{"model_name":"claude-4.6-sonnet-medium","codes":{"1":{"ahc001":"#include \nusing namespace std;\nconst int MAXN = 205;\nint n, px[MAXN], py[MAXN];\nlong long pr[MAXN];\nint ra[MAXN], rb[MAXN], rc[MAXN], rd[MAXN];\n\nvoid solve(vector comp, int x1, int y1, int x2, int y2) {\n int nc = (int)comp.size();\n if (nc == 1) { int i=comp[0]; ra[i]=x1;rb[i]=y1;rc[i]=x2;rd[i]=y2; return; }\n long long tr=0; for(int i:comp) tr+=pr[i];\n vector bx(comp), by(comp);\n sort(bx.begin(),bx.end(),[](int a,int b){return px[a]=nx)continue;int lo=max(cx+1,x1+1),hi=min(nx,x2-1);if(lo>hi)continue;int sx=(int)round(x1+(double)(x2-x1)*pf/tr);sx=max(lo,min(hi,sx));double e=fabs((double)pf/tr-(double)(sx-x1)/(x2-x1));if(e=ny)continue;int lo=max(cy+1,y1+1),hi=min(ny,y2-1);if(lo>hi)continue;int sy=(int)round(y1+(double)(y2-y1)*pf/tr);sy=max(lo,min(hi,sy));double e=fabs((double)pf/tr-(double)(sy-y1)/(y2-y1));if(eL(bx.begin(),bx.begin()+best_kx),R(bx.begin()+best_kx,bx.end());solve(L,x1,y1,best_sx,y2);solve(R,best_sx,y1,x2,y2);}\n else{vectorB(by.begin(),by.begin()+best_ky),T(by.begin()+best_ky,by.end());solve(B,x1,y1,x2,best_sy);solve(T,x1,best_sy,x2,y2);}\n}\n\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n cin>>n; for(int i=0;i>px[i]>>py[i]>>pr[i];\n vector all(n); iota(all.begin(),all.end(),0);\n solve(all,0,0,10000,10000);\n for(int i=0;iH)continue;long long area=(long long)w*hh;double ratio=(area<=ri)?(double)area/ri:(double)ri/area;if(ratio>best_ratio){best_ratio=ratio;bw=w;bh=(int)hh;if(best_ratio>=1.0-1e-9){done=true;break;}}}}\n int a=max(x1,xi+1-bw),b=max(y1,yi+1-bh);\n cout<\nusing namespace std;\ntypedef chrono::steady_clock Clock;\nconst int N=50, MAXM=N*N+1;\nint si,sj,M,tid[N][N],pval[N][N];\nconst int dx[]={-1,1,0,0},dy[]={0,0,-1,1};\nconst char dc[]={'U','D','L','R'};\nmt19937 rng;\nbool tu[MAXM],btu[MAXM];\nint pi_[MAXM],pj_[MAXM],pt_[MAXM],bpi[MAXM],bpj[MAXM],bpt[MAXM];\nchar pmv[MAXM],bpmv[MAXM];\nint plen,blen;long long cscore,bscore;int ci,cj;\nvoid save_best(){if(cscore<=bscore)return;bscore=cscore;blen=plen;memcpy(btu,tu,M);memcpy(bpi,pi_,plen*4);memcpy(bpj,pj_,plen*4);memcpy(bpt,pt_,plen*4);if(plen>1)memcpy(bpmv,pmv,plen-1);}\nvoid restore_best(){cscore=bscore;plen=blen;memcpy(tu,btu,M);memcpy(pi_,bpi,plen*4);memcpy(pj_,bpj,plen*4);memcpy(pt_,bpt,plen*4);if(plen>1)memcpy(pmv,bpmv,plen-1);ci=pi_[plen-1];cj=pj_[plen-1];}\nvoid walk_init(){fill(tu,tu+M,false);plen=1;ci=si;cj=sj;pi_[0]=si;pj_[0]=sj;pt_[0]=tid[si][sj];tu[tid[si][sj]]=true;cscore=pval[si][sj];}\nbool walk_step(double a,double b,double g){int bd=-1;double bh=-1e18;for(int d=0;d<4;d++){int