n \n int bestDelta = -1000; char bestChar = old;\n vector>> bestChanges;\n \n for(char nc = 'A'; nc <= 'H'; nc++) {\n if(nc == old) continue;\n grid[ci][cj] = nc;\n int delta = 0;\n vector>> changes;\n \n for(int idx = 0; idx < m; idx++) {\n auto [r,c,d] = matchPos[idx];\n int len = strs[idx].size();\n if(r >= 0 && posContains(r, c, d, len, ci, cj)) {\n if(!matchAt(grid, idx, r, c, d)) {\n auto nm = findMatch(grid, idx);\n changes.push_back({idx, nm});\n if(get<0>(nm) < 0) delta--;\n }\n } else if(r < 0) {\n for(int p = 0; p < len; p++) { int sc = (cj-p+N)%N; if(matchAt(grid,idx,ci,sc,0)) { delta++; changes.push_back({idx,{ci,sc,0}}); goto nx; } }\n for(int p = 0; p < len; p++) { int sr = (ci-p+N)%N; if(matchAt(grid,idx,sr,cj,1)) { delta++; changes.push_back({idx,{sr,cj,1}}); goto nx; } }\n nx:;\n }\n }\n if(delta > bestDelta) { bestDelta = delta; bestChar = nc; bestChanges = changes; }\n }\n grid[ci][cj] = old;\n \n if(bestDelta >= 0 || (rng()&0xFFFF) < 65536.0 * exp(bestDelta / T)) {\n grid[ci][cj] = bestChar;\n curScore += bestDelta;\n for(auto& [idx, pos] : bestChanges) matchPos[idx] = pos;\n if(curScore > bestScore) { bestScore = curScore; memcpy(bestGrid, grid, sizeof(grid)); }\n }\n }\n \n for(int i = 0; i < N; i++) cout << string(bestGrid[i], bestGrid[i]+N) << '\\n';\n}","ahc005":"#include \n#include \nusing namespace std;\nusing namespace chrono;\n\nint N, si, sj;\nvector grid;\n\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nconst char dir_char[] = {'U', 'D', 'L', 'R'};\n\ninline bool is_road(int i, int j) {\n return i >= 0 && i < N && j >= 0 && j < N && grid[i][j] != '#';\n}\n\npair>, vector>>> dijkstra(int si, int sj) {\n vector> dist(N, vector(N, INT_MAX));\n vector>> parent(N, vector>(N, {-1,-1}));\n priority_queue, vector>, greater<>> pq;\n dist[si][sj] = 0; pq.push({0, si, sj});\n while (!pq.empty()) {\n auto [d, i, j] = pq.top(); pq.pop();\n if (d > dist[i][j]) continue;\n for (int k = 0; k < 4; k++) {\n int ni = i + dx[k], nj = j + dy[k];\n if (is_road(ni, nj)) {\n int c = grid[ni][nj] - '0';\n if (dist[i][j] + c < dist[ni][nj]) {\n dist[ni][nj] = dist[i][j] + c;\n parent[ni][nj] = {i, j};\n pq.push({dist[ni][nj], ni, nj});\n }\n }\n }\n }\n return {dist, parent};\n}\n\nstring get_path(int i1, int j1, int i2, int j2, vector>>& parent) {\n if (i1 == i2 && j1 == j2) return \"\";\n string path;\n int ci = i2, cj = j2;\n while (ci != i1 || cj != j1) {\n auto [pi, pj] = parent[ci][cj];\n for (int k = 0; k < 4; k++) if (pi + dx[k] == ci && pj + dy[k] == cj) { path += dir_char[k]; break; }\n ci = pi; cj = pj;\n }\n reverse(path.begin(), path.end());\n return path;\n}\n\nint calc_path_time(const string& path) {\n int time = 0, ci = si, cj = sj;\n for (char c : path) {\n if (c == 'U') ci--; else if (c == 'D') ci++; else if (c == 'L') cj--; else cj++;\n time += grid[ci][cj] - '0';\n }\n return time;\n}\n\nstring solve(double alpha, int check_limit) {\n vector> visible(N, vector(N, false));\n vector> mark_iter(N, vector(N, 0));\n int current_iter = 0;\n int visible_count = 0, total_roads = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (is_road(i, j)) total_roads++;\n \n auto mark_visible = [&](int i, int j) {\n if (!visible[i][j]) { visible[i][j] = true; visible_count++; }\n for (int jj = j - 1; jj >= 0 && is_road(i, jj); jj--) if (!visible[i][jj]) { visible[i][jj] = true; visible_count++; }\n for (int jj = j + 1; jj < N && is_road(i, jj); jj++) if (!visible[i][jj]) { visible[i][jj] = true; visible_count++; }\n for (int ii = i - 1; ii >= 0 && is_road(ii, j); ii--) if (!visible[ii][j]) { visible[ii][j] = true; visible_count++; }\n for (int ii = i + 1; ii < N && is_road(ii, j); ii++) if (!visible[ii][j]) { visible[ii][j] = true; visible_count++; }\n };\n \n auto count_new_visible = [&](int i, int j) {\n int cnt = !visible[i][j];\n for (int jj = j - 1; jj >= 0 && is_road(i, jj); jj--) cnt += !visible[i][jj];\n for (int jj = j + 1; jj < N && is_road(i, jj); jj++) cnt += !visible[i][jj];\n for (int ii = i - 1; ii >= 0 && is_road(ii, j); ii--) cnt += !visible[ii][j];\n for (int ii = i + 1; ii < N && is_road(ii, j); ii++) cnt += !visible[ii][j];\n return cnt;\n };\n \n auto calc_path_visibility = [&](int si, int sj, const string& path) {\n current_iter++;\n int cnt = 0, ci = si, cj = sj;\n auto add_vis = [&](int i, int j) {\n if (!visible[i][j] && mark_iter[i][j] != current_iter) {\n mark_iter[i][j] = current_iter;\n cnt++;\n }\n };\n for (char c : path) {\n if (c == 'U') ci--; else if (c == 'D') ci++; else if (c == 'L') cj--; else cj++;\n add_vis(ci, cj);\n for (int jj = cj - 1; jj >= 0 && is_road(ci, jj); jj--) add_vis(ci, jj);\n for (int jj = cj + 1; jj < N && is_road(ci, jj); jj++) add_vis(ci, jj);\n for (int ii = ci - 1; ii >= 0 && is_road(ii, cj); ii--) add_vis(ii, cj);\n for (int ii = ci + 1; ii < N && is_road(ii, cj); ii++) add_vis(ii, cj);\n }\n return cnt;\n };\n \n auto [dist_from_start, parent_from_start] = dijkstra(si, sj);\n int cur_i = si, cur_j = sj;\n string result;\n mark_visible(cur_i, cur_j);\n \n while (visible_count < total_roads) {\n auto [dist, parent] = dijkstra(cur_i, cur_j);\n vector> candidates;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) {\n if (dist[i][j] == INT_MAX || dist[i][j] == 0) continue;\n int nv = count_new_visible(i, j);\n if (nv == 0) continue;\n double cost = dist[i][j] + alpha * dist_from_start[i][j];\n candidates.push_back({-(double)nv / cost, i, j});\n }\n if (candidates.empty()) break;\n sort(candidates.begin(), candidates.end());\n \n int best_i = -1, best_j = -1; double best_score = -1e18; string best_path;\n int check_count = min((int)candidates.size(), check_limit);\n for (int c = 0; c < check_count; c++) {\n auto [_, i, j] = candidates[c];\n string path = get_path(cur_i, cur_j, i, j, parent);\n double nv = (check_limit > 1) ? calc_path_visibility(cur_i, cur_j, path) : count_new_visible(i, j);\n if (nv == 0) continue;\n double cost = dist[i][j] + alpha * dist_from_start[i][j];\n double score = nv / cost;\n if (score > best_score) { best_score = score; best_i = i; best_j = j; best_path = path; }\n }\n if (best_i == -1) break;\n result += best_path;\n int ti = cur_i, tj = cur_j;\n for (char c : best_path) {\n if (c == 'U') ti--; else if (c == 'D') ti++; else if (c == 'L') tj--; else tj++;\n mark_visible(ti, tj);\n }\n cur_i = best_i; cur_j = best_j;\n }\n if (cur_i != si || cur_j != sj) {\n auto [dist, parent] = dijkstra(cur_i, cur_j);\n result += get_path(cur_i, cur_j, si, sj, parent);\n }\n return result;\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n auto start = steady_clock::now();\n cin >> N >> si >> sj;\n grid.resize(N);\n for (int i = 0; i < N; i++) cin >> grid[i];\n \n string best_result; int best_time = INT_MAX;\n vector alphas;\n for (int i = 0; i <= 50; i++) alphas.push_back(i * 0.01);\n vector check_limits = {1, 3, 6, 10, 15, 21, 28, 36, 45};\n \n for (double alpha : alphas) {\n if (duration(steady_clock::now() - start).count() > 2.7) break;\n for (int cl : check_limits) {\n string result = solve(alpha, cl);\n int time = calc_path_time(result);\n if (time < best_time) { best_time = time; best_result = result; }\n }\n }\n cout << best_result << endl;\n}","future-contest-2022-qual":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, K, R;\n cin >> N >> M >> K >> R;\n \n vector> d(N, vector(K));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < K; j++)\n cin >> d[i][j];\n \n vector> deps(N), rdeps(N);\n for (int i = 0; i < R; i++) {\n int u, v;\n cin >> u >> v;\n u--; v--;\n deps[v].push_back(u);\n rdeps[u].push_back(v);\n }\n \n vector taskStatus(N, -1);\n vector memberTask(M, -1), memberStartDay(M, 0);\n \n double initSkill = 40.0 / sqrt(K);\n vector> skillEst(M, vector(K, initSkill));\n vector> skillLo(M, vector(K, 0.0));\n \n auto estimateTime = [&](int task, int member) -> double {\n double w = 0;\n for (int k = 0; k < K; k++)\n w += max(0.0, (double)d[task][k] - skillEst[member][k]);\n return max(1.0, w);\n };\n \n auto avgTime = [&](int task) -> double {\n double sum = 0;\n for (int j = 0; j < M; j++) sum += estimateTime(task, j);\n return sum / M;\n };\n \n vector downstream(N, 0);\n for (int i = N - 1; i >= 0; i--) {\n downstream[i] = (int)rdeps[i].size();\n for (int v : rdeps[i]) downstream[i] += downstream[v];\n }\n \n vector wdepth(N);\n auto recalcDepth = [&]() {\n for (int i = N - 1; i >= 0; i--) {\n if (taskStatus[i] == 1) { wdepth[i] = 0; continue; }\n wdepth[i] = avgTime(i);\n double maxChild = 0;\n for (int v : rdeps[i]) maxChild = max(maxChild, wdepth[v]);\n wdepth[i] += maxChild;\n }\n };\n recalcDepth();\n \n for (int day = 1; ; day++) {\n if (day % 25 == 1) recalcDepth();\n \n vector availTasks;\n for (int i = 0; i < N; i++) {\n if (taskStatus[i] != -1) continue;\n bool ok = true;\n for (int dep : deps[i])\n if (taskStatus[dep] != 1) { ok = false; break; }\n if (ok) availTasks.push_back(i);\n }\n \n vector freeMembers;\n for (int j = 0; j < M; j++)\n if (memberTask[j] == -1) freeMembers.push_back(j);\n \n vector> candidates;\n for (int task : availTasks) {\n for (int member : freeMembers) {\n double t = estimateTime(task, member);\n double score = wdepth[task] / max(1.0, t) + 0.001 * downstream[task];\n candidates.push_back({-score, task, member});\n }\n }\n sort(candidates.begin(), candidates.end());\n \n vector> assignments;\n vector usedMember(M, false), usedTask(N, false);\n \n for (auto& [score, task, member] : candidates) {\n if (usedMember[member] || usedTask[task]) continue;\n usedMember[member] = true;\n usedTask[task] = true;\n assignments.push_back({member + 1, task + 1});\n taskStatus[task] = 0;\n memberTask[member] = task;\n memberStartDay[member] = day;\n }\n \n cout << assignments.size();\n for (auto& [a, b] : assignments) cout << \" \" << a << \" \" << b;\n cout << \"\\n\";\n cout.flush();\n \n int n; cin >> n;\n if (n == -1) break;\n \n for (int i = 0; i < n; i++) {\n int f; cin >> f; f--;\n int task = memberTask[f];\n int timeTaken = day - memberStartDay[f] + 1;\n taskStatus[task] = 1;\n memberTask[f] = -1;\n \n if (timeTaken == 1) {\n for (int k = 0; k < K; k++) {\n skillLo[f][k] = max(skillLo[f][k], (double)d[task][k]);\n skillEst[f][k] = max(skillEst[f][k], (double)d[task][k]);\n }\n } else {\n double wEst = (double)timeTaken;\n double currW = 0;\n for (int k = 0; k < K; k++)\n currW += max(0.0, (double)d[task][k] - skillEst[f][k]);\n \n if (currW > 0.5) {\n double factor = wEst / currW;\n factor = 0.65 * factor + 0.35;\n factor = max(0.5, min(1.6, factor));\n \n for (int k = 0; k < K; k++) {\n double gap = d[task][k] - skillEst[f][k];\n if (gap > 0) {\n double newSkill = d[task][k] - gap * factor;\n skillEst[f][k] = max(skillLo[f][k], newSkill);\n }\n }\n } else if (wEst > 4) {\n double totalReq = 0;\n for (int k = 0; k < K; k++) totalReq += d[task][k];\n if (totalReq > 0.5) {\n for (int k = 0; k < K; k++) {\n double reduction = (wEst - 2) * d[task][k] / totalReq;\n skillEst[f][k] = max(skillLo[f][k], skillEst[f][k] - reduction);\n }\n }\n }\n }\n }\n }\n return 0;\n}","ahc006":"#include \nusing namespace std;\n\nconst int N = 1000, M = 50, CX = 400, CY = 400;\nint ordA[N], ordB[N], ordC[N], ordD[N];\nmt19937 rng(chrono::steady_clock::now().time_since_epoch().count());\n\ninline int dist(int x1, int y1, int x2, int y2) {\n return abs(x1 - x2) + abs(y1 - y2);\n}\n\nint buildRoute(const vector& sel, vector>& ev) {\n ev.clear();\n ev.reserve(2 * M);\n bool picked[N] = {}, done[N] = {};\n int cx = CX, cy = CY, cost = 0;\n \n for (int i = 0; i < 2*M; i++) {\n int best = -1, bd = 1e9;\n bool isDel = false;\n for (int j : sel) {\n if (!picked[j]) {\n int d = dist(cx, cy, ordA[j], ordB[j]);\n if (d < bd) { bd = d; best = j; isDel = false; }\n } else if (!done[j]) {\n int d = dist(cx, cy, ordC[j], ordD[j]);\n if (d < bd) { bd = d; best = j; isDel = true; }\n }\n }\n cost += bd;\n if (isDel) { cx = ordC[best]; cy = ordD[best]; done[best] = true; }\n else { cx = ordA[best]; cy = ordB[best]; picked[best] = true; }\n ev.push_back({best, isDel});\n }\n return cost + dist(cx, cy, CX, CY);\n}\n\nint calcCost(const vector>& ev) {\n int cx = CX, cy = CY, cost = 0;\n for (auto& [idx, isDel] : ev) {\n int nx = isDel ? ordC[idx] : ordA[idx];\n int ny = isDel ? ordD[idx] : ordB[idx];\n cost += dist(cx, cy, nx, ny);\n cx = nx; cy = ny;\n }\n return cost + dist(cx, cy, CX, CY);\n}\n\nbool validSwap(vector>& ev, int i, int j) {\n swap(ev[i], ev[j]);\n int pickPos[N];\n memset(pickPos, -1, sizeof(pickPos));\n for (int k = 0; k < (int)ev.size(); k++) {\n if (!ev[k].second) pickPos[ev[k].first] = k;\n else if (pickPos[ev[k].first] < 0 || pickPos[ev[k].first] > k) {\n swap(ev[i], ev[j]);\n return false;\n }\n }\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n auto st = chrono::steady_clock::now();\n for (int i = 0; i < N; i++) cin >> ordA[i] >> ordB[i] >> ordC[i] >> ordD[i];\n \n auto elapsed = [&]() {\n return chrono::duration(chrono::steady_clock::now() - st).count();\n };\n \n vector> byDist(N);\n for (int i = 0; i < N; i++) {\n byDist[i] = {dist(CX, CY, ordA[i], ordB[i]) + dist(CX, CY, ordC[i], ordD[i]), i};\n }\n sort(byDist.begin(), byDist.end());\n \n vector sel(M), unsel(N-M);\n for (int i = 0; i < M; i++) sel[i] = byDist[i].second;\n for (int i = 0; i < N-M; i++) unsel[i] = byDist[M+i].second;\n \n vector> ev, bestEv;\n int cost = buildRoute(sel, ev);\n int bestCost = cost;\n vector bestSel = sel;\n bestEv = ev;\n \n double temp = 3000.0;\n \n while (elapsed() < 1.8) {\n int si = rng() % M;\n int ui = rng() % (N-M);\n swap(sel[si], unsel[ui]);\n \n int nc = buildRoute(sel, ev);\n int delta = nc - cost;\n \n if (delta < 0 || (rng() % 10000) < 10000 * exp(-delta / temp)) {\n cost = nc;\n if (nc < bestCost) {\n bestCost = nc;\n bestSel = sel;\n bestEv = ev;\n }\n } else {\n swap(sel[si], unsel[ui]);\n }\n temp *= 0.99995;\n }\n \n // 2-opt: complete full passes\n bool improved = true;\n while (improved && elapsed() < 1.95) {\n improved = false;\n for (int i = 0; i < 2*M - 1; i++) {\n for (int j = i + 1; j < 2*M; j++) {\n if (elapsed() > 1.95) break;\n if (bestEv[i].first == bestEv[j].first) continue;\n if (validSwap(bestEv, i, j)) {\n int nc = calcCost(bestEv);\n if (nc < bestCost) {\n bestCost = nc;\n improved = true;\n } else {\n swap(bestEv[i], bestEv[j]);\n }\n }\n }\n }\n }\n \n cout << M;\n for (int x : bestSel) cout << \" \" << (x+1);\n cout << \"\\n\" << (2*M+2) << \" \" << CX << \" \" << CY;\n for (auto& [idx, isDel] : bestEv) {\n if (isDel) cout << \" \" << ordC[idx] << \" \" << ordD[idx];\n else cout << \" \" << ordA[idx] << \" \" << ordB[idx];\n }\n cout << \" \" << CX << \" \" << CY << \"\\n\";\n \n return 0;\n}","ahc007":"#include \nusing namespace std;\n\nclass UnionFind {\n vector parent, rank_;\npublic:\n UnionFind(int n) : parent(n), rank_(n, 0) {\n iota(parent.begin(), parent.end(), 0);\n }\n int find(int x) {\n if (parent[x] != x) parent[x] = find(parent[x]);\n return parent[x];\n }\n bool unite(int x, int y) {\n int px = find(x), py = find(y);\n if (px == py) return false;\n if (rank_[px] < rank_[py]) swap(px, py);\n parent[py] = px;\n if (rank_[px] == rank_[py]) rank_[px]++;\n return true;\n }\n};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n const int N = 400, M = 1995;\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) {\n cin >> x[i] >> y[i];\n }\n \n vector u(M), v(M), d(M);\n for (int i = 0; i < M; i++) {\n cin >> u[i] >> v[i];\n double dx = x[u[i]] - x[v[i]];\n double dy = y[u[i]] - y[v[i]];\n d[i] = (int)round(sqrt(dx * dx + dy * dy));\n }\n \n UnionFind uf(N);\n int components = N;\n \n for (int i = 0; i < M; i++) {\n int l;\n cin >> l;\n \n int pu = uf.find(u[i]);\n int pv = uf.find(v[i]);\n \n bool already_connected = (pu == pv);\n double ratio = (double)l / d[i];\n \n bool adopt = false;\n \n if (!already_connected) {\n // Always accept truly excellent deals (ratio close to minimum possible)\n if (ratio <= 1.4) {\n adopt = true;\n }\n else {\n int useful_remaining = 0;\n int same_pair_remaining = 0;\n \n for (int j = i + 1; j < M; j++) {\n int uj = uf.find(u[j]);\n int vj = uf.find(v[j]);\n if (uj != vj) {\n useful_remaining++;\n if ((uj == pu && vj == pv) || (uj == pv && vj == pu)) {\n same_pair_remaining++;\n }\n }\n }\n \n int needed = components - 1;\n \n if (same_pair_remaining == 0) {\n adopt = true;\n }\n else if (useful_remaining < needed * 2) {\n adopt = true;\n }\n else {\n double k = same_pair_remaining;\n double expected_min = 1.0 + 2.0 / (k + 2.0);\n double threshold = expected_min + 0.28;\n \n if (ratio <= threshold) {\n adopt = true;\n }\n }\n }\n }\n \n if (adopt) {\n uf.unite(u[i], v[i]);\n components--;\n }\n \n cout << (adopt ? 1 : 0) << \"\\n\" << flush;\n }\n \n return 0;\n}","ahc008":"#include \nusing namespace std;\n\nint N, M;\nvector> pets;\nvector> humans;\nbool blocked[32][32];\n\nint dx[] = {-1, 1, 0, 0}, dy[] = {0, 0, -1, 1};\nchar wc[] = {'u', 'd', 'l', 'r'}, mc[] = {'U', 'D', 'L', 'R'};\n\nbool pet_at(int x, int y) {\n for (auto& p : pets) if (p[0] == x && p[1] == y) return true;\n return false;\n}\n\nbool pet_adjacent(int x, int y) {\n for (int d = 0; d < 4; d++) if (pet_at(x+dx[d], y+dy[d])) return true;\n return pet_at(x, y);\n}\n\nbool can_place(int x, int y) {\n if (x < 1 || x > 30 || y < 1 || y > 30 || blocked[x][y]) return false;\n for (auto& h : humans) if (h[0] == x && h[1] == y) return false;\n return !pet_adjacent(x, y);\n}\n\nbool passable(int x, int y) {\n return x >= 1 && x <= 30 && y >= 1 && y <= 30 && !blocked[x][y];\n}\n\nint count_adjacent_blocked(int x, int y) {\n int cnt = 0;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx < 1 || nx > 30 || ny < 1 || ny > 30 || blocked[nx][ny]) cnt++;\n }\n return cnt;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N; pets.resize(N);\n for (int i = 0; i < N; i++) cin >> pets[i][0] >> pets[i][1] >> pets[i][2];\n cin >> M; humans.resize(M);\n for (int i = 0; i < M; i++) cin >> humans[i][0] >> humans[i][1];\n \n set> target;\n for (int i = 1; i <= 30; i++) {\n for (int c : {6, 12, 18, 24}) {\n target.insert({i, c});\n target.insert({c, i});\n }\n }\n \n for (int turn = 0; turn < 300; turn++) {\n string action(M, '.');\n set> will_block;\n \n for (int i = 0; i < M; i++) {\n int hx = humans[i][0], hy = humans[i][1];\n \n // Try to build a target wall, prefer ones that extend existing walls\n int bestd = -1, best_adj = -1;\n for (int d = 0; d < 4; d++) {\n int nx = hx + dx[d], ny = hy + dy[d];\n if (target.count({nx, ny}) && can_place(nx, ny) && !will_block.count({nx, ny})) {\n int adj = count_adjacent_blocked(nx, ny);\n if (adj > best_adj) {\n best_adj = adj;\n bestd = d;\n }\n }\n }\n \n if (bestd >= 0) {\n action[i] = wc[bestd];\n will_block.insert({hx + dx[bestd], hy + dy[bestd]});\n } else {\n // Check if we're adjacent to an unbuilt target\n bool near_unbuilt_target = false;\n for (int d = 0; d < 4; d++) {\n int nx = hx + dx[d], ny = hy + dy[d];\n if (nx >= 1 && nx <= 30 && ny >= 1 && ny <= 30 &&\n target.count({nx, ny}) && !blocked[nx][ny]) {\n near_unbuilt_target = true;\n break;\n }\n }\n \n if (near_unbuilt_target) {\n action[i] = '.';\n } else {\n // Move toward closest unbuilt target\n int minD = INT_MAX;\n int moveD = -1;\n \n for (auto& [tx, ty] : target) {\n if (blocked[tx][ty]) continue;\n int dist = abs(hx-tx) + abs(hy-ty);\n if (dist > 0 && dist < minD) {\n minD = dist;\n }\n }\n \n for (int d = 0; d < 4; d++) {\n int nx = hx + dx[d], ny = hy + dy[d];\n if (!passable(nx, ny) || pet_at(nx, ny) || will_block.count({nx, ny})) continue;\n \n for (auto& [tx, ty] : target) {\n if (blocked[tx][ty]) continue;\n int newDist = abs(nx-tx) + abs(ny-ty);\n if (newDist < minD) {\n minD = newDist;\n moveD = d;\n }\n }\n }\n if (moveD >= 0) action[i] = mc[moveD];\n }\n }\n }\n \n cout << action << \"\\n\" << flush;\n \n for (int i = 0; i < M; i++) {\n char a = action[i];\n for (int d = 0; d < 4; d++) {\n if (a == wc[d]) blocked[humans[i][0]+dx[d]][humans[i][1]+dy[d]] = true;\n if (a == mc[d]) { humans[i][0] += dx[d]; humans[i][1] += dy[d]; }\n }\n }\n \n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (char c : s) {\n if (c == 'U') pets[i][0]--;\n else if (c == 'D') pets[i][0]++;\n else if (c == 'L') pets[i][1]--;\n else if (c == 'R') pets[i][1]++;\n }\n }\n }\n return 0;\n}","ahc009":"#include \nusing namespace std;\n\nint N = 20;\nint si, sj, ti, tj;\ndouble p;\nbool hwall[20][19];\nbool vwall[19][20];\n\nbool canMove(int i, int j, char dir) {\n if (dir == 'U') return i > 0 && !vwall[i-1][j];\n if (dir == 'D') return i < 19 && !vwall[i][j];\n if (dir == 'L') return j > 0 && !hwall[i][j-1];\n if (dir == 'R') return j < 19 && !hwall[i][j];\n return false;\n}\n\npair doMove(int i, int j, char dir) {\n if (!canMove(i, j, dir)) return {i, j};\n if (dir == 'U') return {i-1, j};\n if (dir == 'D') return {i+1, j};\n if (dir == 'L') return {i, j-1};\n if (dir == 'R') return {i, j+1};\n return {i, j};\n}\n\ndouble prob[20][20], newProb[20][20];\n\ndouble evaluate(const string& s) {\n if (s.empty() || s.size() > 200) return -1;\n memset(prob, 0, sizeof(prob));\n prob[si][sj] = 1.0;\n double expectedScore = 0;\n for (int t = 1; t <= (int)s.size(); t++) {\n char dir = s[t-1];\n memset(newProb, 0, sizeof(newProb));\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (prob[i][j] < 1e-15) continue;\n auto [ni, nj] = doMove(i, j, dir);\n if (ni == ti && nj == tj) {\n expectedScore += (1-p) * prob[i][j] * (401 - t);\n } else {\n newProb[ni][nj] += (1-p) * prob[i][j];\n }\n newProb[i][j] += p * prob[i][j];\n }\n }\n memcpy(prob, newProb, sizeof(prob));\n }\n return expectedScore;\n}\n\nstring bfsWithOrder(vector& order) {\n vector> dist(N, vector(N, -1));\n vector>> parent(N, vector>(N, {-1,-1}));\n vector> fromDir(N, vector(N, ' '));\n queue> q;\n q.push({si, sj});\n dist[si][sj] = 0;\n while (!q.empty()) {\n auto [i, j] = q.front(); q.pop();\n for (char d : order) {\n auto [ni, nj] = doMove(i, j, d);\n if (ni == i && nj == j) continue;\n if (dist[ni][nj] == -1) {\n dist[ni][nj] = dist[i][j] + 1;\n parent[ni][nj] = {i, j};\n fromDir[ni][nj] = d;\n q.push({ni, nj});\n }\n }\n }\n string path;\n int ci = ti, cj = tj;\n while (ci != si || cj != sj) {\n path += fromDir[ci][cj];\n auto [pi, pj] = parent[ci][cj];\n ci = pi; cj = pj;\n }\n reverse(path.begin(), path.end());\n return path;\n}\n\nmt19937 rng(42);\nstring best;\ndouble bestScore = -1;\nconst char dirs[] = {'U', 'D', 'L', 'R'};\nchrono::steady_clock::time_point startTime;\n\nbool timeUp(int ms) {\n return chrono::duration_cast(chrono::steady_clock::now() - startTime).count() > ms;\n}\n\nvoid updateBest(const string& s, double score) {\n if (score > bestScore) { bestScore = score; best = s; }\n}\n\nvoid localSearch(string& cur, double& curScore, int maxMs) {\n while (!timeUp(maxMs)) {\n bool improved = false;\n \n // Remove\n for (size_t i = 0; i < cur.size() && !improved; i++) {\n string trial = cur.substr(0, i) + cur.substr(i + 1);\n if (!trial.empty()) {\n double score = evaluate(trial);\n if (score > curScore) { cur = trial; curScore = score; updateBest(cur, curScore); improved = true; }\n }\n }\n // Change\n for (size_t i = 0; i < cur.size() && !improved; i++) {\n for (char d : dirs) {\n if (d == cur[i]) continue;\n string trial = cur; trial[i] = d;\n double score = evaluate(trial);\n if (score > curScore) { cur = trial; curScore = score; updateBest(cur, curScore); improved = true; break; }\n }\n }\n // Insert\n if (cur.size() < 200 && !improved) {\n for (size_t i = 0; i <= cur.size() && !improved; i++) {\n for (char d : dirs) {\n string trial = cur.substr(0, i) + d + cur.substr(i);\n double score = evaluate(trial);\n if (score > curScore) { cur = trial; curScore = score; updateBest(cur, curScore); improved = true; break; }\n }\n }\n }\n // Duplicate\n if (cur.size() < 200 && !improved) {\n for (size_t i = 0; i < cur.size() && !improved; i++) {\n string trial = cur.substr(0, i+1) + cur[i] + cur.substr(i+1);\n double score = evaluate(trial);\n if (score > curScore) { cur = trial; curScore = score; updateBest(cur, curScore); improved = true; }\n }\n }\n // Remove segment\n for (int len = 2; len <= 4 && !improved; len++) {\n for (size_t i = 0; i + len <= cur.size() && !improved; i++) {\n string trial = cur.substr(0, i) + cur.substr(i + len);\n if (!trial.empty()) {\n double score = evaluate(trial);\n if (score > curScore) { cur = trial; curScore = score; updateBest(cur, curScore); improved = true; }\n }\n }\n }\n // Duplicate segment\n if (cur.size() < 196 && !improved) {\n for (int len = 2; len <= 4 && !improved; len++) {\n for (size_t i = 0; i + len <= cur.size() && !improved; i++) {\n string trial = cur.substr(0, i + len) + cur.substr(i, len) + cur.substr(i + len);\n if (trial.size() <= 200) {\n double score = evaluate(trial);\n if (score > curScore) { cur = trial; curScore = score; updateBest(cur, curScore); improved = true; }\n }\n }\n }\n }\n \n if (!improved) break;\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n startTime = chrono::steady_clock::now();\n \n cin >> si >> sj >> ti >> tj >> p;\n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < 19; j++) hwall[i][j] = (s[j] == '1');\n }\n for (int i = 0; i < 19; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) vwall[i][j] = (s[j] == '1');\n }\n \n vector order = {'U', 'D', 'L', 'R'};\n set pathSet;\n for (int iter = 0; iter < 50; iter++) {\n shuffle(order.begin(), order.end(), rng);\n pathSet.insert(bfsWithOrder(order));\n }\n vector paths(pathSet.begin(), pathSet.end());\n sort(paths.begin(), paths.end(), [](const string& a, const string& b) { return a.size() < b.size(); });\n \n vector> candidates;\n \n for (const string& path : paths) {\n if (timeUp(250)) break;\n int L = path.size();\n \n for (int rep = 1; rep * L <= 200; rep++) {\n string r; for (char c : path) for (int i = 0; i < rep; i++) r += c;\n double sc = evaluate(r);\n candidates.emplace_back(sc, r);\n updateBest(r, sc);\n }\n for (int rep = 1; rep * L <= 200; rep++) {\n string r; for (int i = 0; i < rep; i++) r += path;\n double sc = evaluate(r);\n candidates.emplace_back(sc, r);\n updateBest(r, sc);\n }\n for (int bonus = 2; bonus <= 8; bonus += 2) {\n for (int base = 1; base * L <= 200; base++) {\n string r; int ci = si, cj = sj;\n for (char c : path) {\n auto [ni, nj] = doMove(ci, cj, c);\n int reps = !canMove(ni, nj, c) ? base + bonus : base;\n for (int i = 0; i < reps && r.size() < 200; i++) r += c;\n ci = ni; cj = nj;\n }\n double sc = evaluate(r);\n candidates.emplace_back(sc, r);\n updateBest(r, sc);\n }\n }\n for (int pr = 1; pr <= 8; pr++) {\n for (int mr = 1; mr * L * pr <= 200 && mr <= 8; mr++) {\n string r;\n for (int i = 0; i < pr; i++) for (char c : path) for (int j = 0; j < mr; j++) r += c;\n double sc = evaluate(r);\n candidates.emplace_back(sc, r);\n updateBest(r, sc);\n }\n }\n }\n \n sort(candidates.rbegin(), candidates.rend());\n \n // Local search on diverse top candidates\n set tried;\n for (int i = 0; i < min(10, (int)candidates.size()) && !timeUp(1200); i++) {\n int len = candidates[i].second.size();\n if (i >= 3 && tried.count(len)) continue;\n tried.insert(len);\n \n string cur = candidates[i].second;\n double curScore = candidates[i].first;\n localSearch(cur, curScore, 1200);\n }\n \n // Random restarts\n while (!timeUp(1890)) {\n string cur = best;\n double curScore = bestScore;\n \n int ops = 1 + rng() % 2;\n for (int i = 0; i < ops; i++) {\n if (cur.empty()) break;\n int t = rng() % 4;\n size_t pos = rng() % cur.size();\n if (t == 0 && cur.size() > 1) cur.erase(pos, 1);\n else if (t == 1 && cur.size() < 200) cur.insert(pos, 1, dirs[rng() % 4]);\n else if (t == 2 && !cur.empty()) cur[pos] = dirs[rng() % 4];\n else if (t == 3 && cur.size() < 200 && !cur.empty()) cur.insert(pos, 1, cur[pos]);\n }\n \n if (!cur.empty() && cur.size() <= 200) {\n curScore = evaluate(cur);\n if (curScore > bestScore * 0.97) {\n localSearch(cur, curScore, 1890);\n }\n }\n }\n \n cout << best << endl;\n return 0;\n}","ahc010":"#include \nusing namespace std;\n\nconst int N = 30;\nint tiles[N][N];\nint rotation[N][N];\n\nconst int di[] = {0, -1, 0, 1};\nconst int dj[] = {-1, 0, 1, 0};\n\nconst int to_arr[8][4] = {\n {1, 0, -1, -1}, {3, -1, -1, 0}, {-1, -1, 3, 2}, {-1, 2, 1, -1},\n {1, 0, 3, 2}, {3, 2, 1, 0}, {2, -1, 0, -1}, {-1, 3, -1, 1},\n};\n\nint state_cache[N][N];\nint visited_gen[N][N][4];\nint current_gen;\n\ninline void updateState(int i, int j) {\n int t = tiles[i][j], r = rotation[i][j];\n if (t < 4) state_cache[i][j] = (t + r) & 3;\n else if (t < 6) state_cache[i][j] = 4 + ((t + r) & 1);\n else state_cache[i][j] = 6 + ((t + r) & 1);\n}\n\ninline int traceLoop(int si, int sj, int sd) {\n int i = si, j = sj, d = sd, length = 0;\n do {\n int d2 = to_arr[state_cache[i][j]][d];\n if (d2 < 0) return 0;\n if (++length > 3600) return 0;\n i += di[d2]; j += dj[d2];\n if ((unsigned)i >= N || (unsigned)j >= N) return 0;\n d = d2 ^ 2;\n } while (i != si || j != sj || d != sd);\n return length;\n}\n\ninline pair computeTopTwoLoops() {\n ++current_gen;\n int top1 = 0, top2 = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n int st = state_cache[i][j];\n for (int d = 0; d < 4; d++) {\n if (to_arr[st][d] < 0 || visited_gen[i][j][d] == current_gen) continue;\n int len = traceLoop(i, j, d);\n if (len > 0) {\n if (len > top1) { top2 = top1; top1 = len; }\n else if (len > top2) { top2 = len; }\n int ci = i, cj = j, cd = d;\n do {\n visited_gen[ci][cj][cd] = current_gen;\n int d2 = to_arr[state_cache[ci][cj]][cd];\n ci += di[d2]; cj += dj[d2];\n cd = d2 ^ 2;\n } while (ci != i || cj != j || cd != d);\n }\n }\n }\n }\n return {top1, top2};\n}\n\nint best_rotation[N][N];\nlong long best_score;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n memset(visited_gen, 0, sizeof(visited_gen));\n current_gen = 0;\n \n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) {\n tiles[i][j] = s[j] - '0';\n rotation[i][j] = 0;\n updateState(i, j);\n }\n }\n \n mt19937 rng(42);\n auto start_time = chrono::steady_clock::now();\n \n auto [l1, l2] = computeTopTwoLoops();\n best_score = (long long)l1 * l2;\n memcpy(best_rotation, rotation, sizeof(rotation));\n long long current_score = best_score;\n \n const double TIME_LIMIT = 1.95;\n int iter = 0;\n \n while (true) {\n if ((++iter & 0xFF) == 0) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start_time).count();\n if (elapsed > TIME_LIMIT) break;\n }\n \n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start_time).count();\n double T = 1000.0 * pow(0.0001, elapsed / TIME_LIMIT);\n \n int i = rng() % N, j = rng() % N;\n int old_rot = rotation[i][j];\n int new_rot = (old_rot + 1 + (rng() % 3)) & 3;\n \n rotation[i][j] = new_rot;\n updateState(i, j);\n \n auto [nl1, nl2] = computeTopTwoLoops();\n long long new_score = (long long)nl1 * nl2;\n \n if (new_score >= current_score || \n (rng() & 0xFFFFFF) < (unsigned)(exp((double)(new_score - current_score) / T) * 0x1000000)) {\n current_score = new_score;\n if (new_score > best_score) {\n best_score = new_score;\n memcpy(best_rotation, rotation, sizeof(rotation));\n }\n } else {\n rotation[i][j] = old_rot;\n updateState(i, j);\n }\n }\n \n string result;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n result += ('0' + best_rotation[i][j]);\n cout << result << endl;\n \n return 0;\n}","ahc011":"#include \nusing namespace std;\n\nint N, T;\nint dr[] = {-1, 1, 0, 0};\nint dc[] = {0, 0, -1, 1};\nchar dc_char[] = {'U', 'D', 'L', 'R'};\nint rev[] = {1, 0, 3, 2};\n\nint hexChar(char c) {\n return (c >= '0' && c <= '9') ? c - '0' : c - 'a' + 10;\n}\n\nint calcScore(const vector>& board) {\n vector> adj(N * N);\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (board[i][j] == 0) continue;\n if (i + 1 < N && board[i+1][j] != 0 && (board[i][j] & 8) && (board[i+1][j] & 2)) {\n adj[i*N+j].push_back((i+1)*N+j);\n adj[(i+1)*N+j].push_back(i*N+j);\n }\n if (j + 1 < N && board[i][j+1] != 0 && (board[i][j] & 4) && (board[i][j+1] & 1)) {\n adj[i*N+j].push_back(i*N+j+1);\n adj[i*N+j+1].push_back(i*N+j);\n }\n }\n }\n vector vis(N * N, false);\n int maxTree = 0;\n for (int s = 0; s < N * N; s++) {\n if (vis[s] || board[s/N][s%N] == 0) continue;\n int cnt = 0, edges = 0;\n queue q; q.push(s); vis[s] = true;\n while (!q.empty()) {\n int u = q.front(); q.pop(); cnt++;\n edges += adj[u].size();\n for (int v : adj[u]) if (!vis[v]) { vis[v] = true; q.push(v); }\n }\n if (edges / 2 == cnt - 1) maxTree = max(maxTree, cnt);\n }\n return maxTree;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> T;\n vector> board(N, vector(N));\n int er, ec;\n for (int i = 0; i < N; i++) {\n string s; cin >> s;\n for (int j = 0; j < N; j++) {\n board[i][j] = hexChar(s[j]);\n if (board[i][j] == 0) { er = i; ec = j; }\n }\n }\n \n string best, cur;\n int bestScore = calcScore(board), curScore = bestScore;\n auto bestBoard = board;\n int bestEr = er, bestEc = ec;\n int lastD = -1;\n int step = 0;\n int stepsWithoutImprove = 0;\n \n mt19937 rng(42);\n auto start = chrono::steady_clock::now();\n \n while (chrono::duration_cast(chrono::steady_clock::now() - start).count() < 2850) {\n if (cur.size() >= (size_t)T || bestScore >= N * N - 1) break;\n step++;\n stepsWithoutImprove++;\n \n vector valid;\n for (int dd = 0; dd < 4; dd++) {\n int nr = er + dr[dd], nc = ec + dc[dd];\n if (nr >= 0 && nr < N && nc >= 0 && nc < N) valid.push_back(dd);\n }\n \n if (lastD >= 0 && valid.size() > 1 && rng() % 100 < 76) {\n valid.erase(remove(valid.begin(), valid.end(), rev[lastD]), valid.end());\n }\n \n int d;\n bool isGreedy = (step % 7 == 0 && valid.size() > 1);\n \n if (isGreedy) {\n int bestD = valid[0], bestS = -1;\n for (int dd : valid) {\n int nr = er + dr[dd], nc = ec + dc[dd];\n swap(board[er][ec], board[nr][nc]);\n int s = calcScore(board);\n swap(board[er][ec], board[nr][nc]);\n if (s > bestS) { bestS = s; bestD = dd; }\n }\n d = bestD;\n } else {\n d = valid[rng() % valid.size()];\n }\n \n int nr = er + dr[d], nc = ec + dc[d];\n swap(board[er][ec], board[nr][nc]);\n cur += dc_char[d];\n int newScore = calcScore(board);\n \n double temp = 1.0 - (double)cur.size() / T;\n bool accept = isGreedy || newScore > curScore || (rng() % 1000 < (int)(118 * temp));\n \n if (accept) {\n er = nr; ec = nc;\n curScore = newScore;\n lastD = d;\n if (curScore > bestScore || (curScore == bestScore && cur.size() < best.size())) {\n bestScore = curScore;\n best = cur;\n bestBoard = board;\n bestEr = er;\n bestEc = ec;\n stepsWithoutImprove = 0;\n }\n } else {\n cur.pop_back();\n swap(board[er][ec], board[nr][nc]);\n }\n \n bool shouldRestart = (cur.size() > best.size() + 130 && rng() % 100 < 5) ||\n (stepsWithoutImprove > 350 && rng() % 100 < 12) ||\n (stepsWithoutImprove > 600 && rng() % 100 < 18);\n \n if (shouldRestart) {\n bool needPerturb = (stepsWithoutImprove > 500);\n \n board = bestBoard;\n er = bestEr;\n ec = bestEc;\n cur = best;\n curScore = bestScore;\n lastD = -1;\n \n // Add perturbation to escape local optimum\n if (needPerturb && cur.size() + 20 < (size_t)T) {\n int perturbMoves = 8 + rng() % 12;\n for (int i = 0; i < perturbMoves; i++) {\n vector pV;\n for (int dd = 0; dd < 4; dd++) {\n int nnr = er + dr[dd], nnc = ec + dc[dd];\n if (nnr >= 0 && nnr < N && nnc >= 0 && nnc < N) pV.push_back(dd);\n }\n int pd = pV[rng() % pV.size()];\n int pnr = er + dr[pd], pnc = ec + dc[pd];\n swap(board[er][ec], board[pnr][pnc]);\n cur += dc_char[pd];\n er = pnr; ec = pnc;\n }\n curScore = calcScore(board);\n }\n \n stepsWithoutImprove = 0;\n }\n }\n \n cout << best << endl;\n return 0;\n}","ahc012":"#include \nusing namespace std;\n\ntypedef long long ll;\n\nint N, K;\nvector a(10);\nvector> berries;\nvector> cuts;\nvector> sides;\n\ninline int side(ll x1, ll y1, ll x2, ll y2, ll px, ll py) {\n __int128 cross = (__int128)(x2 - x1) * (py - y1) - (__int128)(y2 - y1) * (px - x1);\n if (cross > 0) return 1;\n if (cross < 0) return -1;\n return 0;\n}\n\nint calcScore() {\n int numCuts = cuts.size();\n unordered_map pieceCount;\n pieceCount.reserve(N);\n \n for (int j = 0; j < N; j++) {\n bool onLine = false;\n uint64_t h = 0;\n for (int i = 0; i < numCuts; i++) {\n if (sides[i][j] == 0) { onLine = true; break; }\n h = h * 3ULL + (uint64_t)(sides[i][j] + 1);\n }\n if (!onLine) pieceCount[h]++;\n }\n \n vector b(11, 0);\n for (auto& [sig, cnt] : pieceCount) {\n if (cnt >= 1 && cnt <= 10) b[cnt]++;\n }\n \n int total = 0;\n for (int d = 1; d <= 10; d++) total += min(a[d-1], b[d]);\n return total;\n}\n\nvoid updateSides(int idx) {\n while ((int)sides.size() <= idx) sides.push_back(vector(N));\n for (int j = 0; j < N; j++) {\n sides[idx][j] = side(cuts[idx][0], cuts[idx][1], cuts[idx][2], cuts[idx][3],\n berries[j].first, berries[j].second);\n }\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> K;\n for (int i = 0; i < 10; i++) cin >> a[i];\n \n berries.resize(N);\n for (int i = 0; i < N; i++) cin >> berries[i].first >> berries[i].second;\n \n mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());\n \n auto randLine = [&]() -> array {\n ll px = (ll)(rng() % 20001) - 10000;\n ll py = (ll)(rng() % 20001) - 10000;\n ll qx = (ll)(rng() % 20001) - 10000;\n ll qy = (ll)(rng() % 20001) - 10000;\n while (px == qx && py == qy) { qx = (ll)(rng() % 20001) - 10000; qy = (ll)(rng() % 20001) - 10000; }\n return {px, py, qx, qy};\n };\n \n auto perpBisector = [&](int i, int j) -> array {\n if (i == j) return randLine();\n ll dx = berries[j].first - berries[i].first;\n ll dy = berries[j].second - berries[i].second;\n ll mx = berries[i].first + berries[j].first;\n ll my = berries[i].second + berries[j].second;\n return {mx - dy * 1000, my + dx * 1000, mx + dy * 1000, my - dx * 1000};\n };\n \n auto radialLine = [&](double angle) -> array {\n ll px = (ll)(cos(angle) * 15000);\n ll py = (ll)(sin(angle) * 15000);\n if (px == 0 && py == 0) px = 1;\n return {px, py, -px, -py};\n };\n \n auto genLine = [&]() -> array {\n int strat = rng() % 5;\n if (strat == 0) return randLine();\n else if (strat <= 2) return perpBisector(rng() % N, rng() % N);\n else if (strat == 3) return radialLine((double)(rng() % 10000) / 10000.0 * M_PI * 2);\n else {\n int b1 = rng() % N, b2 = rng() % N;\n if (b1 != b2) return {berries[b1].first, berries[b1].second, berries[b2].first, berries[b2].second};\n return randLine();\n }\n };\n \n int bestScore = 0;\n vector> bestCuts;\n \n auto start = chrono::steady_clock::now();\n \n for (int restart = 0; ; restart++) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration_cast(now - start).count();\n if (elapsed > 2850) break;\n \n cuts.clear();\n sides.clear();\n int numCuts = 25 + rng() % 35;\n \n for (int i = 0; i < numCuts; i++) {\n cuts.push_back(genLine());\n updateSides(i);\n }\n \n int curScore = calcScore();\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n \n for (int iter = 0; ; iter++) {\n now = chrono::steady_clock::now();\n elapsed = chrono::duration_cast(now - start).count();\n if (elapsed > 2850) break;\n \n double progress = elapsed / 2850.0;\n double temp = 3.0 * (1.0 - progress) + 0.1;\n int moveType = rng() % 100;\n \n if (moveType < 75 && !cuts.empty()) {\n int idx = rng() % cuts.size();\n auto oldCut = cuts[idx];\n auto oldSide = sides[idx];\n \n cuts[idx] = genLine();\n updateSides(idx);\n \n int newScore = calcScore();\n if (newScore > curScore || (double)(rng() % 1000000) / 1000000.0 < exp((newScore - curScore) / temp)) {\n curScore = newScore;\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n } else {\n cuts[idx] = oldCut;\n sides[idx] = oldSide;\n }\n } else if (moveType < 90 && cuts.size() < (size_t)min(K, 80)) {\n cuts.push_back(genLine());\n updateSides(cuts.size() - 1);\n \n int newScore = calcScore();\n if (newScore >= curScore) {\n curScore = newScore;\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n } else {\n cuts.pop_back();\n sides.pop_back();\n }\n } else if (cuts.size() > 10) {\n int idx = rng() % cuts.size();\n auto oldCut = cuts[idx];\n auto oldSide = sides[idx];\n cuts.erase(cuts.begin() + idx);\n sides.erase(sides.begin() + idx);\n \n int newScore = calcScore();\n if (newScore >= curScore) {\n curScore = newScore;\n if (curScore > bestScore) { bestScore = curScore; bestCuts = cuts; }\n } else {\n cuts.insert(cuts.begin() + idx, oldCut);\n sides.insert(sides.begin() + idx, oldSide);\n }\n }\n }\n }\n \n cout << bestCuts.size() << \"\\n\";\n for (auto& c : bestCuts) cout << c[0] << \" \" << c[1] << \" \" << c[2] << \" \" << c[3] << \"\\n\";\n \n return 0;\n}","ahc014":"#include \nusing namespace std;\n\nint N, M, c;\nset> dots;\nset> usedSegs;\nvector> ops;\n\nbool inGrid(int x, int y) { return x >= 0 && x < N && y >= 0 && y < N; }\nlong long wt(int x, int y) { return (long long)(x-c)*(x-c) + (long long)(y-c)*(y-c) + 1; }\n\nvoid addSeg(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g == 0) return;\n dx /= g; dy /= g;\n for (int i = 0; i < g; i++) {\n int a = x1+i*dx, b = y1+i*dy, e = a+dx, f = b+dy;\n if (a > e || (a == e && b > f)) { swap(a,e); swap(b,f); }\n usedSegs.insert({a,b,e,f});\n }\n}\n\nbool segUsed(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g == 0) return true;\n dx /= g; dy /= g;\n for (int i = 0; i < g; i++) {\n int a = x1+i*dx, b = y1+i*dy, e = a+dx, f = b+dy;\n if (a > e || (a == e && b > f)) { swap(a,e); swap(b,f); }\n if (usedSegs.count({a,b,e,f})) return true;\n }\n return false;\n}\n\nbool dotOnSeg(int x1, int y1, int x2, int y2) {\n int dx = x2-x1, dy = y2-y1, g = __gcd(abs(dx), abs(dy));\n if (g <= 1) return false;\n dx /= g; dy /= g;\n for (int i = 1; i < g; i++)\n if (dots.count({x1+i*dx, y1+i*dy})) return true;\n return false;\n}\n\nbool isValidRect(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4) {\n int v1x = x2-x1, v1y = y2-y1;\n int v2x = x3-x2, v2y = y3-y2;\n if (v1x == 0 && v1y == 0) return false;\n if (v2x == 0 && v2y == 0) return false;\n if (v1x*v2x + v1y*v2y != 0) return false;\n bool axis1 = (v1x == 0 || v1y == 0);\n bool diag1 = (abs(v1x) == abs(v1y));\n if (!axis1 && !diag1) return false;\n bool axis2 = (v2x == 0 || v2y == 0);\n bool diag2 = (abs(v2x) == abs(v2y));\n if (!axis2 && !diag2) return false;\n if (x4 != x1 + v2x || y4 != y1 + v2y) return false;\n return true;\n}\n\nbool tryAdd(int x1, int y1, int x2, int y2, int x3, int y3, int x4, int y4) {\n if (!inGrid(x1,y1) || dots.count({x1,y1})) return false;\n if (!dots.count({x2,y2}) || !dots.count({x3,y3}) || !dots.count({x4,y4})) return false;\n set> pts = {{x1,y1},{x2,y2},{x3,y3},{x4,y4}};\n if (pts.size() != 4) return false;\n if (!isValidRect(x1,y1,x2,y2,x3,y3,x4,y4)) return false;\n if (dotOnSeg(x1,y1,x2,y2) || dotOnSeg(x2,y2,x3,y3) || \n dotOnSeg(x3,y3,x4,y4) || dotOnSeg(x4,y4,x1,y1)) return false;\n if (segUsed(x1,y1,x2,y2) || segUsed(x2,y2,x3,y3) || \n segUsed(x3,y3,x4,y4) || segUsed(x4,y4,x1,y1)) return false;\n \n dots.insert({x1,y1});\n addSeg(x1,y1,x2,y2); addSeg(x2,y2,x3,y3);\n addSeg(x3,y3,x4,y4); addSeg(x4,y4,x1,y1);\n ops.push_back({x1,y1,x2,y2,x3,y3,x4,y4});\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M;\n c = (N-1) / 2;\n for (int i = 0; i < M; i++) { int x, y; cin >> x >> y; dots.insert({x, y}); }\n \n auto tstart = chrono::steady_clock::now();\n mt19937 rng(42);\n \n int fails = 0;\n while (chrono::duration(chrono::steady_clock::now() - tstart).count() < 4.5) {\n vector> dl(dots.begin(), dots.end());\n shuffle(dl.begin(), dl.end(), rng);\n int sz = min((int)dl.size(), 100);\n \n vector>> candidates;\n \n for (int i = 0; i < sz; i++) {\n for (int j = 0; j < sz; j++) {\n if (i == j) continue;\n for (int k = 0; k < sz; k++) {\n if (k == i || k == j) continue;\n auto [ax, ay] = dl[i];\n auto [bx, by] = dl[j];\n auto [cx, cy] = dl[k];\n \n // Try: new point D, with corners D-A-B-C (A opposite to C, B opposite to D)\n // D = A + C - B\n int dx = ax + cx - bx, dy = ay + cy - by;\n if (inGrid(dx, dy) && !dots.count({dx, dy})) {\n long long w = wt(dx, dy);\n candidates.push_back({w, {dx, dy, ax, ay, bx, by, cx, cy}});\n }\n }\n }\n }\n \n sort(candidates.begin(), candidates.end(), greater<>());\n \n bool found = false;\n for (auto& [w, arr] : candidates) {\n if (tryAdd(arr[0],arr[1],arr[2],arr[3],arr[4],arr[5],arr[6],arr[7])) {\n found = true;\n break;\n }\n }\n \n if (!found) {\n if (++fails > 200) break;\n } else {\n fails = 0;\n }\n }\n \n cout << ops.size() << \"\\n\";\n for (auto& op : ops) {\n for (int i = 0; i < 8; i++) cout << op[i] << \" \\n\"[i==7];\n }\n return 0;\n}","ahc015":"#include \nusing namespace std;\n\nconst int N = 10;\n\nstruct State {\n int grid[N][N];\n \n State() { memset(grid, 0, sizeof(grid)); }\n \n int countEmpty() const {\n int cnt = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (grid[i][j] == 0) cnt++;\n return cnt;\n }\n \n void place(int p, int flavor) {\n int cnt = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (grid[i][j] == 0 && ++cnt == p) { grid[i][j] = flavor; return; }\n }\n \n void tilt(int dir) {\n if (dir == 0) {\n for (int j = 0; j < N; j++) {\n int w = 0;\n for (int i = 0; i < N; i++) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[w++][j] = v; }\n }\n } else if (dir == 1) {\n for (int j = 0; j < N; j++) {\n int w = N - 1;\n for (int i = N - 1; i >= 0; i--) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[w--][j] = v; }\n }\n } else if (dir == 2) {\n for (int i = 0; i < N; i++) {\n int w = 0;\n for (int j = 0; j < N; j++) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[i][w++] = v; }\n }\n } else {\n for (int i = 0; i < N; i++) {\n int w = N - 1;\n for (int j = N - 1; j >= 0; j--) if (grid[i][j]) { int v = grid[i][j]; grid[i][j] = 0; grid[i][w--] = v; }\n }\n }\n }\n \n long long calcScore() const {\n bool vis[N][N] = {};\n long long sum = 0;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (grid[i][j] && !vis[i][j]) {\n int f = grid[i][j], sz = 0;\n int stk[100], top = 0;\n stk[top++] = i * N + j;\n vis[i][j] = true;\n while (top > 0) {\n int pos = stk[--top];\n int x = pos / N, y = pos % N;\n sz++;\n if (x > 0 && !vis[x-1][y] && grid[x-1][y] == f) { vis[x-1][y] = true; stk[top++] = (x-1)*N+y; }\n if (x < N-1 && !vis[x+1][y] && grid[x+1][y] == f) { vis[x+1][y] = true; stk[top++] = (x+1)*N+y; }\n if (y > 0 && !vis[x][y-1] && grid[x][y-1] == f) { vis[x][y-1] = true; stk[top++] = x*N+y-1; }\n if (y < N-1 && !vis[x][y+1] && grid[x][y+1] == f) { vis[x][y+1] = true; stk[top++] = x*N+y+1; }\n }\n sum += (long long)sz * sz;\n }\n }\n }\n return sum;\n }\n};\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int f[101];\n for (int t = 1; t <= 100; t++) cin >> f[t];\n \n State state;\n \n for (int t = 1; t <= 100; t++) {\n int p; cin >> p;\n state.place(p, f[t]);\n \n int remaining = 100 - t;\n int depth = min(13, remaining);\n int numSims;\n if (t <= 20) numSims = 42;\n else if (t <= 50) numSims = 38;\n else if (t <= 75) numSims = 32;\n else numSims = 24;\n \n int bestDir = 0;\n long long bestScore = -1;\n \n for (int dir = 0; dir < 4; dir++) {\n mt19937 rng(12345 + t);\n long long totalScore = 0;\n \n for (int sim = 0; sim < numSims; sim++) {\n State s = state;\n s.tilt(dir);\n \n for (int step = 1; step <= depth && t + step <= 100; step++) {\n int empty = s.countEmpty();\n if (empty == 0) break;\n int randPos = (rng() % empty) + 1;\n s.place(randPos, f[t + step]);\n \n int simBest = 0;\n long long simBestScore = -1;\n for (int d = 0; d < 4; d++) {\n State tmp = s;\n tmp.tilt(d);\n long long sc = tmp.calcScore();\n if (sc > simBestScore) { simBestScore = sc; simBest = d; }\n }\n s.tilt(simBest);\n }\n totalScore += s.calcScore();\n }\n \n if (totalScore > bestScore) {\n bestScore = totalScore;\n bestDir = dir;\n }\n }\n \n state.tilt(bestDir);\n const char dirChar[] = {'F', 'B', 'L', 'R'};\n cout << dirChar[bestDir] << '\\n' << flush;\n }\n \n return 0;\n}","ahc016":"#include \nusing namespace std;\n\nint N, M;\ndouble eps;\n\nvector get_sorted_degrees(const string& s) {\n vector deg(N, 0);\n int idx = 0;\n for (int i = 0; i < N; i++) {\n for (int j = i + 1; j < N; j++) {\n if (s[idx++] == '1') {\n deg[i]++;\n deg[j]++;\n }\n }\n }\n sort(deg.begin(), deg.end());\n return deg;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(0);\n \n cin >> M >> eps;\n \n double noise_factor = (eps < 0.001) ? 1.0 : 1.0 / max(0.2, 1.0 - 2.0 * eps);\n \n if (eps < 0.01) {\n N = (int)ceil(sqrt(2.0 * M)) + 2;\n } else if (eps < 0.05) {\n N = (int)ceil(sqrt(2.5 * M)) + 4;\n } else if (eps < 0.15) {\n N = (int)ceil(sqrt(3.0 * M * noise_factor)) + 8;\n } else if (eps < 0.25) {\n N = (int)ceil(sqrt(4.0 * M * noise_factor)) + 15;\n } else if (eps < 0.35) {\n N = (int)ceil(sqrt(5.0 * M * noise_factor)) + 25;\n } else {\n N = (int)ceil(sqrt(6.0 * M * noise_factor)) + 35;\n }\n \n N = max(N, (int)(2.0 * sqrt(M)));\n N = max(N, 8);\n N = min(N, 100);\n \n cout << N << \"\\n\";\n \n int total = N * (N - 1) / 2;\n \n vector G(M);\n vector> expected_deg(M);\n \n for (int i = 0; i < M; i++) {\n string s(total, '0');\n long long edges = (M > 1) ? ((long long)i * total / (M - 1)) : 0;\n \n int filled = 0;\n for (int a = 0; a < N && filled < edges; a++) {\n for (int b = a + 1; b < N && filled < edges; b++) {\n int pos = a * (2 * N - a - 1) / 2 + (b - a - 1);\n s[pos] = '1';\n filled++;\n }\n }\n \n G[i] = s;\n \n vector deg = get_sorted_degrees(s);\n expected_deg[i].resize(N);\n double transform = 1.0 - 2.0 * eps;\n double base = (N - 1) * eps;\n for (int j = 0; j < N; j++) {\n expected_deg[i][j] = deg[j] * transform + base;\n }\n \n cout << s << \"\\n\";\n }\n cout.flush();\n \n // Best weight formula with slight quadratic enhancement for high eps\n double base_weight = 0.4 + min(0.4, eps);\n double quad_factor = (eps > 0.2) ? 0.1 * (eps - 0.2) : 0.0;\n \n for (int q = 0; q < 100; q++) {\n string H;\n cin >> H;\n \n vector deg_h = get_sorted_degrees(H);\n \n int best = 0;\n double best_score = 1e18;\n \n for (int i = 0; i < M; i++) {\n double score = 0;\n for (int j = 0; j < N; j++) {\n double diff = deg_h[j] - expected_deg[i][j];\n double pos = (N > 1) ? (double)j / (N - 1) : 0.5;\n double dist_from_mid = abs(pos - 0.5) * 2.0;\n // Linear + small quadratic component for high eps\n double weight = 1.0 + base_weight * dist_from_mid + quad_factor * dist_from_mid * dist_from_mid;\n score += weight * diff * diff;\n }\n \n if (score < best_score) {\n best_score = score;\n best = i;\n }\n }\n \n cout << best << \"\\n\";\n cout.flush();\n }\n \n return 0;\n}","ahc017":"#include \nusing namespace std;\n\nint N, M, D, K;\nvector> edges;\nvector>> adj;\nvector> adjEdge;\nmt19937 rng(42);\nconst long long INF = 1e9;\n\nvector dijkstraMask(int src, const vector& excl) {\n vector dist(N, INF);\n priority_queue, vector>, greater<>> pq;\n dist[src] = 0;\n pq.push({0, src});\n while (!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if (d > dist[u]) continue;\n for (size_t i = 0; i < adj[u].size(); i++) {\n if (excl[adjEdge[u][i]]) continue;\n auto [v, w] = adj[u][i];\n if (dist[u] + w < dist[v]) {\n dist[v] = dist[u] + w;\n pq.push({dist[v], v});\n }\n }\n }\n return dist;\n}\n\nint numSamples;\nvector samples;\nvector> origDist;\nvector assign_;\nvector cnt;\nvector crit;\nvector critOrder;\n\ndouble evalDay(int d) {\n vector excl(M, false);\n for (int e = 0; e < M; e++) if (assign_[e] == d) excl[e] = true;\n double tot = 0;\n for (int i = 0; i < numSamples; i++) {\n auto dist = dijkstraMask(samples[i], excl);\n for (int v = 0; v < N; v++) if (v != samples[i])\n tot += min(dist[v], INF) - origDist[i][v];\n }\n return tot;\n}\n\nvoid initAssignment(int mode) {\n vector order(M); iota(order.begin(), order.end(), 0);\n if (mode == 0) sort(order.begin(), order.end(), [&](int a, int b) { return crit[a] > crit[b]; });\n else shuffle(order.begin(), order.end(), rng);\n \n assign_.assign(M, 0);\n cnt.assign(D + 1, 0);\n vector> dayV(D + 1);\n \n for (int e : order) {\n int u = edges[e][0], v = edges[e][1];\n int best = 1;\n for (int d = 1; d <= D; d++) {\n if (cnt[d] >= K) continue;\n int c1 = (dayV[d].count(u)?1:0) + (dayV[d].count(v)?1:0);\n int c2 = (dayV[best].count(u)?1:0) + (dayV[best].count(v)?1:0);\n if (cnt[best] >= K || c1 < c2 || (c1 == c2 && cnt[d] < cnt[best])) best = d;\n }\n assign_[e] = best; cnt[best]++;\n dayV[best].insert(u); dayV[best].insert(v);\n }\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n auto start = chrono::steady_clock::now();\n \n cin >> N >> M >> D >> K;\n edges.resize(M); adj.resize(N); adjEdge.resize(N);\n vector deg(N, 0);\n \n for (int i = 0; i < M; i++) {\n int u, v, w; cin >> u >> v >> w; u--; v--;\n edges[i] = {u, v, w};\n adj[u].push_back({v, w}); adj[v].push_back({u, w});\n adjEdge[u].push_back(i); adjEdge[v].push_back(i);\n deg[u]++; deg[v]++;\n }\n for (int i = 0; i < N; i++) { int x, y; cin >> x >> y; }\n \n vector noEdge(M, false);\n crit.resize(M);\n for (int e = 0; e < M; e++) {\n noEdge[e] = true;\n auto dist = dijkstraMask(edges[e][0], noEdge);\n crit[e] = dist[edges[e][1]] - edges[e][2];\n noEdge[e] = false;\n }\n \n critOrder.resize(M); iota(critOrder.begin(), critOrder.end(), 0);\n sort(critOrder.begin(), critOrder.end(), [&](int a, int b) { return crit[a] > crit[b]; });\n \n // Stratified sampling\n vector byDeg(N); iota(byDeg.begin(), byDeg.end(), 0);\n sort(byDeg.begin(), byDeg.end(), [&](int a, int b) { return deg[a] > deg[b]; });\n \n numSamples = min(45, N);\n samples.clear();\n for (int i = 0; i < min(numSamples/3, N); i++) samples.push_back(byDeg[i]);\n shuffle(byDeg.begin(), byDeg.end(), rng);\n for (int v : byDeg) if ((int)samples.size() < numSamples && find(samples.begin(), samples.end(), v) == samples.end())\n samples.push_back(v);\n numSamples = samples.size();\n \n origDist.resize(numSamples);\n for (int i = 0; i < numSamples; i++) origDist[i] = dijkstraMask(samples[i], noEdge);\n \n double globalBest = 1e18;\n vector globalBestAssign;\n \n vector timeLimits = {1.7, 3.5, 5.2};\n \n for (int restart = 0; restart < 3; restart++) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration(now - start).count() > 4.8) break;\n \n rng.seed(42 + restart * 1000);\n initAssignment(restart == 0 ? 0 : 1);\n \n vector dayCost(D + 1);\n double cur = 0;\n for (int d = 1; d <= D; d++) { dayCost[d] = evalDay(d); cur += dayCost[d]; }\n \n double bestScore = cur;\n vector bestAssign = assign_;\n double initTemp = max(1.0, cur / D / 2);\n double temp = initTemp;\n int noImprove = 0;\n \n while (true) {\n now = chrono::steady_clock::now();\n if (chrono::duration(now - start).count() > timeLimits[restart]) break;\n \n if (noImprove > 400) { temp = initTemp * 0.5; noImprove = 0; }\n \n int worstDay = 1, bestDay = 1;\n for (int d = 2; d <= D; d++) {\n if (dayCost[d] > dayCost[worstDay]) worstDay = d;\n if (dayCost[d] < dayCost[bestDay] && cnt[d] < K) bestDay = d;\n }\n \n int e1, d1, d2, moveType = rng() % 10;\n bool isSwap = false;\n int e2 = -1;\n \n if (moveType < 3) {\n e1 = rng() % M; e2 = rng() % M;\n if (assign_[e1] == assign_[e2]) continue;\n d1 = assign_[e1]; d2 = assign_[e2];\n swap(assign_[e1], assign_[e2]);\n isSwap = true;\n } else if (moveType < 6) {\n e1 = rng() % M; d1 = assign_[e1]; d2 = rng() % D + 1;\n if (d1 == d2 || cnt[d2] >= K) continue;\n assign_[e1] = d2; cnt[d1]--; cnt[d2]++;\n } else {\n e1 = -1;\n for (int i = 0; i < min(M/4, M) && e1 == -1; i++)\n if (assign_[critOrder[i]] == worstDay) e1 = critOrder[i];\n if (e1 == -1) for (int i = 0; i < M; i++) if (assign_[i] == worstDay) { e1 = i; break; }\n if (e1 == -1) continue;\n d1 = worstDay; d2 = (cnt[bestDay] < K) ? bestDay : (rng() % D + 1);\n if (d1 == d2 || cnt[d2] >= K) continue;\n assign_[e1] = d2; cnt[d1]--; cnt[d2]++;\n }\n \n double nc1 = evalDay(d1), nc2 = evalDay(d2);\n double delta = (nc1 + nc2) - (dayCost[d1] + dayCost[d2]);\n \n if (delta < 0 || (rng() % 1000000) < 1000000 * exp(-delta / temp)) {\n dayCost[d1] = nc1; dayCost[d2] = nc2; cur += delta;\n if (cur < bestScore) { bestScore = cur; bestAssign = assign_; noImprove = 0; }\n else noImprove++;\n } else {\n if (isSwap) swap(assign_[e1], assign_[e2]);\n else { assign_[e1] = d1; cnt[d1]++; cnt[d2]--; }\n noImprove++;\n }\n temp *= 0.99999;\n if (temp < 0.01) temp = 0.01;\n }\n \n if (bestScore < globalBest) { globalBest = bestScore; globalBestAssign = bestAssign; }\n }\n \n for (int i = 0; i < M; i++) cout << globalBestAssign[i] << \" \\n\"[i == M-1];\n return 0;\n}","ahc019":"#include \nusing namespace std;\n\nint D;\nstring f[2][15], r[2][15];\n\nvector> normalize(vector> c) {\n if (c.empty()) return c;\n sort(c.begin(), c.end());\n auto [mx,my,mz] = c[0];\n for (auto& [x,y,z] : c) { x-=mx; y-=my; z-=mz; }\n sort(c.begin(), c.end());\n return c;\n}\n\nvector> doRotate(vector> c, int r) {\n vector> res;\n for (auto [x,y,z] : c) {\n int nx,ny,nz;\n switch(r) {\n case 0: nx=x;ny=y;nz=z;break; case 1: nx=x;ny=-z;nz=y;break;\n case 2: nx=x;ny=-y;nz=-z;break; case 3: nx=x;ny=z;nz=-y;break;\n case 4: nx=-x;ny=y;nz=-z;break; case 5: nx=-x;ny=-z;nz=-y;break;\n case 6: nx=-x;ny=-y;nz=z;break; case 7: nx=-x;ny=z;nz=y;break;\n case 8: nx=y;ny=-x;nz=z;break; case 9: nx=y;ny=-z;nz=-x;break;\n case 10: nx=y;ny=x;nz=-z;break; case 11: nx=y;ny=z;nz=x;break;\n case 12: nx=-y;ny=x;nz=z;break; case 13: nx=-y;ny=-z;nz=x;break;\n case 14: nx=-y;ny=-x;nz=-z;break; case 15: nx=-y;ny=z;nz=-x;break;\n case 16: nx=z;ny=y;nz=-x;break; case 17: nx=z;ny=x;nz=y;break;\n case 18: nx=z;ny=-y;nz=x;break; case 19: nx=z;ny=-x;nz=-y;break;\n case 20: nx=-z;ny=y;nz=x;break; case 21: nx=-z;ny=-x;nz=y;break;\n case 22: nx=-z;ny=-y;nz=-x;break; default: nx=-z;ny=x;nz=-y;break;\n }\n res.push_back({nx,ny,nz});\n }\n return normalize(res);\n}\n\nvector> canonical(vector> c) {\n auto best = normalize(c);\n for (int r = 1; r < 24; r++) { auto t = doRotate(c,r); if (t < best) best = t; }\n return best;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> D;\n for (int i = 0; i < 2; i++) { for (int k = 0; k < D; k++) cin >> f[i][k]; for (int k = 0; k < D; k++) cin >> r[i][k]; }\n \n auto idx = [&](int x,int y,int z) { return x*D*D+y*D+z; };\n auto valid = [&](int a,int x,int y,int z) { return f[a][z][x]=='1' && r[a][z][y]=='1'; };\n int dx[]={1,-1,0,0,0,0}, dy[]={0,0,1,-1,0,0}, dz[]={0,0,0,0,1,-1};\n \n mt19937 rng(12345);\n double bestCost = 1e18;\n vector bestB[2];\n int bestN = 0;\n auto startTime = chrono::steady_clock::now();\n \n for (int iter = 0; ; iter++) {\n if (chrono::duration(chrono::steady_clock::now() - startTime).count() > 5.5) break;\n \n vector b[2]; for (int i=0;i<2;i++) b[i].assign(D*D*D,0);\n int n = 0; double sharedCost = 0;\n \n for (int x=0;x> q; q.push({x,y,z});\n b[0][idx(x,y,z)] = b[1][idx(x,y,z)] = n; vol++;\n while (!q.empty()) {\n auto [cx,cy,cz] = q.front(); q.pop();\n for (int d=0;d<6;d++) {\n int nx=cx+dx[d],ny=cy+dy[d],nz=cz+dz[d];\n if (nx>=0&&nx=0&&ny=0&&nz> cells[2];\n for (int arr=0;arr<2;arr++) {\n set needF,needR;\n for (int z=0;z0) c=true; if (!c) needF.insert(z*D+x); }\n for (int y=0;y0) c=true; if (!c) needR.insert(z*D+y); }\n }\n vector> cands;\n for (int x=0;x0) shuffle(cands.begin(),cands.end(),rng);\n while (!needF.empty()||!needR.empty()) {\n int bi=-1,bs=0;\n for (int i=0;i<(int)cands.size();i++) {\n auto& [x,y,z,u] = cands[i]; if (u) continue;\n int sc = (needF.count(z*D+x)?1:0) + (needR.count(z*D+y)?1:0);\n if (sc>bs) { bs=sc; bi=i; }\n }\n if (bs==0) break;\n auto& [x,y,z,u] = cands[bi]; u=1;\n cells[arr].push_back({x,y,z});\n needF.erase(z*D+x); needR.erase(z*D+y);\n }\n }\n \n vector>,vector>>> comps[2];\n set> cellSet[2];\n for (int arr=0;arr<2;arr++) for (auto c:cells[arr]) cellSet[arr].insert(c);\n for (int arr=0;arr<2;arr++) {\n set> vis;\n for (auto st:cells[arr]) if (!vis.count(st)) {\n vector> comp;\n queue> q; q.push(st); vis.insert(st);\n while (!q.empty()) {\n auto [cx,cy,cz]=q.front(); q.pop(); comp.push_back({cx,cy,cz});\n for (int d=0;d<6;d++) { tuple nb={cx+dx[d],cy+dy[d],cz+dz[d]}; if (cellSet[arr].count(nb)&&!vis.count(nb)) { vis.insert(nb); q.push(nb); } }\n }\n comps[arr].push_back({comp,canonical(comp)});\n }\n sort(comps[arr].begin(),comps[arr].end(),[](auto& a,auto& b){ return a.first.size()>b.first.size(); });\n }\n \n // Try matching from both directions\n auto tryMatch = [&](int first) -> pair>> {\n vector u0(comps[0].size()),u1(comps[1].size());\n vector> matches;\n double mc = 0;\n auto& primary = (first==0) ? comps[0] : comps[1];\n auto& secondary = (first==0) ? comps[1] : comps[0];\n auto& up = (first==0) ? u0 : u1;\n auto& us = (first==0) ? u1 : u0;\n for (int i=0;i<(int)primary.size();i++) if (!up[i])\n for (int j=0;j<(int)secondary.size();j++)\n if (!us[j]&&primary[i].second==secondary[j].second) {\n mc+=1.0/primary[i].first.size();\n up[i]=us[j]=true;\n if (first==0) matches.push_back({i,j}); else matches.push_back({j,i});\n break;\n }\n int um0=0,um1=0;\n for (int i=0;i<(int)comps[0].size();i++) if (!u0[i]) um0+=comps[0][i].first.size();\n for (int j=0;j<(int)comps[1].size();j++) if (!u1[j]) um1+=comps[1][j].first.size();\n return {mc+max(um0,um1), matches};\n };\n \n auto [cost0, matches0] = tryMatch(0);\n auto [cost1, matches1] = tryMatch(1);\n auto& matches = (cost0 <= cost1) ? matches0 : matches1;\n double matchCost = min(cost0, cost1);\n \n vector u0(comps[0].size()),u1(comps[1].size());\n for (auto [i,j] : matches) {\n n++; sharedCost+=1.0/comps[0][i].first.size();\n for (auto [x,y,z]:comps[0][i].first) b[0][idx(x,y,z)]=n;\n for (auto [x,y,z]:comps[1][j].first) b[1][idx(x,y,z)]=n;\n u0[i]=u1[j]=true;\n }\n \n vector> unmatch[2];\n for (int i=0;i<(int)comps[0].size();i++) if (!u0[i]) for (auto c:comps[0][i].first) unmatch[0].push_back(c);\n for (int j=0;j<(int)comps[1].size();j++) if (!u1[j]) for (auto c:comps[1][j].first) unmatch[1].push_back(c);\n \n int m0=unmatch[0].size(),m1=unmatch[1].size();\n double cost = sharedCost + max(m0,m1);\n \n if (cost < bestCost) {\n bestCost=cost; bestN=n+max(m0,m1); bestB[0]=b[0]; bestB[1]=b[1];\n for (int i=0;i\nusing namespace std;\n\nint N, M, K;\nvector> V, R;\nvector> E;\nvector>> adj;\nvector> distVV;\nvector> parentV;\n\ndouble getDist(int i, int k) {\n double dx = V[i].first - R[k].first, dy = V[i].second - R[k].second;\n return sqrt(dx*dx + dy*dy);\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> K;\n V.resize(N); R.resize(K); E.resize(M); adj.resize(N);\n \n for(int i = 0; i < N; i++) cin >> V[i].first >> V[i].second;\n for(int j = 0; j < M; j++) {\n int u, v; long long w;\n cin >> u >> v >> w; u--; v--;\n E[j] = {u, v, w};\n adj[u].push_back({v, j});\n adj[v].push_back({u, j});\n }\n for(int k = 0; k < K; k++) cin >> R[k].first >> R[k].second;\n \n // Precompute distances\n vector> distVR(N, vector(K));\n for(int i = 0; i < N; i++)\n for(int k = 0; k < K; k++)\n distVR[i][k] = getDist(i, k);\n \n // All-pairs shortest paths\n distVV.assign(N, vector(N, LLONG_MAX/2));\n parentV.assign(N, vector(N, -1));\n \n for(int s = 0; s < N; s++) {\n distVV[s][s] = 0;\n priority_queue, vector>, greater<>> pq;\n pq.push({0, s});\n while(!pq.empty()) {\n auto [d, u] = pq.top(); pq.pop();\n if(d > distVV[s][u]) continue;\n for(auto [v, eid] : adj[u]) {\n long long w = get<2>(E[eid]);\n if(distVV[s][u] + w < distVV[s][v]) {\n distVV[s][v] = distVV[s][u] + w;\n parentV[s][v] = u;\n pq.push({distVV[s][v], v});\n }\n }\n }\n }\n \n auto computeP = [&](const vector& asgn) {\n vector P(N, 0);\n for(int k = 0; k < K; k++) {\n int v = asgn[k];\n P[v] = max(P[v], (int)ceil(distVR[v][k] - 1e-9));\n }\n return P;\n };\n \n auto buildTree = [&](const vector& P) {\n vector B(M, 0);\n for(int i = 0; i < N; i++) if(P[i] > 0) {\n int cur = i;\n while(cur != 0 && parentV[0][cur] != -1) {\n int p = parentV[0][cur];\n for(auto& [nxt, eid] : adj[cur]) if(nxt == p) { B[eid] = 1; break; }\n cur = p;\n }\n }\n return B;\n };\n \n auto getReachable = [&](const vector& B) {\n vector reach; vector vis(N, false);\n queue q; q.push(0); vis[0] = true;\n while(!q.empty()) {\n int u = q.front(); q.pop(); reach.push_back(u);\n for(auto& [v, eid] : adj[u]) if(B[eid] && !vis[v]) { vis[v] = true; q.push(v); }\n }\n return reach;\n };\n \n auto calcCost = [&](const vector& P, const vector& B) {\n long long cost = 0;\n for(int i = 0; i < N; i++) cost += (long long)P[i] * P[i];\n for(int j = 0; j < M; j++) if(B[j]) cost += get<2>(E[j]);\n return cost;\n };\n \n vector bestP(N), bestB(M), bestAsgn(K);\n long long bestCost = LLONG_MAX;\n \n for(double factor : {0.0, 0.001, 0.005, 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1.0}) {\n vector asgn(K);\n for(int k = 0; k < K; k++) {\n int best = -1; double bestScore = 1e18;\n for(int i = 0; i < N; i++) {\n if(distVR[i][k] > 5000) continue;\n double score = distVR[i][k] * distVR[i][k] + factor * distVV[0][i];\n if(score < bestScore) { bestScore = score; best = i; }\n }\n asgn[k] = best;\n }\n \n for(int phase = 0; phase < 3; phase++) {\n auto P = computeP(asgn);\n auto B = buildTree(P);\n \n for(int iter = 0; iter < 20; iter++) {\n auto reach = getReachable(B);\n bool improved = false;\n for(int k = 0; k < K; k++) {\n double curD = distVR[asgn[k]][k];\n for(int v : reach) {\n if(distVR[v][k] < curD - 0.01 && distVR[v][k] <= 5000) {\n asgn[k] = v; curD = distVR[v][k]; improved = true;\n }\n }\n }\n if(!improved) break;\n P = computeP(asgn); B = buildTree(P);\n }\n \n // Outlier optimization\n for(int iter = 0; iter < 10; iter++) {\n auto reach = getReachable(B);\n vector> vRes(N);\n for(int k = 0; k < K; k++) vRes[asgn[k]].push_back(k);\n \n bool improved = false;\n for(int v : reach) {\n if(vRes[v].size() <= 1) continue;\n int fk = -1; double maxD = 0;\n for(int k : vRes[v]) if(distVR[v][k] > maxD) { maxD = distVR[v][k]; fk = k; }\n \n for(int nv : reach) {\n if(nv == v || distVR[nv][fk] > 5000) continue;\n double newMaxV = 0;\n for(int k : vRes[v]) if(k != fk) newMaxV = max(newMaxV, distVR[v][k]);\n double oldMaxNV = 0;\n for(int k : vRes[nv]) oldMaxNV = max(oldMaxNV, distVR[nv][k]);\n double newMaxNV = max(oldMaxNV, distVR[nv][fk]);\n double delta = (newMaxV*newMaxV - maxD*maxD) + (newMaxNV*newMaxNV - oldMaxNV*oldMaxNV);\n if(delta < -1) { asgn[fk] = nv; improved = true; break; }\n }\n }\n if(!improved) break;\n P = computeP(asgn); B = buildTree(P);\n }\n }\n \n auto P = computeP(asgn);\n auto B = buildTree(P);\n long long cost = calcCost(P, B);\n if(cost < bestCost) { bestCost = cost; bestP = P; bestB = B; bestAsgn = asgn; }\n }\n \n for(int i = 0; i < N; i++) cout << bestP[i] << \" \\n\"[i==N-1];\n for(int j = 0; j < M; j++) cout << bestB[j] << \" \\n\"[j==M-1];\n}","ahc021":"#include \nusing namespace std;\n\nconst int N = 30;\nint b[N][N];\nvector> ops;\n\nvoid do_swap(int x1, int y1, int x2, int y2) {\n ops.push_back({x1, y1, x2, y2});\n swap(b[x1][y1], b[x2][y2]);\n}\n\nvoid sift_down(int x, int y) {\n while (x < N - 1) {\n int min_child_y = (b[x + 1][y + 1] < b[x + 1][y]) ? (y + 1) : y;\n if (b[x][y] > b[x + 1][min_child_y]) {\n do_swap(x, y, x + 1, min_child_y);\n x = x + 1;\n y = min_child_y;\n } else {\n break;\n }\n }\n}\n\nbool has_violation(int x, int y) {\n if (x >= N - 1) return false;\n return b[x][y] > b[x + 1][y] || b[x][y] > b[x + 1][y + 1];\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n for (int x = 0; x < N; x++) {\n for (int y = 0; y <= x; y++) {\n cin >> b[x][y];\n }\n }\n \n // Greedy: always process the highest-valued violation\n while (true) {\n int best_val = -1, best_x = -1, best_y = -1;\n for (int x = 0; x < N - 1; x++) {\n for (int y = 0; y <= x; y++) {\n if (has_violation(x, y) && b[x][y] > best_val) {\n best_val = b[x][y];\n best_x = x;\n best_y = y;\n }\n }\n }\n if (best_val == -1) break;\n sift_down(best_x, best_y);\n }\n \n cout << ops.size() << \"\\n\";\n for (auto& [x1, y1, x2, y2] : ops) {\n cout << x1 << \" \" << y1 << \" \" << x2 << \" \" << y2 << \"\\n\";\n }\n \n return 0;\n}","toyota2023summer-final":"#include \nusing namespace std;\n\nint D, N;\nint ex, ey;\nconst int dx[] = {-1, 1, 0, 0};\nconst int dy[] = {0, 0, -1, 1};\nvector> grid;\nvector> initDepth;\n\nvoid computeInitDepth() {\n initDepth.assign(D, vector(D, -1));\n queue> q;\n q.push({ex, ey});\n initDepth[ex][ey] = 0;\n \n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && initDepth[nx][ny] == -1 && grid[nx][ny] != -2) {\n initDepth[nx][ny] = initDepth[x][y] + 1;\n q.push({nx, ny});\n }\n }\n }\n}\n\nint countReachableEmpty() {\n int count = 0;\n vector> vis(D, vector(D, false));\n queue> q;\n q.push({ex, ey});\n vis[ex][ey] = true;\n \n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n if (!(x == ex && y == ey) && grid[x][y] == -1) count++;\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && !vis[nx][ny] && grid[nx][ny] == -1) {\n vis[nx][ny] = true;\n q.push({nx, ny});\n }\n }\n }\n return count;\n}\n\nvector> findReachableEmpty() {\n vector> result;\n vector> vis(D, vector(D, false));\n queue> q;\n q.push({ex, ey});\n vis[ex][ey] = true;\n \n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n if (!(x == ex && y == ey)) result.push_back({x, y});\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && !vis[nx][ny] && grid[nx][ny] == -1) {\n vis[nx][ny] = true;\n q.push({nx, ny});\n }\n }\n }\n return result;\n}\n\nvector> findReachableContainers() {\n vector> result;\n vector> vis(D, vector(D, false));\n queue> q;\n q.push({ex, ey});\n vis[ex][ey] = true;\n \n while (!q.empty()) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < D && ny >= 0 && ny < D && !vis[nx][ny] && grid[nx][ny] != -2) {\n vis[nx][ny] = true;\n if (grid[nx][ny] >= 0) result.push_back({nx, ny});\n else q.push({nx, ny});\n }\n }\n }\n return result;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> D >> N;\n ex = 0; ey = (D - 1) / 2;\n grid.assign(D, vector(D, -1));\n \n for (int i = 0; i < N; i++) {\n int x, y; cin >> x >> y;\n grid[x][y] = -2;\n }\n \n computeInitDepth();\n int total = D * D - 1 - N;\n \n for (int iter = 0; iter < total; iter++) {\n int t; cin >> t;\n \n vector> reach = findReachableEmpty();\n int currentCount = (int)reach.size();\n \n vector>> sortedSafe;\n for (int i = 0; i < (int)reach.size(); i++) {\n auto [px, py] = reach[i];\n grid[px][py] = 999;\n int newCount = countReachableEmpty();\n grid[px][py] = -1;\n if (newCount == currentCount - 1) {\n int score = initDepth[px][py] * 1000 + i;\n sortedSafe.push_back({score, {px, py}});\n }\n }\n \n pair best;\n if (sortedSafe.empty()) {\n best = reach.back();\n } else {\n sort(sortedSafe.begin(), sortedSafe.end());\n \n int idx;\n if (sortedSafe.size() == 1 || total <= 1) {\n idx = 0;\n } else {\n // Square root mapping: gives more spread for low-numbered containers\n double normalized = (double)t / (total - 1);\n double mapped = sqrt(normalized);\n idx = (int)(mapped * (sortedSafe.size() - 1) + 0.5);\n idx = max(0, min((int)sortedSafe.size() - 1, idx));\n }\n best = sortedSafe[idx].second;\n }\n \n grid[best.first][best.second] = t;\n cout << best.first << \" \" << best.second << endl;\n }\n \n for (int iter = 0; iter < total; iter++) {\n vector> reachable = findReachableContainers();\n \n pair best = reachable[0];\n for (auto& pos : reachable) {\n if (grid[pos.first][pos.second] < grid[best.first][best.second]) {\n best = pos;\n }\n }\n \n cout << best.first << \" \" << best.second << \"\\n\";\n grid[best.first][best.second] = -1;\n }\n \n return 0;\n}","ahc024":"#include \nusing namespace std;\n\nint n, m;\nint dx[] = {0, 0, 1, -1};\nint dy[] = {1, -1, 0, 0};\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> n >> m;\n vector> orig(n, vector(n));\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) cin >> orig[i][j];\n \n set adjToZero;\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++)\n if (i == 0 || i == n-1 || j == 0 || j == n-1) adjToZero.insert(orig[i][j]);\n \n map, int> initEdge;\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) {\n int c = orig[i][j];\n if (i == 0 || i == n-1 || j == 0 || j == n-1) initEdge[{0,c}]++;\n if (j+1 < n && orig[i][j+1] != c) initEdge[{min(c,orig[i][j+1]), max(c,orig[i][j+1])}]++;\n if (i+1 < n && orig[i+1][j] != c) initEdge[{min(c,orig[i+1][j]), max(c,orig[i+1][j])}]++;\n }\n set> required;\n for (auto& [p, cnt] : initEdge) if (cnt > 0) required.insert(p);\n \n vector initCount(m+1);\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) initCount[orig[i][j]]++;\n \n auto start = chrono::steady_clock::now();\n vector> best = orig;\n int bestScore = 0;\n \n auto output = [&](vector>& g) {\n for (int i = 0; i < n; i++) {\n for (int j = 0; j < n; j++) { cout << g[i][j]; if (j < n-1) cout << \" \"; }\n cout << \"\\n\";\n }\n cout.flush();\n };\n output(best);\n \n auto solve = [&](int seed) {\n auto grid = orig;\n auto edgeCount = initEdge;\n auto colorCount = initCount;\n mt19937 rng(seed);\n \n auto canRemove = [&](int i, int j) -> bool {\n int c = grid[i][j];\n if (c == 0 || colorCount[c] <= 1) return false;\n \n vector> sameNeigh;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n) {\n int nc = grid[ni][nj];\n if (nc == c) sameNeigh.push_back({ni, nj});\n else if (nc != 0 && !adjToZero.count(nc)) return false;\n }\n }\n if (sameNeigh.empty()) return false;\n \n map, int> delta;\n if (i == 0 || i == n-1 || j == 0 || j == n-1) delta[{0, c}]--;\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n) {\n int nc = grid[ni][nj];\n if (nc != c && nc != 0) { delta[{min(c,nc), max(c,nc)}]--; delta[{0, nc}]++; }\n }\n }\n for (auto& [e, d] : delta)\n if (required.count(e) && edgeCount[e] + d <= 0) return false;\n \n // Check connectivity\n if (sameNeigh.size() >= 2) {\n grid[i][j] = 0;\n vector> vis(n, vector(n));\n queue> q;\n q.push(sameNeigh[0]);\n vis[sameNeigh[0].first][sameNeigh[0].second] = true;\n int toFind = sameNeigh.size() - 1;\n while (!q.empty() && toFind > 0) {\n auto [x, y] = q.front(); q.pop();\n for (int d = 0; d < 4; d++) {\n int nx = x + dx[d], ny = y + dy[d];\n if (nx >= 0 && nx < n && ny >= 0 && ny < n && !vis[nx][ny] && grid[nx][ny] == c) {\n vis[nx][ny] = true;\n q.push({nx, ny});\n for (size_t k = 1; k < sameNeigh.size(); k++)\n if (sameNeigh[k] == make_pair(nx, ny)) toFind--;\n }\n }\n }\n if (toFind > 0) { grid[i][j] = c; return false; }\n } else {\n grid[i][j] = 0;\n }\n \n for (auto& [e, d] : delta) edgeCount[e] += d;\n colorCount[c]--;\n return true;\n };\n \n // BFS from boundary\n vector> dist(n, vector(n, -1));\n vector> order;\n queue> bq;\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) {\n if (i == 0 || i == n-1 || j == 0 || j == n-1) { \n dist[i][j] = 0; bq.push({i,j}); order.push_back({i,j});\n }\n }\n while (!bq.empty()) {\n auto [i, j] = bq.front(); bq.pop();\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n && dist[ni][nj] == -1) {\n dist[ni][nj] = dist[i][j] + 1;\n bq.push({ni, nj});\n order.push_back({ni, nj});\n }\n }\n }\n \n // Shuffle within same distance\n for (int d = 0; d <= 25; d++) {\n int start_idx = 0, end_idx = 0;\n for (size_t i = 0; i < order.size(); i++) {\n if (dist[order[i].first][order[i].second] == d) {\n if (start_idx == end_idx) start_idx = i;\n end_idx = i + 1;\n }\n }\n if (end_idx > start_idx)\n shuffle(order.begin() + start_idx, order.begin() + end_idx, rng);\n }\n \n vector> adj0(n, vector(n));\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++)\n adj0[i][j] = (dist[i][j] == 0);\n \n for (int round = 0; round < 10; round++) {\n bool changed = false;\n for (auto [i, j] : order) {\n if (grid[i][j] != 0 && adj0[i][j] && canRemove(i, j)) {\n for (int d = 0; d < 4; d++) {\n int ni = i + dx[d], nj = j + dy[d];\n if (ni >= 0 && ni < n && nj >= 0 && nj < n) adj0[ni][nj] = true;\n }\n changed = true;\n }\n }\n if (!changed) break;\n }\n \n return grid;\n };\n \n for (int seed = 0; seed < 800; seed++) {\n auto elapsed = chrono::steady_clock::now() - start;\n if (chrono::duration_cast(elapsed).count() > 1900) break;\n \n auto grid = solve(seed);\n int sc = 0;\n for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) if (grid[i][j] == 0) sc++;\n if (sc > bestScore) { bestScore = sc; best = grid; output(best); }\n }\n \n return 0;\n}","ahc025":"#include \nusing namespace std;\n\nint N, D, Q;\nint query_count = 0;\n\nchar query(const vector& L, const vector& R) {\n cout << L.size() << \" \" << R.size();\n for (int x : L) cout << \" \" << x;\n for (int x : R) cout << \" \" << x;\n cout << \"\\n\" << flush;\n char c;\n cin >> c;\n query_count++;\n return c;\n}\n\nvector sorted_items;\n\nvoid merge_sort(int l, int r) {\n if (r - l <= 1 || query_count >= Q) return;\n int m = (l + r) / 2;\n merge_sort(l, m);\n merge_sort(m, r);\n \n vector left(sorted_items.begin() + l, sorted_items.begin() + m);\n vector right(sorted_items.begin() + m, sorted_items.begin() + r);\n \n int i = 0, j = 0, k = l;\n while (i < (int)left.size() && j < (int)right.size()) {\n if (query_count >= Q) {\n while (i < (int)left.size()) sorted_items[k++] = left[i++];\n while (j < (int)right.size()) sorted_items[k++] = right[j++];\n return;\n }\n char c = query({left[i]}, {right[j]});\n if (c != '>') sorted_items[k++] = left[i++];\n else sorted_items[k++] = right[j++];\n }\n while (i < (int)left.size()) sorted_items[k++] = left[i++];\n while (j < (int)right.size()) sorted_items[k++] = right[j++];\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> D >> Q;\n \n sorted_items.resize(N);\n iota(sorted_items.begin(), sorted_items.end(), 0);\n merge_sort(0, N);\n \n vector rank_of(N);\n for (int i = 0; i < N; i++) rank_of[sorted_items[i]] = i;\n \n vector w(N);\n for (int i = 0; i < N; i++) w[i] = i + 1;\n \n int remaining = Q - query_count;\n int est_budget = remaining / 3;\n \n for (int j = N - 1; j >= 1 && est_budget > 0; j--) {\n int lo = 1, hi = j;\n while (lo < hi && est_budget > 0 && query_count < Q) {\n int mid = (lo + hi) / 2;\n vector L, R = {sorted_items[j]};\n for (int t = 0; t < mid; t++) L.push_back(sorted_items[t]);\n char c = query(L, R);\n est_budget--;\n if (c == '>' || c == '=') hi = mid;\n else lo = mid + 1;\n }\n double sum = 0;\n for (int t = 0; t < lo; t++) sum += w[t];\n w[j] = max(w[j], sum);\n }\n \n vector set_weight(D, 0);\n vector assignment(N);\n vector> sets(D);\n \n for (int i = N - 1; i >= 0; i--) {\n int item = sorted_items[i];\n int best = 0;\n for (int j = 1; j < D; j++)\n if (set_weight[j] < set_weight[best]) best = j;\n assignment[item] = best;\n set_weight[best] += w[i];\n sets[best].push_back(item);\n }\n \n bool improved = true;\n while (improved && query_count + 3 < Q) {\n improved = false;\n for (int a = 0; a < D && query_count + 3 < Q; a++) {\n for (int b = a + 1; b < D && query_count + 3 < Q; b++) {\n if (sets[a].empty() || sets[b].empty()) continue;\n \n char cmp = query(sets[a], sets[b]);\n if (cmp == '=') continue;\n \n int heavy = (cmp == '>') ? a : b;\n int light = (cmp == '>') ? b : a;\n if (sets[heavy].size() <= 1) continue;\n \n vector> ranked;\n for (int item : sets[heavy])\n ranked.push_back({rank_of[item], item});\n sort(ranked.begin(), ranked.end());\n \n int tries = min((int)ranked.size() - 1, 2);\n for (int k = 0; k < tries && query_count + 1 < Q; k++) {\n int move_item = ranked[k].second;\n int move_rank = ranked[k].first;\n \n vector new_heavy, new_light = sets[light];\n for (int item : sets[heavy])\n if (item != move_item) new_heavy.push_back(item);\n new_light.push_back(move_item);\n \n char new_cmp = query(new_heavy, new_light);\n \n if (new_cmp == '=' || new_cmp != cmp) {\n sets[heavy] = new_heavy;\n sets[light] = new_light;\n assignment[move_item] = light;\n set_weight[heavy] -= w[move_rank];\n set_weight[light] += w[move_rank];\n improved = true;\n break;\n }\n }\n }\n }\n }\n \n while (query_count < Q) query({sorted_items[0]}, {sorted_items[1]});\n \n for (int i = 0; i < N; i++)\n cout << assignment[i] << \" \\n\"[i == N - 1];\n \n return 0;\n}","ahc026":"#include \nusing namespace std;\n\nint simulate(const vector>& init_stacks, int n, int m, \n vector>& ops, mt19937& rng, int noise_level, int policy, bool random_mode) {\n \n vector> stacks = init_stacks;\n vector pos(n + 1);\n vector stack_min(m, INT_MAX);\n \n for (int i = 0; i < m; i++) {\n for (int b : stacks[i]) {\n pos[b] = i;\n stack_min[i] = min(stack_min[i], b);\n }\n }\n \n ops.clear();\n int total_energy = 0;\n \n for (int v = 1; v <= n; v++) {\n int si = pos[v];\n auto& st = stacks[si];\n \n int idx = 0;\n while (st[idx] != v) idx++;\n \n if (idx < (int)st.size() - 1) {\n int cnt = (int)st.size() - idx - 1;\n int bottom_box = st[idx + 1];\n \n int max_moving = 0, min_moving = n + 1;\n for (int j = idx + 1; j < (int)st.size(); j++) {\n max_moving = max(max_moving, st[j]);\n min_moving = min(min_moving, st[j]);\n }\n \n int best_dest = -1;\n \n if (random_mode && (rng() % 15) == 0) {\n best_dest = rng() % m;\n if (best_dest >= si) best_dest = (best_dest + 1) % m;\n if (best_dest == si) best_dest = (si + 1) % m;\n } else {\n int best_score = INT_MIN;\n \n for (int i = 0; i < m; i++) {\n if (i == si) continue;\n \n int score = 0;\n int empty_bonus = n * 3;\n int safe_bonus = n * 3;\n int top_bonus = 50;\n int height_penalty = 2;\n int unsafe_cnt_mult = 3;\n int empty_extra = n - min_moving;\n \n switch (policy) {\n case 0: break;\n case 1: empty_bonus = n * 4; break;\n case 2: safe_bonus = n * 4; top_bonus = 80; break;\n case 3: height_penalty = 4; break;\n case 4: top_bonus = 100; break;\n case 5: unsafe_cnt_mult = 2; break;\n case 6: empty_bonus = n * 2; safe_bonus = n * 4; break;\n case 7: unsafe_cnt_mult = 4; height_penalty = 1; break;\n case 8: empty_bonus = n * 5; height_penalty = 3; break;\n case 9: top_bonus = 30; unsafe_cnt_mult = 4; break;\n case 10: empty_extra = min_moving; unsafe_cnt_mult = 2; break;\n case 11: height_penalty = 5; top_bonus = 40; break;\n case 12: safe_bonus = n * 2; unsafe_cnt_mult = 1; break;\n case 13: top_bonus = 150; height_penalty = 3; break;\n case 14: unsafe_cnt_mult = 5; empty_bonus = n * 4; break;\n case 15: safe_bonus = n * 5; height_penalty = 1; break;\n case 16: empty_bonus = n * 3; top_bonus = 70; height_penalty = 3; break;\n case 17: unsafe_cnt_mult = 3; empty_extra = 0; break;\n }\n \n if (stacks[i].empty()) {\n score = empty_bonus + empty_extra;\n } else {\n int min_d = stack_min[i];\n \n if (min_d > min_moving) {\n score = safe_bonus;\n if (stacks[i].back() > max_moving) {\n score += top_bonus;\n }\n } else {\n score = min_d - cnt * unsafe_cnt_mult;\n }\n \n score -= (int)stacks[i].size() * height_penalty;\n }\n \n if (noise_level > 0) {\n score += rng() % (noise_level + 1);\n }\n \n if (score > best_score) {\n best_score = score;\n best_dest = i;\n }\n }\n }\n \n total_energy += cnt + 1;\n ops.push_back({bottom_box, best_dest + 1});\n \n for (int j = idx + 1; j < (int)st.size(); j++) {\n int b = st[j];\n stacks[best_dest].push_back(b);\n pos[b] = best_dest;\n stack_min[best_dest] = min(stack_min[best_dest], b);\n }\n st.resize(idx + 1);\n stack_min[si] = st.empty() ? INT_MAX : *min_element(st.begin(), st.end());\n }\n \n ops.push_back({v, 0});\n st.pop_back();\n if (st.empty()) stack_min[si] = INT_MAX;\n else if (stack_min[si] == v) stack_min[si] = *min_element(st.begin(), st.end());\n }\n \n return total_energy;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n, m;\n cin >> n >> m;\n \n vector> init_stacks(m);\n \n for (int i = 0; i < m; i++) {\n int h = n / m;\n for (int j = 0; j < h; j++) {\n int x;\n cin >> x;\n init_stacks[i].push_back(x);\n }\n }\n \n vector> best_ops;\n int best_energy = INT_MAX;\n \n auto start_time = chrono::steady_clock::now();\n \n vector noise_levels = {0, 2, 5, 8, 12, 16, 20, 25, 30, 38, 48, 60, 75, 95};\n int num_policies = 18;\n \n for (int seed = 0; ; seed++) {\n auto current_time = chrono::steady_clock::now();\n auto elapsed = chrono::duration_cast(current_time - start_time).count();\n if (elapsed > 1900) break;\n \n int noise_level = noise_levels[seed % noise_levels.size()];\n int policy = (seed / noise_levels.size()) % num_policies;\n bool random_mode = (seed % 18 == 17);\n \n mt19937 rng(seed);\n vector> ops;\n int energy = simulate(init_stacks, n, m, ops, rng, noise_level, policy, random_mode);\n \n if (energy < best_energy) {\n best_energy = energy;\n best_ops = ops;\n }\n }\n \n for (auto& [a, b] : best_ops) {\n cout << a << \" \" << b << \"\\n\";\n }\n \n return 0;\n}","ahc027":"#include \nusing namespace std;\n\nint N;\nvector h, v;\nvector> d;\nlong long totalD;\nmt19937 rng(42);\n\nint di[] = {0, 1, 0, -1};\nint dj[] = {1, 0, -1, 0};\nchar dirChar[] = {'R', 'D', 'L', 'U'};\n\nbool canMove(int i, int j, int dir) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (ni < 0 || ni >= N || nj < 0 || nj >= N) return false;\n if (dir == 0) return v[i][j] == '0';\n if (dir == 1) return h[i][j] == '0';\n if (dir == 2) return j > 0 && v[i][j-1] == '0';\n return i > 0 && h[i-1][j] == '0';\n}\n\nlong double fastEvaluate(const string& path) {\n int L = path.size();\n vector> contrib(N, vector(N, 0));\n long long contribSum = 0;\n int ci = 0, cj = 0;\n \n auto move = [&](int t, char c) {\n int dir = (c == 'R') ? 0 : (c == 'D') ? 1 : (c == 'L') ? 2 : 3;\n ci += di[dir]; cj += dj[dir];\n contribSum -= contrib[ci][cj];\n contrib[ci][cj] = (long long)d[ci][cj] * t;\n contribSum += contrib[ci][cj];\n };\n \n for (int t = 1; t <= L; t++) move(t, path[t-1]);\n \n long double totalSum = 0;\n for (int t = L + 1; t <= 2 * L; t++) {\n totalSum += (long long)totalD * t - contribSum;\n move(t, path[(t-1) % L]);\n }\n return totalSum / L;\n}\n\nvector> getVisits(const string& path) {\n vector> cnt(N, vector(N, 0));\n int ci = 0, cj = 0;\n cnt[0][0] = 1;\n for (char c : path) {\n int dir = (c == 'R') ? 0 : (c == 'D') ? 1 : (c == 'L') ? 2 : 3;\n ci += di[dir]; cj += dj[dir];\n cnt[ci][cj]++;\n }\n return cnt;\n}\n\nstring generatePath(int mode) {\n vector> visited(N, vector(N, false));\n string path;\n \n function dfs = [&](int i, int j) {\n visited[i][j] = true;\n vector> children;\n for (int dir = 0; dir < 4; dir++) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (ni >= 0 && ni < N && nj >= 0 && nj < N && !visited[ni][nj] && canMove(i, j, dir)) {\n children.push_back({d[ni][nj], dir});\n }\n }\n if (mode == 0) sort(children.begin(), children.end());\n else if (mode == 1) sort(children.rbegin(), children.rend());\n else shuffle(children.begin(), children.end(), rng);\n \n for (auto& [dval, dir] : children) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (!visited[ni][nj]) {\n path += dirChar[dir];\n dfs(ni, nj);\n path += dirChar[(dir + 2) % 4];\n }\n }\n };\n dfs(0, 0);\n return path;\n}\n\nvector> allLoops;\n\nvoid precomputeLoops() {\n vector> par(N, vector(N, -1));\n queue> bfs;\n bfs.push({0, 0});\n par[0][0] = -2;\n \n while (!bfs.empty()) {\n auto [i, j] = bfs.front(); bfs.pop();\n for (int dir = 0; dir < 4; dir++) {\n int ni = i + di[dir], nj = j + dj[dir];\n if (ni >= 0 && ni < N && nj >= 0 && nj < N && par[ni][nj] == -1 && canMove(i, j, dir)) {\n par[ni][nj] = (dir + 2) % 4;\n bfs.push({ni, nj});\n }\n }\n }\n \n for (int ti = 0; ti < N; ti++) {\n for (int tj = 0; tj < N; tj++) {\n if (ti == 0 && tj == 0) continue;\n string toTarget, fromTarget;\n int ci = ti, cj = tj;\n while (ci != 0 || cj != 0) {\n int pdir = par[ci][cj];\n fromTarget += dirChar[pdir];\n toTarget += dirChar[(pdir + 2) % 4];\n ci += di[pdir]; cj += dj[pdir];\n }\n reverse(toTarget.begin(), toTarget.end());\n allLoops.push_back({d[ti][tj], ti, tj, toTarget + fromTarget});\n }\n }\n sort(allLoops.rbegin(), allLoops.rend());\n}\n\nstring bestPath;\nlong double bestScore = 1e18;\n\nlong double tryPath(const string& path) {\n if (path.size() > 100000) return 1e18;\n long double score = fastEvaluate(path);\n if (score < bestScore) { bestScore = score; bestPath = path; }\n return score;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n h.resize(N - 1);\n v.resize(N);\n d.resize(N, vector(N));\n \n for (int i = 0; i < N - 1; i++) cin >> h[i];\n for (int i = 0; i < N; i++) cin >> v[i];\n totalD = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n cin >> d[i][j];\n totalD += d[i][j];\n }\n \n precomputeLoops();\n \n vector> topPaths;\n \n for (int mode = 0; mode < 2; mode++) {\n string p = generatePath(mode);\n topPaths.push_back({tryPath(p), p});\n }\n \n auto startTime = chrono::steady_clock::now();\n while (chrono::duration_cast(chrono::steady_clock::now() - startTime).count() < 1300) {\n string p = generatePath(2);\n topPaths.push_back({tryPath(p), p});\n }\n \n sort(topPaths.begin(), topPaths.end());\n if (topPaths.size() > 8) topPaths.resize(8);\n \n auto addLoopsD = [&](string bp) {\n string cur = bp;\n long double cs = fastEvaluate(cur);\n for (int it = 0; it < 30; it++) {\n bool imp = false;\n for (auto& [dv, ti, tj, lp] : allLoops) {\n if (cur.size() + lp.size() > 100000) continue;\n long double sc = fastEvaluate(cur + lp);\n if (sc < cs) {\n cs = sc; cur += lp; imp = true;\n if (sc < bestScore) { bestScore = sc; bestPath = cur; }\n break;\n }\n }\n if (!imp) break;\n }\n };\n \n auto addLoopsV = [&](string bp) {\n string cur = bp;\n long double cs = fastEvaluate(cur);\n for (int it = 0; it < 30; it++) {\n bool imp = false;\n auto vis = getVisits(cur);\n vector> pri;\n for (int i = 0; i < (int)allLoops.size(); i++) {\n auto& [dv, ti, tj, lp] = allLoops[i];\n pri.push_back({(double)dv / max(1, vis[ti][tj]), i});\n }\n sort(pri.rbegin(), pri.rend());\n for (auto& [p, idx] : pri) {\n auto& [dv, ti, tj, lp] = allLoops[idx];\n if (cur.size() + lp.size() > 100000) continue;\n long double sc = fastEvaluate(cur + lp);\n if (sc < cs) {\n cs = sc; cur += lp; imp = true;\n if (sc < bestScore) { bestScore = sc; bestPath = cur; }\n break;\n }\n }\n if (!imp) break;\n }\n };\n \n for (auto& [bs, bp] : topPaths) {\n addLoopsD(bp);\n addLoopsV(bp);\n }\n \n for (int c = 0; c < min(12, (int)allLoops.size()); c++) {\n auto& [dv, ti, tj, lp] = allLoops[c];\n string cand = bestPath;\n long double last = bestScore;\n for (int r = 1; r <= 40 && cand.size() + lp.size() <= 100000; r++) {\n cand += lp;\n long double sc = tryPath(cand);\n if (sc > last) break;\n last = sc;\n }\n }\n \n cout << bestPath << endl;\n return 0;\n}","ahc028":"#include \nusing namespace std;\n\nint N, M, si, sj;\nmap>> charPos;\n\nint calcOverlap(const string& a, const string& b) {\n int maxOv = min(a.length(), b.length());\n for (int ov = maxOv; ov >= 1; ov--) {\n bool match = true;\n size_t aStart = a.length() - ov;\n for (int k = 0; k < ov && match; k++)\n if (a[aStart + k] != b[k]) match = false;\n if (match) return ov;\n }\n return 0;\n}\n\nstring buildSuperstring(const vector& strings) {\n int n = strings.size();\n vector> preOv(n, vector(n, 0));\n for (int i = 0; i < n; i++)\n for (int j = 0; j < n; j++)\n if (i != j) preOv[i][j] = calcOverlap(strings[i], strings[j]);\n \n vector startWith(n), endWith(n);\n for (int i = 0; i < n; i++) startWith[i] = endWith[i] = i;\n \n vector active(n, true);\n vector current = strings;\n \n for (int iter = 0; iter < n - 1; iter++) {\n int bestOv = -1, bestI = -1, bestJ = -1;\n for (int i = 0; i < n; i++) {\n if (!active[i]) continue;\n for (int j = 0; j < n; j++) {\n if (!active[j] || i == j) continue;\n int ov = preOv[endWith[i]][startWith[j]];\n if (ov > bestOv) { bestOv = ov; bestI = i; bestJ = j; }\n }\n }\n current[bestI] += current[bestJ].substr(bestOv);\n endWith[bestI] = endWith[bestJ];\n active[bestJ] = false;\n }\n for (int i = 0; i < n; i++) if (active[i]) return current[i];\n return \"\";\n}\n\npair>> computePath(const string& ss) {\n int n = ss.length();\n if (n == 0) return {0, {}};\n vector> dp(n);\n for (int pos = n - 1; pos >= 0; pos--) {\n const auto& positions = charPos[ss[pos]];\n dp[pos].assign(positions.size(), 0);\n if (pos < n - 1) {\n const auto& nextPos = charPos[ss[pos + 1]];\n for (size_t idx = 0; idx < positions.size(); idx++) {\n int r = positions[idx].first, c = positions[idx].second, best = INT_MAX;\n for (size_t ni = 0; ni < nextPos.size(); ni++)\n best = min(best, abs(nextPos[ni].first-r)+abs(nextPos[ni].second-c)+1+dp[pos+1][ni]);\n dp[pos][idx] = best;\n }\n }\n }\n const auto& pos0 = charPos[ss[0]];\n int bestCost = INT_MAX;\n for (size_t idx = 0; idx < pos0.size(); idx++)\n bestCost = min(bestCost, abs(pos0[idx].first-si)+abs(pos0[idx].second-sj)+1+dp[0][idx]);\n vector> path(n);\n int curI = si, curJ = sj;\n for (int pos = 0; pos < n; pos++) {\n const auto& positions = charPos[ss[pos]];\n int best = INT_MAX, bIdx = 0;\n for (size_t idx = 0; idx < positions.size(); idx++) {\n int total = abs(positions[idx].first-curI)+abs(positions[idx].second-curJ)+1+dp[pos][idx];\n if (total < best) { best = total; bIdx = idx; }\n }\n path[pos] = positions[bIdx];\n curI = path[pos].first; curJ = path[pos].second;\n }\n return {bestCost, path};\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> M >> si >> sj;\n for (int i = 0; i < N; i++) {\n string row; cin >> row;\n for (int j = 0; j < N; j++) charPos[row[j]].push_back({i, j});\n }\n vector t(M);\n for (int i = 0; i < M; i++) cin >> t[i];\n \n mt19937 rng(12345);\n vector> bestPath;\n int bestCost = INT_MAX;\n auto startTime = chrono::steady_clock::now();\n \n for (int iter = 0; ; iter++) {\n if (iter > 0 && chrono::duration_cast(\n chrono::steady_clock::now() - startTime).count() > 1850) break;\n \n vector input = t;\n if (iter == 1) sort(input.begin(), input.end());\n else if (iter == 2) sort(input.begin(), input.end(), greater());\n else if (iter == 3) sort(input.begin(), input.end(), [](auto& a, auto& b){ return a.back() < b.back(); });\n else if (iter == 4) sort(input.begin(), input.end(), [](auto& a, auto& b){ return a[0] < b[0]; });\n else if (iter > 4) shuffle(input.begin(), input.end(), rng);\n \n string ss = buildSuperstring(input);\n auto [cost, path] = computePath(ss);\n if (cost < bestCost) { bestCost = cost; bestPath = path; }\n }\n \n for (auto& [i, j] : bestPath) cout << i << \" \" << j << \"\\n\";\n return 0;\n}","ahc030":"#include \nusing namespace std;\n\nint N, M;\ndouble eps;\nvector>> shapes;\nmap, int> drilled;\nset> confirmed_oil, confirmed_no_oil;\nint qcount = 0;\nint maxQ;\n\nint queryDrill(int i, int j) {\n pair key = make_pair(i, j);\n if (drilled.count(key)) return drilled[key];\n cout << \"q 1 \" << i << \" \" << j << \"\\n\" << flush;\n qcount++;\n int v; cin >> v;\n drilled[key] = v;\n if (v > 0) confirmed_oil.insert(key);\n else confirmed_no_oil.insert(key);\n return v;\n}\n\nint queryDivine(const vector>& cells) {\n cout << \"q \" << cells.size();\n for (auto& c : cells) cout << \" \" << c.first << \" \" << c.second;\n cout << \"\\n\" << flush;\n qcount++;\n int v; cin >> v;\n return v;\n}\n\nint submit(set> oil) {\n for (auto& c : confirmed_oil) oil.insert(c);\n cout << \"a \" << oil.size();\n for (auto& c : oil) cout << \" \" << c.first << \" \" << c.second;\n cout << \"\\n\" << flush;\n qcount++;\n int r; cin >> r;\n return r;\n}\n\nvector>>> placements;\n\nvoid filterPlacements() {\n for (int m = 0; m < M; m++) {\n vector>> valid;\n for (auto& p : placements[m]) {\n bool ok = true;\n for (auto& c : confirmed_no_oil)\n if (p.count(c)) { ok = false; break; }\n if (ok) valid.push_back(p);\n }\n if (!valid.empty()) placements[m] = valid;\n }\n}\n\nbool allUnique() {\n for (int m = 0; m < M; m++)\n if (placements[m].size() > 1) return false;\n return true;\n}\n\nset> getAnswer() {\n set> answer;\n for (int m = 0; m < M; m++)\n if (!placements[m].empty())\n for (auto& c : placements[m][0]) answer.insert(c);\n return answer;\n}\n\nset> getPossible() {\n set> possible;\n for (int m = 0; m < M; m++)\n for (auto& p : placements[m])\n for (auto& c : p) possible.insert(c);\n return possible;\n}\n\npair getBestCell(const vector>& prob) {\n map, vector> cellCounts;\n \n for (int m = 0; m < M; m++) {\n for (auto& p : placements[m])\n for (auto& c : p) {\n if (cellCounts.find(c) == cellCounts.end())\n cellCounts[c] = vector(M, 0);\n cellCounts[c][m]++;\n }\n }\n \n // Find field with most remaining placements\n int maxField = 0;\n for (int m = 1; m < M; m++)\n if (placements[m].size() > placements[maxField].size())\n maxField = m;\n \n pair best = {-1, -1};\n double bestScore = -1e18;\n \n for (auto& kv : cellCounts) {\n pair cell = kv.first;\n vector& counts = kv.second;\n \n if (drilled.count(cell)) continue;\n \n bool valid = true;\n for (int m = 0; m < M; m++) {\n if ((int)placements[m].size() - counts[m] <= 0) {\n valid = false; break;\n }\n }\n if (!valid) continue;\n \n double p = prob[cell.first][cell.second];\n \n // Entropy-based scoring with log reduction\n double entropyGain = 0;\n double logReduction = 0;\n for (int m = 0; m < M; m++) {\n int sz = placements[m].size();\n if (sz <= 1) continue;\n double ratio = (double)counts[m] / sz;\n entropyGain += ratio * (1 - ratio) * 4 * log((double)sz);\n logReduction += log((double)sz) - log((double)(sz - counts[m]));\n }\n \n // Bonus for splitting the most uncertain field evenly\n double splitBonus = 0;\n if (placements[maxField].size() > 1) {\n int cnt = counts[maxField];\n int sz = placements[maxField].size();\n double ratio = (double)cnt / sz;\n splitBonus = ratio * (1 - ratio) * 4;\n }\n \n double score = (1.0 - p) * (entropyGain + logReduction * 0.5 + splitBonus * 2.0);\n \n if (score > bestScore) {\n bestScore = score;\n best = cell;\n }\n }\n return best;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> eps;\n maxQ = 2 * N * N;\n shapes.resize(M);\n \n for (int m = 0; m < M; m++) {\n int d; cin >> d;\n shapes[m].resize(d);\n for (int i = 0; i < d; i++)\n cin >> shapes[m][i].first >> shapes[m][i].second;\n }\n \n placements.resize(M);\n for (int m = 0; m < M; m++) {\n int maxI = 0, maxJ = 0;\n for (auto& c : shapes[m]) {\n maxI = max(maxI, c.first);\n maxJ = max(maxJ, c.second);\n }\n for (int di = 0; di + maxI < N; di++)\n for (int dj = 0; dj + maxJ < N; dj++) {\n set> cells;\n for (auto& c : shapes[m])\n cells.insert({di + c.first, dj + c.second});\n placements[m].push_back(cells);\n }\n }\n \n // Compute structural probability\n vector> structProb(N, vector(N, 0.1));\n map, int> freq;\n int totalPlacements = 0;\n for (int m = 0; m < M; m++) {\n for (auto& p : placements[m]) {\n totalPlacements++;\n for (auto& c : p) freq[c]++;\n }\n }\n for (auto& kv : freq)\n structProb[kv.first.first][kv.first.second] = min(0.8, (double)kv.second / max(1, totalPlacements));\n \n vector> prob(N, vector(N, 0.3));\n \n // Always do row divination\n for (int i = 0; i < N; i++) {\n vector> row;\n for (int j = 0; j < N; j++) row.push_back({i, j});\n int est = queryDivine(row);\n double denom = max(0.6, 1.0 - 2.0 * eps);\n double trueEst = max(0.0, (est - N * eps) / denom);\n double divProb = min(0.9, max(0.1, trueEst / N));\n \n for (int j = 0; j < N; j++) {\n if (eps <= 0.08) {\n prob[i][j] = divProb;\n } else {\n double w = max(0.3, 1.0 - eps * 3); // More structural weight as eps increases\n prob[i][j] = w * divProb + (1-w) * structProb[i][j];\n }\n }\n }\n \n // Column divination for low eps\n if (eps <= 0.05) {\n for (int j = 0; j < N; j++) {\n vector> col;\n for (int i = 0; i < N; i++) col.push_back({i, j});\n int est = queryDivine(col);\n double denom = max(0.01, 1.0 - 2.0 * eps);\n double trueEst = max(0.0, (est - N * eps) / denom);\n for (int i = 0; i < N; i++)\n prob[i][j] = (prob[i][j] + min(0.9, max(0.1, trueEst / N))) / 2.0;\n }\n }\n \n while (qcount < maxQ - 5 && !allUnique()) {\n filterPlacements();\n auto cell = getBestCell(prob);\n if (cell.first < 0) break;\n queryDrill(cell.first, cell.second);\n }\n \n filterPlacements();\n set> answer = allUnique() ? getAnswer() : getPossible();\n for (auto& c : confirmed_no_oil) answer.erase(c);\n \n if (!submit(answer)) {\n while (qcount < maxQ - 2) {\n filterPlacements();\n if (allUnique()) break;\n auto cell = getBestCell(prob);\n if (cell.first < 0) {\n auto possible = getPossible();\n for (auto& c : possible)\n if (!drilled.count(c)) { cell = c; break; }\n }\n if (cell.first < 0) break;\n queryDrill(cell.first, cell.second);\n }\n filterPlacements();\n answer = allUnique() ? getAnswer() : getPossible();\n for (auto& c : confirmed_no_oil) answer.erase(c);\n if (!submit(answer)) submit(confirmed_oil);\n }\n \n return 0;\n}","ahc031":"#include \nusing namespace std;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int W, D, N;\n cin >> W >> D >> N;\n \n vector> a(D, vector(N));\n for (int d = 0; d < D; d++) {\n for (int k = 0; k < N; k++) {\n cin >> a[d][k];\n }\n }\n \n vector prevH(N, 0);\n \n for (int d = 0; d < D; d++) {\n vector h(N);\n int totalH = 0;\n \n for (int k = 0; k < N; k++) {\n h[k] = (a[d][k] + W - 1) / W;\n if (h[k] == 0) h[k] = 1;\n totalH += h[k];\n }\n \n if (totalH > W) {\n while (totalH > W) {\n int bestK = -1;\n int maxSlack = INT_MIN;\n for (int k = 0; k < N; k++) {\n if (h[k] > 1) {\n int slack = h[k] * W - a[d][k];\n if (slack > maxSlack) {\n maxSlack = slack;\n bestK = k;\n }\n }\n }\n if (bestK == -1) break;\n h[bestK]--;\n totalH--;\n }\n } else if (totalH < W) {\n // Distribute extra space matching previous day where possible\n int extra = W - totalH;\n for (int k = 0; k < N && extra > 0; k++) {\n if (prevH[k] > h[k]) {\n int add = min(extra, prevH[k] - h[k]);\n h[k] += add;\n extra -= add;\n }\n }\n // Remaining extra goes to largest\n if (extra > 0) {\n h[N-1] += extra;\n }\n }\n \n int y = 0;\n for (int k = 0; k < N; k++) {\n cout << y << \" 0 \" << y + h[k] << \" \" << W << \"\\n\";\n y += h[k];\n }\n \n prevH = h;\n }\n \n return 0;\n}","ahc032":"#include \nusing namespace std;\n\nconst long long P = 998244353;\nint N, M, K;\nvector> a_init;\nvector, 3>> stamps;\n\nvoid applyOp(vector>& a, int m, int p, int q) {\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n a[p+i][q+j] = (a[p+i][q+j] + stamps[m][i][j]) % P;\n}\n\nlong long calcGain(const vector>& a, int m, int p, int q) {\n long long gain = 0;\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n gain += (a[p+i][q+j] + stamps[m][i][j]) % P - a[p+i][q+j];\n return gain;\n}\n\nlong long calcScore(const vector>& a) {\n long long s = 0;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n s += a[i][j];\n return s;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(0);\n \n cin >> N >> M >> K;\n a_init.assign(N, vector(N));\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n cin >> a_init[i][j];\n a_init[i][j] %= P;\n }\n \n stamps.resize(M);\n for (int m = 0; m < M; m++)\n for (int i = 0; i < 3; i++)\n for (int j = 0; j < 3; j++)\n cin >> stamps[m][i][j];\n \n auto start = chrono::steady_clock::now();\n auto elapsed = [&]() { return chrono::duration(chrono::steady_clock::now() - start).count(); };\n \n vector> best_ops;\n long long best_score = calcScore(a_init);\n \n mt19937 rng(42);\n \n for (int trial = 0; elapsed() < 1.9; trial++) {\n vector> ops;\n auto a = a_init;\n \n // Randomized greedy\n for (int op = 0; op < K; op++) {\n vector> cands;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N-3; p++)\n for (int q = 0; q <= N-3; q++) {\n long long gain = calcGain(a, m, p, q);\n if (gain > 0) cands.push_back({gain, m, p, q});\n }\n if (cands.empty()) break;\n sort(cands.rbegin(), cands.rend());\n int pick = (trial == 0) ? 0 : rng() % min((int)cands.size(), 2 + trial / 3);\n auto [g, m, p, q] = cands[pick];\n applyOp(a, m, p, q);\n ops.push_back({m, p, q});\n }\n \n long long score = calcScore(a);\n \n // Local optimization passes\n for (int iter = 0; iter < 5 && elapsed() < 1.9; iter++) {\n bool improved = false;\n \n // Try replacing each operation\n for (int idx = 0; idx < (int)ops.size() && elapsed() < 1.9; idx++) {\n auto orig = ops[idx];\n auto a2 = a_init;\n for (int k = 0; k < (int)ops.size(); k++)\n if (k != idx) {\n auto [m,p,q] = ops[k];\n applyOp(a2, m, p, q);\n }\n \n long long bestGain = 0;\n int bm=-1, bp=-1, bq=-1;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N-3; p++)\n for (int q = 0; q <= N-3; q++) {\n long long gain = calcGain(a2, m, p, q);\n if (gain > bestGain) { bestGain = gain; bm=m; bp=p; bq=q; }\n }\n \n if (bm != -1) {\n auto newOp = make_tuple(bm, bp, bq);\n if (newOp != orig) {\n ops[idx] = newOp;\n a = a2;\n applyOp(a, bm, bp, bq);\n long long newScore = calcScore(a);\n if (newScore > score) {\n score = newScore;\n improved = true;\n }\n }\n }\n }\n \n // Try removing operations\n for (int idx = (int)ops.size()-1; idx >= 0 && elapsed() < 1.9; idx--) {\n auto a2 = a_init;\n for (int k = 0; k < (int)ops.size(); k++)\n if (k != idx) {\n auto [m,p,q] = ops[k];\n applyOp(a2, m, p, q);\n }\n long long newScore = calcScore(a2);\n if (newScore >= score) {\n ops.erase(ops.begin() + idx);\n a = a2;\n score = newScore;\n improved = true;\n }\n }\n \n // Try adding more operations\n while (ops.size() < (size_t)K && elapsed() < 1.9) {\n long long bestGain = 0;\n int bm=-1, bp=-1, bq=-1;\n for (int m = 0; m < M; m++)\n for (int p = 0; p <= N-3; p++)\n for (int q = 0; q <= N-3; q++) {\n long long gain = calcGain(a, m, p, q);\n if (gain > bestGain) { bestGain = gain; bm=m; bp=p; bq=q; }\n }\n if (bm == -1) break;\n applyOp(a, bm, bp, bq);\n ops.push_back({bm, bp, bq});\n score += bestGain;\n improved = true;\n }\n \n if (!improved) break;\n }\n \n if (score > best_score) {\n best_score = score;\n best_ops = ops;\n }\n }\n \n cout << best_ops.size() << \"\\n\";\n for (auto& [m,p,q] : best_ops) cout << m << \" \" << p << \" \" << q << \"\\n\";\n}","ahc033":"#include \nusing namespace std;\n\nconst int N = 5;\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int n; cin >> n;\n int A[N][N];\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n cin >> A[i][j];\n \n string ans[N];\n int grid[N][N]; memset(grid, -1, sizeof(grid));\n int cr = 0, cc = 0, hold = -1;\n int next_in[N] = {0};\n set dispatched;\n \n for (int t = 0; t < 9000; t++) {\n for (int i = 0; i < N; i++) {\n if (next_in[i] < N && grid[i][0] == -1) {\n bool blocked = (cr == i && cc == 0 && hold != -1);\n if (!blocked) grid[i][0] = A[i][next_in[i]++];\n }\n }\n \n char moves[N];\n for (int c = 0; c < N; c++) moves[c] = '.';\n \n if (t == 0) {\n for (int c = 1; c < N; c++) moves[c] = 'B';\n }\n \n int min_undispatched[N];\n for (int i = 0; i < N; i++) {\n min_undispatched[i] = i * N;\n while (min_undispatched[i] < (i+1)*N && dispatched.count(min_undispatched[i]))\n min_undispatched[i]++;\n }\n \n int min_on_grid[N];\n for (int i = 0; i < N; i++) min_on_grid[i] = N * N;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (grid[i][j] != -1) {\n int cont = grid[i][j];\n min_on_grid[cont / N] = min(min_on_grid[cont / N], cont);\n }\n }\n }\n \n if (hold == -1) {\n int best_r = -1, best_c = -1, best_score = -1000000;\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n if (grid[i][j] != -1) {\n int cont = grid[i][j];\n int target = cont / N;\n int dist = abs(i - cr) + abs(j - cc);\n int deliver_dist = abs(i - target) + (N - 1 - j);\n \n int score = -dist * 5 - deliver_dist;\n \n if (cont == min_undispatched[target]) {\n score += 10000; // Must pick these\n } else {\n // Penalize by potential inversions\n int inversions = cont - min_undispatched[target];\n score -= inversions * 80;\n \n if (cont == min_on_grid[target]) {\n score += 200; // Small bonus for min on grid\n }\n }\n \n if (score > best_score) {\n best_score = score;\n best_r = i; best_c = j;\n }\n }\n }\n }\n \n if (best_r != -1) {\n if (best_r == cr && best_c == cc) {\n moves[0] = 'P';\n } else if (best_r > cr) moves[0] = 'D';\n else if (best_r < cr) moves[0] = 'U';\n else if (best_c > cc) moves[0] = 'R';\n else moves[0] = 'L';\n } else if (cc > 0) {\n moves[0] = 'L';\n }\n } else {\n int target = hold / N;\n if (cr != target) {\n if (target > cr) moves[0] = 'D';\n else moves[0] = 'U';\n } else if (cc < N-1) {\n moves[0] = 'R';\n } else {\n moves[0] = 'Q';\n }\n }\n \n if (moves[0] == 'P') { hold = grid[cr][cc]; grid[cr][cc] = -1; }\n else if (moves[0] == 'Q') { \n if (cc == N-1) dispatched.insert(hold);\n grid[cr][cc] = hold; \n hold = -1; \n }\n else if (moves[0] == 'R') cc++;\n else if (moves[0] == 'L') cc--;\n else if (moves[0] == 'U') cr--;\n else if (moves[0] == 'D') cr++;\n \n for (int i = 0; i < N; i++) grid[i][N-1] = -1;\n for (int c = 0; c < N; c++) ans[c] += moves[c];\n \n bool done = true;\n for (int i = 0; i < N; i++) if (next_in[i] < N) done = false;\n if (hold != -1) done = false;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (grid[i][j] != -1) done = false;\n if (done) break;\n }\n \n for (int i = 0; i < N; i++) cout << ans[i] << \"\\n\";\n return 0;\n}","ahc034":"#include \nusing namespace std;\n\nint N;\nmt19937 rng;\n\nstruct State {\n vector> h;\n vector ops;\n int cx, cy, load;\n long long cost;\n \n State(const vector>& grid) : h(grid), cx(0), cy(0), load(0), cost(0) {}\n \n void do_load(int d) {\n if (d <= 0) return;\n ops.push_back(\"+\" + to_string(d));\n load += d; h[cx][cy] -= d; cost += d;\n }\n \n void do_unload(int d) {\n if (d <= 0) return;\n ops.push_back(\"-\" + to_string(d));\n load -= d; h[cx][cy] += d; cost += d;\n }\n \n void move_one(char dir) {\n cost += 100 + load;\n ops.push_back(string(1, dir));\n if (dir == 'U') cx--; else if (dir == 'D') cx++;\n else if (dir == 'L') cy--; else if (dir == 'R') cy++;\n }\n \n void process_cell() {\n if (h[cx][cy] > 0) do_load(h[cx][cy]);\n if (h[cx][cy] < 0 && load > 0) do_unload(min(load, -h[cx][cy]));\n }\n \n int calc_path_work(int fx, int fy, int tx, int ty, int init_load, bool vert_first) {\n int work = 0, sim_load = init_load, x = fx, y = fy;\n auto process = [&](int px, int py) {\n if (h[px][py] > 0) { work += h[px][py]; sim_load += h[px][py]; }\n else if (h[px][py] < 0 && sim_load > 0) {\n int u = min(sim_load, -h[px][py]); work += u; sim_load -= u;\n }\n };\n if (vert_first) {\n while (x != tx) { x += (tx > x) ? 1 : -1; process(x, y); }\n while (y != ty) { y += (ty > y) ? 1 : -1; process(x, y); }\n } else {\n while (y != ty) { y += (ty > y) ? 1 : -1; process(x, y); }\n while (x != tx) { x += (tx > x) ? 1 : -1; process(x, y); }\n }\n return work;\n }\n \n int best_path_work(int fx, int fy, int tx, int ty, int init_load) {\n return max(calc_path_work(fx, fy, tx, ty, init_load, true),\n calc_path_work(fx, fy, tx, ty, init_load, false));\n }\n \n void move_to(int tx, int ty) {\n int vw = calc_path_work(cx, cy, tx, ty, load, true);\n int hw = calc_path_work(cx, cy, tx, ty, load, false);\n if (vw >= hw) {\n while (cx < tx) { move_one('D'); process_cell(); }\n while (cx > tx) { move_one('U'); process_cell(); }\n while (cy < ty) { move_one('R'); process_cell(); }\n while (cy > ty) { move_one('L'); process_cell(); }\n } else {\n while (cy < ty) { move_one('R'); process_cell(); }\n while (cy > ty) { move_one('L'); process_cell(); }\n while (cx < tx) { move_one('D'); process_cell(); }\n while (cx > tx) { move_one('U'); process_cell(); }\n }\n }\n \n void solve(int pw, int ta, int dp, int rand_level = 0) {\n while (true) {\n if (load == 0) {\n vector> cands;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (h[i][j] > 0) {\n int d = abs(i-cx) + abs(j-cy);\n int score = best_path_work(cx,cy,i,j,0)*pw + h[i][j]*ta - d*dp;\n cands.push_back({score, i, j});\n }\n if (cands.empty()) break;\n sort(cands.rbegin(), cands.rend());\n int idx = 0;\n if (rand_level > 0 && cands.size() > 1) idx = rng() % min((int)cands.size(), rand_level + 1);\n auto [sc, si, sj] = cands[idx];\n move_to(si, sj);\n if (h[cx][cy] > 0) do_load(h[cx][cy]);\n } else {\n vector> cands;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (h[i][j] < 0) {\n int d = abs(i-cx) + abs(j-cy);\n int score = best_path_work(cx,cy,i,j,load)*pw + min(-h[i][j],load)*ta - d*dp;\n cands.push_back({score, i, j});\n }\n if (cands.empty()) break;\n sort(cands.rbegin(), cands.rend());\n int idx = 0;\n if (rand_level > 0 && cands.size() > 1) idx = rng() % min((int)cands.size(), rand_level + 1);\n auto [sc, ti, tj] = cands[idx];\n move_to(ti, tj);\n if (h[cx][cy] < 0 && load > 0) do_unload(min(load, -h[cx][cy]));\n }\n }\n }\n};\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N;\n vector> h(N, vector(N));\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cin >> h[i][j];\n \n State best(h);\n best.cost = LLONG_MAX;\n \n // Expanded deterministic parameter grid\n for (int pw = 1; pw <= 7; pw++)\n for (int ta = 0; ta <= 4; ta++)\n for (int dp = 2; dp <= 9; dp++) {\n State s(h); s.solve(pw, ta, dp);\n if (s.cost < best.cost) best = s;\n }\n \n // Diverse base parameters for randomization\n vector> base_params = {\n {3,1,5},{4,1,5},{2,1,5},{3,2,5},{4,2,5},{2,1,4},{5,1,6},\n {3,1,4},{4,1,4},{2,2,5},{3,0,5},{4,0,5},{1,1,4},{6,1,7},\n {3,1,6},{4,2,6},{5,2,5},{2,0,4},{3,3,5},{4,1,3}\n };\n \n for (int seed = 0; seed < 25; seed++) {\n rng.seed(seed);\n for (auto [pw, ta, dp] : base_params)\n for (int rl = 1; rl <= 5; rl++) {\n State s(h); s.solve(pw, ta, dp, rl);\n if (s.cost < best.cost) best = s;\n }\n }\n \n // Random parameter exploration\n for (int seed = 100; seed < 200; seed++) {\n rng.seed(seed);\n int pw = 1 + rng() % 7;\n int ta = rng() % 5;\n int dp = 2 + rng() % 8;\n int rl = 1 + rng() % 5;\n State s(h); s.solve(pw, ta, dp, rl);\n if (s.cost < best.cost) best = s;\n }\n \n for (auto& op : best.ops) cout << op << \"\\n\";\n return 0;\n}","ahc035":"#include \n#include \n#include \n#include \n\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, T;\n cin >> N >> M >> T;\n\n int seed_count = 2 * N * (N - 1);\n vector> X(seed_count, vector(M, 0));\n\n for (int i = 0; i < seed_count; i++) {\n for (int j = 0; j < M; j++) {\n cin >> X[i][j];\n }\n }\n\n for (int t = 0; t < T; t++) {\n vector maxVal(M, 0);\n for (int l = 0; l < M; l++) {\n for (int i = 0; i < seed_count; i++) {\n maxVal[l] = max(maxVal[l], X[i][l]);\n }\n }\n \n auto getValue = [&](int idx) {\n int total = 0;\n for (int l = 0; l < M; l++) total += X[idx][l];\n return total;\n };\n \n auto getMaxCount = [&](int idx) {\n int cnt = 0;\n for (int l = 0; l < M; l++) {\n if (X[idx][l] == maxVal[l]) cnt++;\n }\n return cnt;\n };\n \n auto getMaxSum = [&](int idx) {\n int sum = 0;\n for (int l = 0; l < M; l++) {\n if (X[idx][l] == maxVal[l]) sum += X[idx][l];\n }\n return sum;\n };\n \n // Selection: include maxSum to prefer seeds with important max values\n vector> seed_scores(seed_count);\n for (int i = 0; i < seed_count; i++) {\n double score = getValue(i) + getMaxCount(i) * 1000.0 + getMaxSum(i) * 2.0;\n seed_scores[i] = {score, i};\n }\n \n sort(seed_scores.begin(), seed_scores.end(), greater>());\n \n vector selected(N * N);\n for (int i = 0; i < N * N; i++) {\n selected[i] = seed_scores[i].second;\n }\n \n // Placement: best formula from before\n sort(selected.begin(), selected.end(), [&](int a, int b) {\n double sa = getValue(a) + getMaxCount(a) * 400.0 + getMaxSum(a) * 2.0;\n double sb = getValue(b) + getMaxCount(b) * 400.0 + getMaxSum(b) * 2.0;\n if (sa != sb) return sa > sb;\n return getValue(a) > getValue(b);\n });\n \n vector> pos_order;\n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n pos_order.push_back({i, j});\n }\n }\n \n double cx = (N - 1) / 2.0;\n double cy = (N - 1) / 2.0;\n sort(pos_order.begin(), pos_order.end(), [&](auto& a, auto& b) {\n double da = abs(a.first - cx) + abs(a.second - cy);\n double db = abs(b.first - cx) + abs(b.second - cy);\n if (da != db) return da < db;\n if (a.first != b.first) return a.first < b.first;\n return a.second < b.second;\n });\n \n vector> A(N, vector(N, -1));\n for (int i = 0; i < N * N; i++) {\n A[pos_order[i].first][pos_order[i].second] = selected[i];\n }\n \n for (int i = 0; i < N; i++) {\n for (int j = 0; j < N; j++) {\n cout << A[i][j];\n if (j < N - 1) cout << \" \";\n else cout << \"\\n\";\n }\n }\n cout.flush();\n\n for (int i = 0; i < seed_count; i++) {\n for (int j = 0; j < M; j++) {\n cin >> X[i][j];\n }\n }\n }\n\n return 0;\n}","ahc038":"#include \nusing namespace std;\n\nint N, M, V;\nconst int DX[] = {0, 1, 0, -1};\nconst int DY[] = {1, 0, -1, 0};\n\nint rx, ry;\nvector dirs;\nvector lens;\nvector holding;\nint numF;\n\npair fingertip(int i) { \n return {rx + DX[dirs[i]] * lens[i], ry + DY[dirs[i]] * lens[i]}; \n}\nbool valid(int x, int y) { return x >= 0 && x < N && y >= 0 && y < N; }\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> M >> V;\n vector grid(N), target(N);\n for (int i = 0; i < N; i++) cin >> grid[i];\n for (int i = 0; i < N; i++) cin >> target[i];\n \n numF = V - 1;\n \n // Use varied edge lengths for better coverage\n lens.resize(numF);\n for (int i = 0; i < numF; i++) {\n lens[i] = min(i + 1, N - 1);\n }\n \n cout << numF + 1 << \"\\n\";\n for (int i = 0; i < numF; i++) cout << \"0 \" << lens[i] << \"\\n\";\n \n // Calculate centroid for better starting position\n set> pickup, dropS;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++) {\n if (grid[i][j] == '1' && target[i][j] == '0') pickup.insert({i, j});\n if (target[i][j] == '1' && grid[i][j] == '0') dropS.insert({i, j});\n }\n \n int sumX = 0, sumY = 0, cnt = 0;\n for (auto& p : pickup) { sumX += p.first; sumY += p.second; cnt++; }\n for (auto& p : dropS) { sumX += p.first; sumY += p.second; cnt++; }\n \n rx = cnt > 0 ? sumX / cnt : N / 2;\n ry = cnt > 0 ? sumY / cnt : N / 2;\n rx = max(0, min(N - 1, rx));\n ry = max(0, min(N - 1, ry));\n \n cout << rx << \" \" << ry << \"\\n\";\n \n dirs.assign(numF, 0);\n holding.assign(numF, false);\n \n vector ops;\n \n while (ops.size() < 95000 && (!pickup.empty() || !dropS.empty() || \n any_of(holding.begin(), holding.end(), [](bool h){return h;}))) {\n \n vector rot(numF, '.'), act(numF, '.');\n bool acted = false;\n \n for (int i = 0; i < numF; i++) {\n auto [fx, fy] = fingertip(i);\n if (!valid(fx, fy)) continue;\n if (!holding[i] && pickup.count({fx, fy})) {\n act[i] = 'P'; pickup.erase({fx, fy}); holding[i] = true; acted = true;\n } else if (holding[i] && dropS.count({fx, fy})) {\n act[i] = 'P'; dropS.erase({fx, fy}); holding[i] = false; acted = true;\n }\n }\n if (acted) {\n string s = \".