ni=ci+dx[d],nj=cj+dy[d];if((unsigned)ni>=(unsigned)N||(unsigned)nj>=(unsigned)N)continue;int t=tid[ni][nj];if(tu[t])continue;tu[t]=true;int deg=0;double nv=0;for(int d2=0;d2<4;d2++){int nni=ni+dx[d2],nnj=nj+dy[d2];if((unsigned)nni>=(unsigned)N||(unsigned)nnj>=(unsigned)N)continue;if(!tu[tid[nni][nnj]]){deg++;nv+=pval[nni][nnj];}}tu[t]=false;double h=a*pval[ni][nj]+g*nv-b*deg+uniform_real_distribution(-0.5,0.5)(rng);if(h>bh){bh=h;bd=d;}}if(bd==-1)return false;int ni=ci+dx[bd],nj=cj+dy[bd];tu[tid[ni][nj]]=true;cscore+=pval[ni][nj];pmv[plen-1]=dc[bd];pi_[plen]=ni;pj_[plen]=nj;pt_[plen]=tid[ni][nj];plen++;ci=ni;cj=nj;return true;}\nvoid walk_extend(double a,double b,double g){while(walk_step(a,b,g));}\nvoid walk_undo(int steps){steps=min(steps,plen-1);while(steps-->0){plen--;tu[pt_[plen]]=false;cscore-=pval[pi_[plen]][pj_[plen]];}ci=pi_[plen-1];cj=pj_[plen-1];}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n rng.seed(chrono::steady_clock::now().time_since_epoch().count());\n cin>>si>>sj;\n for(int i=0;i>tid[i][j];\n for(int i=0;i>pval[i][j];\n M=0;for(int i=0;i(0.5,2.0)(rng);\n double b=uniform_real_distribution(0,25)(rng);\n double g=uniform_real_distribution(0,0.5)(rng);\n if(iter%4==0||blen<=1){walk_init();}\n else{restore_best();walk_undo(uniform_int_distribution(1,blen-1)(rng));}\n walk_extend(a,b,g);save_best();iter++;\n }\n cout<\nusing namespace std;\n\nconst int N = 30;\ndouble mu_h[N][N-1], mu_v[N-1][N];\ndouble sig2_h[N][N-1], sig2_v[N-1][N];\n\nstring dijkstra(int sr, int sc, int tr, int tc) {\n static double dist[N*N];\n static int par[N*N];\n static char pdir[N*N];\n fill(dist, dist+N*N, 1e18);\n priority_queue, vector>, greater<>> pq;\n int src=sr*N+sc, dst=tr*N+tc;\n dist[src]=0; pq.push({0.0,src});\n while (!pq.empty()) {\n auto [d,u]=pq.top(); pq.pop();\n if (d>dist[u]+1e-9) continue;\n if (u==dst) break;\n int r=u/N, c=u%N;\n auto relax=[&](int nr,int nc,char dir,double w){\n int nv=nr*N+nc; double nd=d+w;\n if(nd0) relax(r-1,c,'U',mu_v[r-1][c]);\n if(r0) relax(r,c-1,'L',mu_h[r][c-1]);\n if(c>sr>>sc>>tr>>tc;\n string path=dijkstra(sr,sc,tr,tc);\n cout<>obs;\n struct E{bool is_h;int i,j;};\n vector edges;\n double pred=0,path_sig2=0;\n int r=sr,c=sc;\n for(char ch:path){\n if(ch=='U'){edges.push_back({false,r-1,c});pred+=mu_v[r-1][c];path_sig2+=sig2_v[r-1][c];r--;}\n else if(ch=='D'){edges.push_back({false,r,c});pred+=mu_v[r][c];path_sig2+=sig2_v[r][c];r++;}\n else if(ch=='L'){edges.push_back({true,r,c-1});pred+=mu_h[r][c-1];path_sig2+=sig2_h[r][c-1];c--;}\n else{edges.push_back({true,r,c});pred+=mu_h[r][c];path_sig2+=sig2_h[r][c];c++;}\n }\n if(edges.empty()) continue;\n double noise_var=(double)obs*obs/300.0;\n double total_var=path_sig2+noise_var;\n double residual=(double)obs-pred;\n for(auto& e:edges){\n double& mu=e.is_h?mu_h[e.i][e.j]:mu_v[e.i][e.j];\n double& sig2=e.is_h?sig2_h[e.i][e.j]:sig2_v[e.i][e.j];\n double K=sig2/total_var;\n mu=clamp(mu+K*residual,1000.0,9000.0);\n sig2=max(sig2*(1.0-K),1e4);\n }\n }\n return 0;\n}","ahc004":"#include \nusing namespace std;\nconst int N=20,MAXM=800,MAXL=12;\nint M;\nint8_t grid[N][N],h_mm[N][MAXM][N],v_mm[N][MAXM][N],S[MAXM][MAXL];\nint match_count[MAXM],slen[MAXM];\nint8_t char_pos[MAXM][8][MAXL],char_pos_cnt[MAXM][8];\nuint8_t char_appears[MAXM];\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n int n;cin>>n>>M;\n for(int k=0;k>s;slen[k]=s.size();char_appears[k]=0;memset(char_pos_cnt[k],0,sizeof(char_pos_cnt[k]));for(int p=0;p0);}\n int best_score=score;int8_t best_grid[N][N];memcpy(best_grid,grid,sizeof(grid));\n auto t0=chrono::steady_clock::now();\n const double T_start=5.0,T_end=0.001,TL=2.85;double T=T_start;\n for(int iter=0;;iter++){\n if((iter&0xFFF)==0){double el=chrono::duration(chrono::steady_clock::now()-t0).count();if(el>=TL)break;T=T_start*pow(T_end/T_start,el/TL);}\n int r=rng()%N,c=rng()%N,nc=rng()%8,oc=grid[r][c];\n if(nc==oc)continue;\n uint8_t mask=(1u<0)-(match_count[k]>0);}\n if(delta<0&&(double)rng()>=exp((double)delta/T)*4294967295.0)continue;\n for(int k=0;kbest_score){best_score=score;memcpy(best_grid,grid,sizeof(grid));}\n }\n for(int i=0;i\nusing namespace std;\nint N, si, sj;\nvector grid;\nbool isRoad(int r, int c) { return r>=0&&r=0&&c,vector> dijkstra(int src) {\n vector dist(N*N,INF),par(N*N,-1);\n priority_queue,vector>,greater<>> pq;\n dist[src]=0; pq.push({0,src});\n const int DR[]={-1,1,0,0},DC[]={0,0,-1,1};\n while(!pq.empty()){auto[dd,u]=pq.top();pq.pop();if(dd>dist[u])continue;int r=u/N,c=u%N;for(int i=0;i<4;i++){int nr=r+DR[i],nc=c+DC[i];if(!isRoad(nr,nc))continue;int v=nr*N+nc,nd=dd+(grid[nr][nc]-'0');if(nd>N>>si>>sj;grid.resize(N);for(int i=0;i>grid[i];\n vector roads;vector rIdx(N*N,-1);\n for(int r=0;r> vis(R);\n for(int i=0;i=0&&isRoad(r,c-dd);dd++)vis[i].push_back(rIdx[r*N+(c-dd)]);for(int dd=1;r+dd=0&&isRoad(r-dd,c);dd++)vis[i].push_back(rIdx[(r-dd)*N+c]);}\n vector covered(R,false);int uncov=R;vector cnt(R);for(int i=0;i> pqsc;for(int i=0;i sents;\n while(uncov>0){int best=-1;while(!pqsc.empty()){auto[cv,id]=pqsc.top();pqsc.pop();if(cv==cnt[id]){best=id;break;}}if(best<0)break;sents.push_back(roads[best]);for(int j:vis[best])if(!covered[j]){covered[j]=true;uncov--;for(int k:vis[j]){cnt[k]--;pqsc.push({cnt[k],k});}}}\n int stSq=si*N+sj;{auto