\";\n for (int i = 0; i < numF; i++) s += '.';\n s += '.';\n for (int i = 0; i < numF; i++) s += act[i];\n ops.push_back(s);\n continue;\n }\n \n int bestF = -1, bestDir = 0, bestCost = INT_MAX;\n pair bestTarget;\n \n for (int i = 0; i < numF; i++) {\n auto& targets = holding[i] ? dropS : pickup;\n if (targets.empty()) continue;\n \n for (auto& t : targets) {\n for (int d = 0; d < 4; d++) {\n int nrx = t.first - DX[d] * lens[i];\n int nry = t.second - DY[d] * lens[i];\n if (!valid(nrx, nry)) continue;\n int diff = (d - dirs[i] + 4) % 4;\n int rotCost = min(diff, 4 - diff);\n int cost = abs(nrx - rx) + abs(nry - ry) + rotCost;\n if (cost < bestCost) {\n bestCost = cost; bestF = i;\n bestTarget = t; bestDir = d;\n }\n }\n }\n }\n \n if (bestF == -1) break;\n \n int trx = bestTarget.first - DX[bestDir] * lens[bestF];\n int tr_y = bestTarget.second - DY[bestDir] * lens[bestF];\n char mv = '.';\n \n if (rx < trx && valid(rx + 1, ry)) { mv = 'D'; rx++; }\n else if (rx > trx && valid(rx - 1, ry)) { mv = 'U'; rx--; }\n else if (ry < tr_y && valid(rx, ry + 1)) { mv = 'R'; ry++; }\n else if (ry > tr_y && valid(rx, ry - 1)) { mv = 'L'; ry--; }\n \n if (dirs[bestF] != bestDir) {\n int diff = (bestDir - dirs[bestF] + 4) % 4;\n if (diff == 1) { rot[bestF] = 'R'; dirs[bestF] = (dirs[bestF] + 1) % 4; }\n else if (diff == 3) { rot[bestF] = 'L'; dirs[bestF] = (dirs[bestF] + 3) % 4; }\n else { rot[bestF] = 'R'; dirs[bestF] = (dirs[bestF] + 1) % 4; }\n }\n \n if (mv == '.' && rot[bestF] == '.') {\n if (valid(rx + 1, ry)) { mv = 'D'; rx++; }\n else if (valid(rx - 1, ry)) { mv = 'U'; rx--; }\n else if (valid(rx, ry + 1)) { mv = 'R'; ry++; }\n else if (valid(rx, ry - 1)) { mv = 'L'; ry--; }\n else { rot[bestF] = 'R'; dirs[bestF] = (dirs[bestF] + 1) % 4; }\n }\n \n string s; s += mv;\n for (int i = 0; i < numF; i++) s += rot[i];\n s += '.';\n for (int i = 0; i < numF; i++) s += act[i];\n ops.push_back(s);\n }\n \n for (auto& op : ops) cout << op << \"\\n\";\n return 0;\n}","ahc039":"#include \nusing namespace std;\n\nint nx, ny;\nvector xs, ys;\nvector> grid;\n\nint query(int y1, int x1, int y2, int x2) {\n if (x1 > x2 || y1 > y2) return 0;\n return grid[y2+1][x2+1] - grid[y1][x2+1] - grid[y2+1][x1] + grid[y1][x1];\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N; cin >> N;\n vector> mackerel(N), sardine(N);\n for (int i = 0; i < N; i++) cin >> mackerel[i].first >> mackerel[i].second;\n for (int i = 0; i < N; i++) cin >> sardine[i].first >> sardine[i].second;\n \n for (auto& p : mackerel) { xs.push_back(p.first); ys.push_back(p.second); }\n for (auto& p : sardine) { xs.push_back(p.first); ys.push_back(p.second); }\n \n sort(xs.begin(), xs.end()); xs.erase(unique(xs.begin(), xs.end()), xs.end());\n sort(ys.begin(), ys.end()); ys.erase(unique(ys.begin(), ys.end()), ys.end());\n \n nx = xs.size(); ny = ys.size();\n map x_idx, y_idx;\n for (int i = 0; i < nx; i++) x_idx[xs[i]] = i;\n for (int i = 0; i < ny; i++) y_idx[ys[i]] = i;\n \n grid.assign(ny+1, vector(nx+1, 0));\n for (auto& p : mackerel) grid[y_idx[p.second]+1][x_idx[p.first]+1]++;\n for (auto& p : sardine) grid[y_idx[p.second]+1][x_idx[p.first]+1]--;\n for (int i = 1; i <= ny; i++)\n for (int j = 1; j <= nx; j++)\n grid[i][j] += grid[i-1][j] + grid[i][j-1] - grid[i-1][j-1];\n \n int best_score = 0, bx1 = 0, by1 = 0, bx2 = 0, by2 = 0;\n int best_type = 0, best_c1 = -1, best_c2 = -1;\n int best_cx[4], best_cy[4];\n \n for (int seed = 1; seed <= 8; seed++) {\n mt19937 rng(seed * 41 + 17);\n vector> candidates;\n int init_best = 0;\n \n for (int iter = 0; iter < 280000; iter++) {\n int i1 = rng() % N, i2 = rng() % N;\n int x1i = x_idx[mackerel[i1].first], y1i = y_idx[mackerel[i1].second];\n int x2i = x_idx[mackerel[i2].first], y2i = y_idx[mackerel[i2].second];\n if (x1i > x2i) swap(x1i, x2i); if (y1i > y2i) swap(y1i, y2i);\n int score = query(y1i, x1i, y2i, x2i);\n if (score > init_best - 150) candidates.push_back({score, x1i, y1i, x2i, y2i});\n if (score > init_best) init_best = score;\n }\n \n sort(candidates.rbegin(), candidates.rend());\n if (candidates.size() > 30) candidates.resize(30);\n \n for (auto& [sc, rx1, ry1, rx2, ry2] : candidates) {\n int cx1 = rx1, cy1 = ry1, cx2 = rx2, cy2 = ry2;\n for (int round = 0; round < 3; round++) {\n for (int x = 0; x <= cx2; x++) if (query(cy1, x, cy2, cx2) > query(cy1, cx1, cy2, cx2)) cx1 = x;\n for (int x = cx1; x < nx; x++) if (query(cy1, cx1, cy2, x) > query(cy1, cx1, cy2, cx2)) cx2 = x;\n for (int y = 0; y <= cy2; y++) if (query(y, cx1, cy2, cx2) > query(cy1, cx1, cy2, cx2)) cy1 = y;\n for (int y = cy1; y < ny; y++) if (query(cy1, cx1, y, cx2) > query(cy1, cx1, cy2, cx2)) cy2 = y;\n }\n int rect_score = query(cy1, cx1, cy2, cx2);\n if (rect_score > best_score) { best_score = rect_score; bx1 = cx1; by1 = cy1; bx2 = cx2; by2 = cy2; best_type = 0; }\n \n if (cx2 > cx1 + 1 && cy2 > cy1 + 1) {\n int cut_imp[4] = {0,0,0,0}, cut_cx[4], cut_cy[4];\n for (int iter = 0; iter < 3000; iter++) {\n int c = rng() % 4;\n int ccx = cx1 + 1 + rng() % (cx2 - cx1 - 1);\n int ccy = cy1 + 1 + rng() % (cy2 - cy1 - 1);\n int cut = 0;\n if (c == 0) cut = query(cy1, cx1, ccy-1, ccx-1);\n else if (c == 1) cut = query(cy1, ccx+1, ccy-1, cx2);\n else if (c == 2) cut = query(ccy+1, ccx+1, cy2, cx2);\n else cut = query(ccy+1, cx1, cy2, ccx-1);\n if (-cut > cut_imp[c]) { cut_imp[c] = -cut; cut_cx[c] = ccx; cut_cy[c] = ccy; }\n }\n \n for (int c = 0; c < 4; c++)\n if (rect_score + cut_imp[c] > best_score) {\n best_score = rect_score + cut_imp[c]; bx1 = cx1; by1 = cy1; bx2 = cx2; by2 = cy2;\n best_type = 1; best_c1 = c;\n for (int i = 0; i < 4; i++) { best_cx[i] = cut_cx[i]; best_cy[i] = cut_cy[i]; }\n }\n \n if (cut_imp[0] > 0 && cut_imp[2] > 0 && cut_cx[0] < cut_cx[2] && cut_cy[0] < cut_cy[2])\n if (rect_score + cut_imp[0] + cut_imp[2] > best_score) {\n best_score = rect_score + cut_imp[0] + cut_imp[2]; bx1 = cx1; by1 = cy1; bx2 = cx2; by2 = cy2;\n best_type = 2; best_c1 = 0; best_c2 = 2;\n for (int i = 0; i < 4; i++) { best_cx[i] = cut_cx[i]; best_cy[i] = cut_cy[i]; }\n }\n if (cut_imp[1] > 0 && cut_imp[3] > 0 && cut_cx[3] < cut_cx[1] && cut_cy[1] < cut_cy[3])\n if (rect_score + cut_imp[1] + cut_imp[3] > best_score) {\n best_score = rect_score + cut_imp[1] + cut_imp[3]; bx1 = cx1; by1 = cy1; bx2 = cx2; by2 = cy2;\n best_type = 2; best_c1 = 1; best_c2 = 3;\n for (int i = 0; i < 4; i++) { best_cx[i] = cut_cx[i]; best_cy[i] = cut_cy[i]; }\n }\n }\n }\n }\n \n if (best_score <= 0) { cout << \"4\\n0 0\\n1 0\\n1 1\\n0 1\\n\"; return 0; }\n int ox1 = xs[bx1], oy1 = ys[by1], ox2 = xs[bx2], oy2 = ys[by2];\n \n if (best_type == 0) cout << \"4\\n\" << ox1 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy2 << \"\\n\" << ox1 << \" \" << oy2 << \"\\n\";\n else if (best_type == 1) {\n int ocx = xs[best_cx[best_c1]], ocy = ys[best_cy[best_c1]];\n cout << \"6\\n\";\n if (best_c1 == 0) cout << ocx << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy2 << \"\\n\" << ox1 << \" \" << oy2 << \"\\n\" << ox1 << \" \" << ocy << \"\\n\" << ocx << \" \" << ocy << \"\\n\";\n else if (best_c1 == 1) cout << ox1 << \" \" << oy1 << \"\\n\" << ocx << \" \" << oy1 << \"\\n\" << ocx << \" \" << ocy << \"\\n\" << ox2 << \" \" << ocy << \"\\n\" << ox2 << \" \" << oy2 << \"\\n\" << ox1 << \" \" << oy2 << \"\\n\";\n else if (best_c1 == 2) cout << ox1 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << ocy << \"\\n\" << ocx << \" \" << ocy << \"\\n\" << ocx << \" \" << oy2 << \"\\n\" << ox1 << \" \" << oy2 << \"\\n\";\n else cout << ox1 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy2 << \"\\n\" << ocx << \" \" << oy2 << \"\\n\" << ocx << \" \" << ocy << \"\\n\" << ox1 << \" \" << ocy << \"\\n\";\n } else {\n int ocx0 = xs[best_cx[best_c1]], ocy0 = ys[best_cy[best_c1]], ocx2 = xs[best_cx[best_c2]], ocy2 = ys[best_cy[best_c2]];\n cout << \"8\\n\";\n if (best_c1 == 0) cout << ocx0 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << oy1 << \"\\n\" << ox2 << \" \" << ocy2 << \"\\n\" << ocx2 << \" \" << ocy2 << \"\\n\" << ocx2 << \" \" << oy2 << \"\\n\" << ox1 << \" \" << oy2 << \"\\n\" << ox1 << \" \" << ocy0 << \"\\n\" << ocx0 << \" \" << ocy0 << \"\\n\";\n else cout << ox1 << \" \" << oy1 << \"\\n\" << ocx0 << \" \" << oy1 << \"\\n\" << ocx0 << \" \" << ocy0 << \"\\n\" << ox2 << \" \" << ocy0 << \"\\n\" << ox2 << \" \" << oy2 << \"\\n\" << ocx2 << \" \" << oy2 << \"\\n\" << ocx2 << \" \" << ocy2 << \"\\n\" << ox1 << \" \" << ocy2 << \"\\n\";\n }\n return 0;\n}","ahc040":"#include \nusing namespace std;\n\nint N, T;\nlong long sigma;\nvector w, h;\n\nstruct PlacedRect { long long x1, y1, x2, y2; int id; };\n\npair simulate(const vector>& ops) {\n vector placed;\n long long W = 0, H = 0;\n for (auto& [p, r, d, b] : ops) {\n long long rw = w[p], rh = h[p];\n if (r) swap(rw, rh);\n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n placed.push_back({x, y, x + rw, y + rh, p});\n W = max(W, x + rw); H = max(H, y + rh);\n }\n return {W, H};\n}\n\nmt19937 rng(42);\n\nvector> genGreedy(double wBias, int maxBase = 15) {\n vector> ops;\n vector placed;\n long long curW = 0, curH = 0;\n \n for (int i = 0; i < N; i++) {\n double best = 1e18; \n tuple bc = {0,'U',-1};\n \n for (int r = 0; r < 2; r++) {\n long long rw = w[i], rh = h[i]; \n if (r) swap(rw, rh);\n \n for (char d : {'U','L'}) {\n for (int b = -1; b < i; b++) {\n if (b >= 0 && i - b > maxBase) continue;\n \n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n double sc = wBias * max(curW, x+rw) + max(curH, y+rh);\n if (sc < best) { best = sc; bc = {r, d, b}; }\n }\n }\n }\n \n auto [r, d, b] = bc;\n long long rw = w[i], rh = h[i]; if (r) swap(rw, rh);\n long long x = 0, y = 0;\n if (d == 'U') {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { x = pr.x2; break; }\n for (auto& pr : placed) if (x < pr.x2 && x + rw > pr.x1) y = max(y, pr.y2);\n } else {\n if (b >= 0) for (auto& pr : placed) if (pr.id == b) { y = pr.y2; break; }\n for (auto& pr : placed) if (y < pr.y2 && y + rh > pr.y1) x = max(x, pr.x2);\n }\n placed.push_back({x, y, x+rw, y+rh, i}); \n curW = max(curW, x+rw); curH = max(curH, y+rh);\n ops.push_back({i, r, d, b});\n }\n return ops;\n}\n\nvector> genShelf(double widthFactor, int rotMode) {\n long long totalArea = 0;\n for (int i = 0; i < N; i++) totalArea += w[i] * h[i];\n long long targetW = max(1LL, (long long)(sqrt((double)totalArea) * widthFactor));\n \n vector> ops;\n long long curX = 0;\n int lastInShelf = -1, shelfStart = -1;\n \n for (int i = 0; i < N; i++) {\n int r = (rotMode == 0) ? 0 : (rotMode == 1) ? 1 : (h[i] > w[i] ? 1 : 0);\n long long rw = w[i], rh = h[i]; if (r) swap(rw, rh);\n \n if (curX + rw > targetW && lastInShelf >= 0) {\n ops.push_back({i, r, 'L', shelfStart});\n shelfStart = i; curX = rw; lastInShelf = i;\n } else {\n if (lastInShelf < 0) {\n ops.push_back({i, r, 'U', -1});\n shelfStart = i;\n } else {\n ops.push_back({i, r, 'U', lastInShelf});\n }\n curX += rw; lastInShelf = i;\n }\n }\n return ops;\n}\n\nvector> genStrip(char dir, int rotMode) {\n vector> ops;\n for (int i = 0; i < N; i++) {\n int r = (rotMode == 0) ? 0 : (rotMode == 1) ? 1 : \n ((dir == 'U') ? (w[i] < h[i] ? 1 : 0) : (h[i] < w[i] ? 1 : 0));\n ops.push_back({i, r, dir, -1});\n }\n return ops;\n}\n\nvector> mutate(vector> ops, int intensity) {\n int numMut = 1 + rng() % (intensity + 1);\n for (int m = 0; m < numMut; m++) {\n int i = rng() % N;\n auto& [p, r, d, b] = ops[i];\n int choice = rng() % 3;\n if (choice == 0) r = 1 - r;\n else if (choice == 1) d = (d == 'U') ? 'L' : 'U';\n else if (i > 0) b = (int)(rng() % (i + 1)) - 1;\n }\n return ops;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> T >> sigma;\n w.resize(N); h.resize(N);\n for (int i = 0; i < N; i++) cin >> w[i] >> h[i];\n \n auto startTime = chrono::steady_clock::now();\n vector>>> candidates;\n \n auto addCandidate = [&](vector> ops) {\n auto [sw, sh] = simulate(ops);\n candidates.push_back({sw + sh, ops});\n };\n \n // Diverse greedy with different biases\n for (double bias : {0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.5, 2.0}) {\n addCandidate(genGreedy(bias));\n }\n \n // Shelf packing with different widths\n for (double wf : {0.6, 0.8, 1.0, 1.2, 1.5, 2.0}) {\n for (int rm = 0; rm < 3; rm++) {\n addCandidate(genShelf(wf, rm));\n }\n }\n \n // Strip packing\n for (char d : {'U', 'L'}) {\n for (int rm = 0; rm < 3; rm++) {\n addCandidate(genStrip(d, rm));\n }\n }\n \n sort(candidates.begin(), candidates.end());\n auto bestOps = candidates[0].second;\n long long bestSim = candidates[0].first;\n \n // Hill climbing with time limit\n while (true) {\n auto now = chrono::steady_clock::now();\n if (chrono::duration_cast(now - startTime).count() > 2500) break;\n if ((int)candidates.size() >= T * 3) break;\n \n int srcIdx = (rng() % 100 < 70) ? 0 : rng() % min((int)candidates.size(), 10);\n int intensity = 1 + (rng() % 3);\n auto ops = mutate(candidates[srcIdx].second, intensity);\n auto [sw, sh] = simulate(ops);\n \n if (sw + sh <= bestSim * 1.05) {\n candidates.push_back({sw + sh, ops});\n if (sw + sh < bestSim) { \n bestSim = sw + sh; \n bestOps = ops;\n }\n }\n }\n \n sort(candidates.begin(), candidates.end());\n \n // Remove duplicates\n vector>>> unique_cands;\n set>> seen;\n for (auto& c : candidates) {\n if (seen.find(c.second) == seen.end()) {\n seen.insert(c.second);\n unique_cands.push_back(c);\n }\n if ((int)unique_cands.size() >= T) break;\n }\n candidates = unique_cands;\n \n // Fill remaining slots\n while ((int)candidates.size() < T) {\n auto ops = mutate(bestOps, 2);\n auto [sw, sh] = simulate(ops);\n candidates.push_back({sw + sh, ops});\n }\n \n sort(candidates.begin(), candidates.end());\n \n for (int t = 0; t < T; t++) {\n auto& ops = candidates[t].second;\n cout << ops.size() << \"\\n\";\n for (auto& [p, r, d, b] : ops) cout << p << \" \" << r << \" \" << d << \" \" << b << \"\\n\";\n cout.flush();\n long long W, H; cin >> W >> H;\n }\n \n return 0;\n}","ahc041":"#include \nusing namespace std;\n\nint N, M, H;\nvector A;\nvector> adj;\nvector parent_arr;\nvector depth_arr;\nvector> children;\nvector sub_h;\nvector sub_sum;\nmt19937 rng(42);\n\nchrono::steady_clock::time_point start_time;\nint elapsed() {\n return chrono::duration_cast(\n chrono::steady_clock::now() - start_time).count();\n}\n\nlong long compute_score() {\n long long score = 0;\n for (int i = 0; i < N; i++) {\n score += (long long)(depth_arr[i] + 1) * A[i];\n }\n return score;\n}\n\nvoid rebuild_all() {\n for (int i = 0; i < N; i++) children[i].clear();\n for (int i = 0; i < N; i++) {\n if (parent_arr[i] != -1) {\n children[parent_arr[i]].push_back(i);\n }\n }\n \n fill(depth_arr.begin(), depth_arr.end(), -1);\n queue q;\n for (int i = 0; i < N; i++) {\n if (parent_arr[i] == -1) {\n depth_arr[i] = 0;\n q.push(i);\n }\n }\n while (!q.empty()) {\n int u = q.front(); q.pop();\n for (int c : children[u]) {\n depth_arr[c] = depth_arr[u] + 1;\n q.push(c);\n }\n }\n \n function(int)> calc = [&](int v) -> pair {\n int h = 0, s = A[v];\n for (int c : children[v]) {\n auto [ch, cs] = calc(c);\n h = max(h, 1 + ch);\n s += cs;\n }\n sub_h[v] = h;\n sub_sum[v] = s;\n return {h, s};\n };\n for (int i = 0; i < N; i++) {\n if (parent_arr[i] == -1) calc(i);\n }\n}\n\nvoid dfs(int u) {\n vector> neighbors;\n for (int v : adj[u]) {\n if (depth_arr[v] == -1) {\n neighbors.push_back({-A[v], v});\n }\n }\n sort(neighbors.begin(), neighbors.end());\n \n for (auto& [neg_beauty, v] : neighbors) {\n if (depth_arr[v] == -1 && depth_arr[u] < H) {\n parent_arr[v] = u;\n depth_arr[v] = depth_arr[u] + 1;\n dfs(v);\n }\n }\n}\n\nbool is_ancestor(int anc, int desc) {\n for (int i = 0; i <= H && desc != -1; i++) {\n if (desc == anc) return true;\n desc = parent_arr[desc];\n }\n return false;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n start_time = chrono::steady_clock::now();\n \n cin >> N >> M >> H;\n \n A.resize(N);\n for (int i = 0; i < N; i++) cin >> A[i];\n \n adj.resize(N);\n for (int i = 0; i < M; i++) {\n int u, v;\n cin >> u >> v;\n adj[u].push_back(v);\n adj[v].push_back(u);\n }\n \n for (int i = 0; i < N; i++) {\n int x, y;\n cin >> x >> y;\n }\n \n parent_arr.resize(N);\n depth_arr.resize(N);\n children.resize(N);\n sub_h.resize(N);\n sub_sum.resize(N);\n \n vector best_parent(N, -1);\n long long best_score = 0;\n \n // Multiple restarts with diverse strategies\n for (int trial = 0; trial < 800 && elapsed() < 500; trial++) {\n fill(parent_arr.begin(), parent_arr.end(), -1);\n fill(depth_arr.begin(), depth_arr.end(), -1);\n \n vector order(N);\n iota(order.begin(), order.end(), 0);\n \n if (trial == 0) {\n sort(order.begin(), order.end(), [&](int a, int b) { return A[a] < A[b]; });\n } else if (trial == 1) {\n sort(order.begin(), order.end(), [&](int a, int b) { return adj[a].size() < adj[b].size(); });\n } else if (trial == 2) {\n sort(order.begin(), order.end(), [&](int a, int b) { \n return A[a] * (int)adj[a].size() < A[b] * (int)adj[b].size(); \n });\n } else if (trial == 3) {\n sort(order.begin(), order.end(), [&](int a, int b) { \n return (double)A[a] / adj[a].size() < (double)A[b] / adj[b].size(); \n });\n } else {\n vector keys(N);\n for (int i = 0; i < N; i++) keys[i] = A[i] + (rng() % 100);\n sort(order.begin(), order.end(), [&](int a, int b) { return keys[a] < keys[b]; });\n }\n \n for (int start : order) {\n if (depth_arr[start] != -1) continue;\n depth_arr[start] = 0;\n parent_arr[start] = -1;\n dfs(start);\n }\n \n long long score = compute_score();\n if (score > best_score) {\n best_score = score;\n best_parent = parent_arr;\n }\n }\n \n parent_arr = best_parent;\n rebuild_all();\n \n // Local search with persistence\n vector vorder(N);\n iota(vorder.begin(), vorder.end(), 0);\n \n int no_improve_count = 0;\n for (int phase = 0; phase < 1000 && elapsed() < 1850; phase++) {\n bool improved = false;\n \n int strategy = phase % 6;\n if (strategy == 0) {\n sort(vorder.begin(), vorder.end(), [&](int a, int b) { return A[a] > A[b]; });\n } else if (strategy == 1) {\n sort(vorder.begin(), vorder.end(), [&](int a, int b) { return depth_arr[a] < depth_arr[b]; });\n } else if (strategy == 2) {\n sort(vorder.begin(), vorder.end(), [&](int a, int b) { \n return A[a] * (H - depth_arr[a]) > A[b] * (H - depth_arr[b]); \n });\n } else if (strategy == 3) {\n sort(vorder.begin(), vorder.end(), [&](int a, int b) { return sub_sum[a] > sub_sum[b]; });\n } else if (strategy == 4) {\n sort(vorder.begin(), vorder.end(), [&](int a, int b) { return A[a] < A[b]; }); // Low beauty first\n } else {\n shuffle(vorder.begin(), vorder.end(), rng);\n }\n \n // Operation 1: Reparent to go deeper\n for (int v : vorder) {\n if (elapsed() > 1850) break;\n \n int cur_depth = depth_arr[v];\n int best_new_parent = -1;\n int best_gain = 0;\n \n for (int u : adj[v]) {\n if (u == parent_arr[v]) continue;\n if (is_ancestor(v, u)) continue;\n \n int new_depth = depth_arr[u] + 1;\n if (new_depth + sub_h[v] <= H && new_depth > cur_depth) {\n int total_gain = (new_depth - cur_depth) * sub_sum[v];\n if (total_gain > best_gain) {\n best_gain = total_gain;\n best_new_parent = u;\n }\n }\n }\n \n if (best_new_parent != -1) {\n parent_arr[v] = best_new_parent;\n rebuild_all();\n improved = true;\n }\n }\n \n // Operation 2: Attach roots\n for (int r : vorder) {\n if (elapsed() > 1850) break;\n if (parent_arr[r] != -1) continue;\n \n int best_p = -1;\n int best_gain = 0;\n \n for (int u : adj[r]) {\n int new_depth = depth_arr[u] + 1;\n if (new_depth + sub_h[r] <= H) {\n int gain = new_depth * sub_sum[r];\n if (gain > best_gain) {\n best_gain = gain;\n best_p = u;\n }\n }\n }\n \n if (best_p != -1) {\n parent_arr[r] = best_p;\n rebuild_all();\n improved = true;\n }\n }\n \n long long cur_score = compute_score();\n if (cur_score > best_score) {\n best_score = cur_score;\n best_parent = parent_arr;\n no_improve_count = 0;\n } else {\n no_improve_count++;\n }\n \n // Allow more phases even without improvement\n if (!improved) {\n if (no_improve_count > 12) break;\n }\n }\n \n for (int i = 0; i < N; i++) {\n cout << best_parent[i];\n if (i < N - 1) cout << \" \";\n }\n cout << \"\\n\";\n \n return 0;\n}","ahc042":"#include \nusing namespace std;\n\nint N, M;\nint oni_r[50], oni_c[50];\nint valid_cnt[50], valid[50][4], dist[50][4];\nint asgn[50], batch_max[80];\n\ninline int get_key(int k, int d) { return d * 20 + ((d <= 1) ? oni_c[k] : oni_r[k]); }\n\nint full_cost() {\n memset(batch_max, 0, sizeof(batch_max));\n for (int k = 0; k < M; k++) {\n int key = get_key(k, asgn[k]);\n batch_max[key] = max(batch_max[key], dist[k][asgn[k]]);\n }\n int t = 0; for (int i = 0; i < 80; i++) t += batch_max[i];\n return 2 * t;\n}\n\nint try_change(int k, int new_d) {\n int old_d = asgn[k];\n if (old_d == new_d) return 0;\n int old_key = get_key(k, old_d), new_key = get_key(k, new_d);\n int old_cost = 2 * (batch_max[old_key] + batch_max[new_key]);\n \n int new_old_max = 0;\n for (int i = 0; i < M; i++) if (i != k && get_key(i, asgn[i]) == old_key)\n new_old_max = max(new_old_max, dist[i][asgn[i]]);\n int new_new_max = max(batch_max[new_key], dist[k][new_d]);\n \n return 2 * (new_old_max + new_new_max) - old_cost;\n}\n\nvoid apply_change(int k, int new_d) {\n int old_key = get_key(k, asgn[k]), new_key = get_key(k, new_d);\n asgn[k] = new_d;\n int new_old_max = 0;\n for (int i = 0; i < M; i++) if (get_key(i, asgn[i]) == old_key)\n new_old_max = max(new_old_max, dist[i][asgn[i]]);\n batch_max[old_key] = new_old_max;\n batch_max[new_key] = max(batch_max[new_key], dist[k][new_d]);\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n auto start = chrono::steady_clock::now();\n auto elapsed = [&]() { return chrono::duration(chrono::steady_clock::now() - start).count(); };\n \n cin >> N;\n vector board(N);\n for (int i = 0; i < N; i++) cin >> board[i];\n \n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (board[i][j] == 'x') {\n oni_r[M] = i; oni_c[M] = j; M++;\n }\n \n for (int k = 0; k < M; k++) {\n int r = oni_r[k], c = oni_c[k];\n bool ok = true; for (int i = 0; i < r && ok; i++) if (board[i][c] == 'o') ok = false;\n if (ok) { valid[k][valid_cnt[k]] = 0; dist[k][0] = r + 1; valid_cnt[k]++; }\n ok = true; for (int i = r+1; i < N && ok; i++) if (board[i][c] == 'o') ok = false;\n if (ok) { valid[k][valid_cnt[k]] = 1; dist[k][1] = N - r; valid_cnt[k]++; }\n ok = true; for (int j = 0; j < c && ok; j++) if (board[r][j] == 'o') ok = false;\n if (ok) { valid[k][valid_cnt[k]] = 2; dist[k][2] = c + 1; valid_cnt[k]++; }\n ok = true; for (int j = c+1; j < N && ok; j++) if (board[r][j] == 'o') ok = false;\n if (ok) { valid[k][valid_cnt[k]] = 3; dist[k][3] = N - c; valid_cnt[k]++; }\n }\n \n mt19937 rng(42);\n int best_asgn[50], best_cost = INT_MAX;\n \n auto local_search = [&]() {\n int cur = full_cost();\n for (int it = 0; it < 30; it++) {\n bool imp = false;\n for (int k = 0; k < M; k++) for (int vi = 0; vi < valid_cnt[k]; vi++) {\n int d = valid[k][vi]; if (d == asgn[k]) continue;\n int delta = try_change(k, d);\n if (delta < 0) { apply_change(k, d); cur += delta; imp = true; }\n }\n if (!imp) break;\n }\n if (cur < best_cost) { best_cost = cur; memcpy(best_asgn, asgn, sizeof(asgn)); }\n };\n \n // Initial: minimum individual distance\n for (int k = 0; k < M; k++) {\n int bd = valid[k][0];\n for (int vi = 0; vi < valid_cnt[k]; vi++) if (dist[k][valid[k][vi]] < dist[k][bd]) bd = valid[k][vi];\n asgn[k] = bd;\n }\n local_search();\n \n // Prefer each direction\n for (int p = 0; p < 4; p++) {\n for (int k = 0; k < M; k++) {\n asgn[k] = valid[k][0];\n for (int vi = 0; vi < valid_cnt[k]; vi++) if (valid[k][vi] == p) { asgn[k] = p; break; }\n }\n local_search();\n }\n \n // Greedy incremental\n vector order(M); iota(order.begin(), order.end(), 0);\n for (int t = 0; t < 30 && elapsed() < 0.3; t++) {\n shuffle(order.begin(), order.end(), rng);\n memset(asgn, -1, sizeof(asgn)); memset(batch_max, 0, sizeof(batch_max));\n for (int k : order) {\n int bd = valid[k][0], bc = INT_MAX;\n for (int vi = 0; vi < valid_cnt[k]; vi++) {\n int d = valid[k][vi], key = get_key(k, d);\n int add = max(0, dist[k][d] - batch_max[key]);\n if (add < bc) { bc = add; bd = d; }\n }\n asgn[k] = bd; batch_max[get_key(k, bd)] = max(batch_max[get_key(k, bd)], dist[k][bd]);\n }\n local_search();\n }\n \n // SA with restarts\n memcpy(asgn, best_asgn, sizeof(asgn)); full_cost();\n int cur_cost = best_cost;\n double temp = 10.0;\n int no_improve = 0;\n while (elapsed() < 1.9) {\n int k = rng() % M;\n if (valid_cnt[k] <= 1) continue;\n int new_d = valid[k][rng() % valid_cnt[k]];\n if (new_d == asgn[k]) continue;\n int delta = try_change(k, new_d);\n if (delta < 0 || (rng() % 10000) < 10000 * exp(-delta / temp)) {\n apply_change(k, new_d); cur_cost += delta;\n if (cur_cost < best_cost) { best_cost = cur_cost; memcpy(best_asgn, asgn, sizeof(asgn)); no_improve = 0; }\n else no_improve++;\n } else no_improve++;\n temp *= 0.999995;\n if (no_improve > 50000) { memcpy(asgn, best_asgn, sizeof(asgn)); full_cost(); cur_cost = best_cost; temp = 5.0; no_improve = 0; }\n }\n \n map batches;\n for (int k = 0; k < M; k++) batches[get_key(k, best_asgn[k])] = max(batches[get_key(k, best_asgn[k])], dist[k][best_asgn[k]]);\n \n for (auto& [key, mx] : batches) {\n int dir = key / 20, idx = key % 20;\n char c1 = (dir == 0 ? 'U' : dir == 1 ? 'D' : dir == 2 ? 'L' : 'R');\n char c2 = (dir == 0 ? 'D' : dir == 1 ? 'U' : dir == 2 ? 'R' : 'L');\n for (int t = 0; t < mx; t++) cout << c1 << \" \" << idx << \"\\n\";\n for (int t = 0; t < mx; t++) cout << c2 << \" \" << idx << \"\\n\";\n }\n return 0;\n}","ahc044":"#include \nusing namespace std;\n\nint N, L;\nvector T;\n\nlong long simulate(const vector& a, const vector& b, vector& t) {\n fill(t.begin(), t.end(), 0);\n int x = 0;\n for (int week = 0; week < L; week++) {\n t[x]++;\n x = (t[x] & 1) ? a[x] : b[x];\n }\n long long error = 0;\n for (int i = 0; i < N; i++) error += abs(t[i] - T[i]);\n return error;\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n cin >> N >> L;\n T.resize(N);\n for (int i = 0; i < N; i++) cin >> T[i];\n \n vector weighted;\n for (int i = 0; i < N; i++) {\n int cnt = max(1, T[i] / 100);\n for (int j = 0; j < cnt; j++) weighted.push_back(i);\n }\n \n vector sorted_idx(N);\n iota(sorted_idx.begin(), sorted_idx.end(), 0);\n sort(sorted_idx.begin(), sorted_idx.end(), [](int x, int y) { return T[x] > T[y]; });\n \n vector best_a(N), best_b(N), t(N);\n long long global_best = LLONG_MAX;\n \n auto start = chrono::steady_clock::now();\n double sa_time_limit = 1.60;\n \n vector seeds = {12345, 67890, 11111, 99999};\n for (int seed : seeds) {\n mt19937 rng(seed);\n \n for (int restart = 0; ; restart++) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > sa_time_limit) break;\n \n vector a(N), b(N);\n \n if (restart == 0) {\n for (int i = 0; i < N; i++) {\n a[sorted_idx[i]] = sorted_idx[(i + 1) % N];\n b[sorted_idx[i]] = sorted_idx[(i + 1) % N];\n }\n } else if (restart == 1) {\n for (int i = 0; i < N; i++) {\n a[sorted_idx[i]] = sorted_idx[(i + 1) % N];\n b[sorted_idx[i]] = sorted_idx[(i + 2) % N];\n }\n } else if (restart % 3 == 0 && global_best < LLONG_MAX) {\n a = best_a; b = best_b;\n for (int k = 0; k < N/4; k++) {\n int idx = rng() % N;\n a[idx] = weighted[rng() % weighted.size()];\n b[idx] = weighted[rng() % weighted.size()];\n }\n } else {\n for (int i = 0; i < N; i++) {\n a[i] = weighted[rng() % weighted.size()];\n b[i] = weighted[rng() % weighted.size()];\n }\n }\n \n long long cur_error = simulate(a, b, t);\n long long local_best = cur_error;\n vector local_a = a, local_b = b;\n \n double restart_budget = min(0.22, (sa_time_limit - elapsed) * 0.6);\n double restart_start = elapsed;\n \n while (true) {\n now = chrono::steady_clock::now();\n elapsed = chrono::duration(now - start).count();\n if (elapsed > sa_time_limit || elapsed - restart_start > restart_budget) break;\n \n double progress = (elapsed - restart_start) / restart_budget;\n double temp = 2500.0 * pow(0.0001, progress);\n \n int i = rng() % N;\n int old_a = a[i], old_b = b[i];\n \n int choice = rng() % 4;\n if (choice == 0) a[i] = weighted[rng() % weighted.size()];\n else if (choice == 1) b[i] = weighted[rng() % weighted.size()];\n else if (choice == 2) a[i] = rng() % N;\n else b[i] = rng() % N;\n \n long long new_error = simulate(a, b, t);\n double delta = new_error - cur_error;\n \n if (delta <= 0 || exp(-delta / temp) > (rng() % 1000000) / 1000000.0) {\n cur_error = new_error;\n if (new_error < local_best) {\n local_best = new_error;\n local_a = a; local_b = b;\n }\n } else {\n a[i] = old_a; b[i] = old_b;\n }\n }\n \n if (local_best < global_best) {\n global_best = local_best;\n best_a = local_a; best_b = local_b;\n }\n }\n }\n \n // Extended greedy hill climbing with single seed\n mt19937 rng(777);\n while (true) {\n auto now = chrono::steady_clock::now();\n double elapsed = chrono::duration(now - start).count();\n if (elapsed > 1.97) break;\n \n int i = rng() % N;\n int old_a = best_a[i], old_b = best_b[i];\n \n int choice = rng() % 5;\n if (choice == 0) best_a[i] = weighted[rng() % weighted.size()];\n else if (choice == 1) best_b[i] = weighted[rng() % weighted.size()];\n else if (choice == 2) best_a[i] = rng() % N;\n else if (choice == 3) best_b[i] = rng() % N;\n else { best_a[i] = weighted[rng() % weighted.size()]; best_b[i] = weighted[rng() % weighted.size()]; }\n \n long long new_error = simulate(best_a, best_b, t);\n if (new_error < global_best) {\n global_best = new_error;\n } else {\n best_a[i] = old_a; best_b[i] = old_b;\n }\n }\n \n for (int i = 0; i < N; i++) cout << best_a[i] << \" \" << best_b[i] << \"\\n\";\n return 0;\n}","ahc045":"#include \nusing namespace std;\n\nint queries_used = 0;\nint Q_limit;\n\nvector> query(vector& cities) {\n if (queries_used >= Q_limit || cities.size() < 2) return {};\n cout << \"? \" << cities.size();\n for (int c : cities) cout << \" \" << c;\n cout << endl;\n \n vector> edges;\n for (size_t i = 0; i + 1 < cities.size(); i++) {\n int a, b;\n cin >> a >> b;\n edges.emplace_back(a, b);\n }\n queries_used++;\n return edges;\n}\n\ndouble estDist(double x1, double y1, double x2, double y2) {\n double dx = x1 - x2, dy = y1 - y2;\n return sqrt(dx*dx + dy*dy);\n}\n\nint main() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M, Q, L, W;\n cin >> N >> M >> Q >> L >> W;\n Q_limit = Q;\n \n vector G(M);\n for (int i = 0; i < M; i++) cin >> G[i];\n \n vector x(N), y(N);\n for (int i = 0; i < N; i++) {\n int lx, rx, ly, ry;\n cin >> lx >> rx >> ly >> ry;\n x[i] = (lx + rx) / 2.0;\n y[i] = (ly + ry) / 2.0;\n }\n \n // Greedy nearest-neighbor grouping\n vector used(N, false);\n vector> groups(M);\n \n vector groupOrder(M);\n iota(groupOrder.begin(), groupOrder.end(), 0);\n sort(groupOrder.begin(), groupOrder.end(), [&](int a, int b) {\n return G[a] > G[b];\n });\n \n for (int gi : groupOrder) {\n int g = G[gi];\n double cx = 0, cy = 0;\n int cnt = 0;\n for (int i = 0; i < N; i++) {\n if (!used[i]) { cx += x[i]; cy += y[i]; cnt++; }\n }\n if (cnt > 0) { cx /= cnt; cy /= cnt; }\n \n int start = -1;\n double minD = 1e18;\n for (int i = 0; i < N; i++) {\n if (!used[i]) {\n double d = estDist(x[i], y[i], cx, cy);\n if (d < minD) { minD = d; start = i; }\n }\n }\n \n groups[gi].push_back(start);\n used[start] = true;\n \n while ((int)groups[gi].size() < g) {\n int best = -1;\n double bestD = 1e18;\n for (int i = 0; i < N; i++) {\n if (used[i]) continue;\n double minDistToGroup = 1e18;\n for (int c : groups[gi]) {\n minDistToGroup = min(minDistToGroup, estDist(x[i], y[i], x[c], y[c]));\n }\n if (minDistToGroup < bestD) {\n bestD = minDistToGroup;\n best = i;\n }\n }\n groups[gi].push_back(best);\n used[best] = true;\n }\n }\n \n // Local TSP-like reordering within each group\n for (int k = 0; k < M; k++) {\n int g = groups[k].size();\n if (g <= 2) continue;\n \n vector ordered;\n vector inOrder(g, false);\n ordered.push_back(0);\n inOrder[0] = true;\n \n while ((int)ordered.size() < g) {\n int last = ordered.back();\n int best = -1;\n double bestD = 1e18;\n for (int i = 0; i < g; i++) {\n if (inOrder[i]) continue;\n double d = estDist(x[groups[k][last]], y[groups[k][last]], \n x[groups[k][i]], y[groups[k][i]]);\n if (d < bestD) { bestD = d; best = i; }\n }\n ordered.push_back(best);\n inOrder[best] = true;\n }\n \n vector newGroup(g);\n for (int i = 0; i < g; i++) newGroup[i] = groups[k][ordered[i]];\n groups[k] = newGroup;\n }\n \n // Calculate total minimum queries needed\n int totalMinQueries = 0;\n for (int k = 0; k < M; k++) {\n int g = groups[k].size();\n if (g <= 1) continue;\n else if (g <= L) totalMinQueries += 1;\n else totalMinQueries += (g - 2) / (L - 1) + 1;\n }\n \n vector>> edges(M);\n vector>> all_edges_per_group(M);\n \n // First pass: ensure connectivity\n for (int k = 0; k < M; k++) {\n int g = groups[k].size();\n if (g == 1) continue;\n \n if (g <= L && queries_used < Q) {\n edges[k] = query(groups[k]);\n } else {\n int remainingBudget = Q - queries_used;\n int remainingGroups = 0;\n for (int j = k; j < M; j++) if (groups[j].size() > (size_t)L) remainingGroups++;\n \n int step = L - 1;\n if (remainingBudget > totalMinQueries * 2 && remainingGroups > 0) {\n step = max(1, (L - 1) / 2);\n }\n \n // Main sliding window\n for (int i = 0; i < g && queries_used < Q; i += step) {\n int end = min(i + L, g);\n if (end - i >= 2) {\n vector subset(groups[k].begin() + i, groups[k].begin() + end);\n auto e = query(subset);\n all_edges_per_group[k].insert(all_edges_per_group[k].end(), e.begin(), e.end());\n }\n if (end >= g) break;\n }\n \n // Second pass with offset\n if (step > 1 && queries_used < Q && g > L) {\n for (int i = step/2; i + 1 < g && queries_used < Q; i += step) {\n int end = min(i + L, g);\n if (end - i >= 2) {\n vector subset(groups[k].begin() + i, groups[k].begin() + end);\n auto e = query(subset);\n all_edges_per_group[k].insert(all_edges_per_group[k].end(), e.begin(), e.end());\n }\n if (end >= g) break;\n }\n }\n \n // Build MST\n map city_to_local;\n for (int i = 0; i < g; i++) city_to_local[groups[k][i]] = i;\n \n vector parent(g);\n iota(parent.begin(), parent.end(), 0);\n function find = [&](int u) -> int {\n return parent[u] == u ? u : parent[u] = find(parent[u]);\n };\n \n auto& ae = all_edges_per_group[k];\n sort(ae.begin(), ae.end(), [&](auto& a, auto& b) {\n double da = estDist(x[a.first], y[a.first], x[a.second], y[a.second]);\n double db = estDist(x[b.first], y[b.first], x[b.second], y[b.second]);\n return da < db;\n });\n \n for (auto& e : ae) {\n int u = city_to_local[e.first];\n int v = city_to_local[e.second];\n if (find(u) != find(v)) {\n parent[find(u)] = find(v);\n edges[k].push_back(e);\n }\n }\n \n // Fallback\n while ((int)edges[k].size() < g - 1) {\n double best_dist = 1e18;\n int best_u = -1, best_v = -1;\n for (int i = 0; i < g; i++) {\n for (int j = i + 1; j < g; j++) {\n if (find(i) != find(j)) {\n double d = estDist(x[groups[k][i]], y[groups[k][i]], \n x[groups[k][j]], y[groups[k][j]]);\n if (d < best_dist) {\n best_dist = d;\n best_u = i; best_v = j;\n }\n }\n }\n }\n if (best_u >= 0) {\n parent[find(best_u)] = find(best_v);\n edges[k].push_back({groups[k][best_u], groups[k][best_v]});\n } else break;\n }\n }\n }\n \n // Use remaining queries for large groups - random sampling\n mt19937 rng(42);\n vector largeGroups;\n for (int k = 0; k < M; k++) {\n if ((int)groups[k].size() > L) largeGroups.push_back(k);\n }\n \n while (queries_used < Q && !largeGroups.empty()) {\n int k = largeGroups[rng() % largeGroups.size()];\n int g = groups[k].size();\n \n // Sample L random cities\n vector indices(g);\n iota(indices.begin(), indices.end(), 0);\n shuffle(indices.begin(), indices.end(), rng);\n \n vector subset;\n for (int i = 0; i < min(L, g); i++) {\n subset.push_back(groups[k][indices[i]]);\n }\n \n auto e = query(subset);\n // Check if any edge improves our MST\n for (auto& edge : e) {\n bool found = false;\n for (auto& existing : edges[k]) {\n if ((existing.first == edge.first && existing.second == edge.second) ||\n (existing.first == edge.second && existing.second == edge.first)) {\n found = true;\n break;\n }\n }\n if (!found) {\n all_edges_per_group[k].push_back(edge);\n }\n }\n }\n \n cout << \"!\" << endl;\n for (int k = 0; k < M; k++) {\n for (int c : groups[k]) cout << c << \" \";\n cout << \"\\n\";\n for (auto& e : edges[k]) {\n cout << e.first << \" \" << e.second << \"\\n\";\n }\n }\n \n return 0;\n}","ahc046":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n \n int N, M;\n cin >> N >> M;\n \n vector> targets(M);\n for (int i = 0; i < M; i++) {\n cin >> targets[i].first >> targets[i].second;\n }\n \n vector actions;\n int curR = targets[0].first, curC = targets[0].second;\n \n for (int i = 1; i < M; i++) {\n int tR = targets[i].first, tC = targets[i].second;\n \n int moveCost = abs(tR - curR) + abs(tC - curC);\n int bestCost = moveCost;\n int bestStrategy = 0;\n \n // Edge target strategies (1-4)\n if (tR == 0 && curR > 0) {\n int cost = abs(tC - curC) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 1; }\n }\n if (tR == N - 1 && curR < N - 1) {\n int cost = abs(tC - curC) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 2; }\n }\n if (tC == 0 && curC > 0) {\n int cost = abs(tR - curR) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 3; }\n }\n if (tC == N - 1 && curC < N - 1) {\n int cost = abs(tR - curR) + 1;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 4; }\n }\n \n // Slide-first strategies (5-8)\n if (curR > 0) {\n int cost = 1 + tR + abs(tC - curC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 5; }\n }\n if (curR < N - 1) {\n int cost = 1 + (N - 1 - tR) + abs(tC - curC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 6; }\n }\n if (curC > 0) {\n int cost = 1 + tC + abs(tR - curR);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 7; }\n }\n if (curC < N - 1) {\n int cost = 1 + (N - 1 - tC) + abs(tR - curR);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 8; }\n }\n \n // Double-slide to corners (9-12)\n if (curR > 0 && curC > 0) { // to (0,0)\n int cost = 2 + tR + tC;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 9; }\n }\n if (curR > 0 && curC < N - 1) { // to (0, N-1)\n int cost = 2 + tR + (N - 1 - tC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 10; }\n }\n if (curR < N - 1 && curC > 0) { // to (N-1, 0)\n int cost = 2 + (N - 1 - tR) + tC;\n if (cost < bestCost) { bestCost = cost; bestStrategy = 11; }\n }\n if (curR < N - 1 && curC < N - 1) { // to (N-1, N-1)\n int cost = 2 + (N - 1 - tR) + (N - 1 - tC);\n if (cost < bestCost) { bestCost = cost; bestStrategy = 12; }\n }\n \n switch (bestStrategy) {\n case 0:\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n break;\n case 1: case 2: case 3: case 4:\n if (bestStrategy <= 2) {\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n actions.push_back(bestStrategy == 1 ? \"S U\" : \"S D\");\n curR = (bestStrategy == 1) ? 0 : N - 1;\n } else {\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n actions.push_back(bestStrategy == 3 ? \"S L\" : \"S R\");\n curC = (bestStrategy == 3) ? 0 : N - 1;\n }\n break;\n case 5: actions.push_back(\"S U\"); curR = 0; goto moveToTarget;\n case 6: actions.push_back(\"S D\"); curR = N - 1; goto moveToTarget;\n case 7: actions.push_back(\"S L\"); curC = 0; goto moveToTarget;\n case 8: actions.push_back(\"S R\"); curC = N - 1; goto moveToTarget;\n case 9: actions.push_back(\"S U\"); curR = 0; actions.push_back(\"S L\"); curC = 0; goto moveToTarget;\n case 10: actions.push_back(\"S U\"); curR = 0; actions.push_back(\"S R\"); curC = N - 1; goto moveToTarget;\n case 11: actions.push_back(\"S D\"); curR = N - 1; actions.push_back(\"S L\"); curC = 0; goto moveToTarget;\n case 12: actions.push_back(\"S D\"); curR = N - 1; actions.push_back(\"S R\"); curC = N - 1; goto moveToTarget;\n moveToTarget:\n while (curR < tR) { actions.push_back(\"M D\"); curR++; }\n while (curR > tR) { actions.push_back(\"M U\"); curR--; }\n while (curC < tC) { actions.push_back(\"M R\"); curC++; }\n while (curC > tC) { actions.push_back(\"M L\"); curC--; }\n break;\n }\n }\n \n for (const string& action : actions) {\n cout << action << \"\\n\";\n }\n \n return 0;\n}"}}}