it=find(sents.begin(),sents.end(),stSq);if(it==sents.end())sents.insert(sents.begin(),stSq);else swap(*it,sents[0]);}\n int S=sents.size();\n {vector covCnt(R,0);for(int sq:sents)for(int j:vis[rIdx[sq]])covCnt[j]++;bool changed=true;while(changed){changed=false;for(int i=S-1;i>=1;i--){if(sents[i]<0)continue;int ridx=rIdx[sents[i]];bool red=true;for(int j:vis[ridx])if(covCnt[j]<=1){red=false;break;}if(red){for(int j:vis[ridx])covCnt[j]--;sents[i]=-1;changed=true;}}}sents.erase(remove(sents.begin(),sents.end(),-1),sents.end());S=sents.size();}\n vector> allDist(S),allPar(S);\n for(int i=0;i> dm(S,vector(S,INF));for(int i=0;i tvis(S,false);vector tour={0};tvis[0]=true;\n for(int s=1;s path;for(int cur=toSq;cur!=srcSq;cur=allPar[fi][cur])path.push_back(cur);reverse(path.begin(),path.end());int pp=srcSq;for(int nx:path){int pr=pp/N,pc=pp%N,nr=nx/N,nc=nx%N;if(nrpr)res+='D';else if(nc\nusing namespace std;\n\nint N, M, K, R;\nvector> d, succs;\nvector task_st, task_pre, task_w, worker_t, task_sd;\nvector> sk;\nvector> lb;\nvector>> obs;\nvector cp;\nvector> et;\nint cur_day;\ndouble prior_sk;\n\nvoid upd_et(int w) {\n for (int i = 0; i < N; i++) {\n double ww = 0;\n for (int k = 0; k < K; k++) { double df = d[i][k] - sk[w][k]; if (df > 0) ww += df; }\n et[i][w] = ww < 0.5 ? 1.0 : ww;\n }\n}\n\nvoid calc_cp() {\n cp.assign(N, 0.0);\n for (int i = N-1; i >= 0; i--) {\n if (task_st[i] == 2) continue;\n double mn;\n if (task_st[i] == 1) { double rem = task_sd[i] + et[i][task_w[i]] - cur_day; mn = max(1.0, rem); }\n else { mn = et[i][0]; for (int j = 1; j < M; j++) mn = min(mn, et[i][j]); }\n double mx = 0;\n for (int v : succs[i]) mx = max(mx, cp[v]);\n cp[i] = mn + mx;\n }\n}\n\nvoid refit(int w) {\n int n = (int)obs[w].size();\n double decay = exp(-0.1 * n);\n for (int k = 0; k < K; k++) sk[w][k] = max((double)lb[w][k], prior_sk * decay);\n double lr = 1.0;\n for (int it = 0; it < 200; it++) {\n double delta[20] = {}; double loss = 0;\n for (auto& [ti, to] : obs[w]) {\n double wh = 0;\n for (int k = 0; k < K; k++) { double df = d[ti][k] - sk[w][k]; if (df > 0) wh += df; }\n double tgt = to == 1 ? 0.0 : (double)to, err = wh - tgt;\n loss += err * err;\n for (int k = 0; k < K; k++) {\n if (d[ti][k] > sk[w][k]) delta[k] += err;\n else if (err < -0.5 && d[ti][k] > 0) delta[k] += 0.3 * err;\n }\n }\n bool ch = false;\n for (int k = 0; k < K; k++) {\n double ns = max((double)lb[w][k], max(0.0, sk[w][k] + lr * delta[k] / n));\n if (ns != sk[w][k]) { sk[w][k] = ns; ch = true; }\n }\n if (!ch || loss / n < 0.1) break;\n lr *= 0.95;\n }\n upd_et(w);\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> M >> K >> R;\n d.assign(N, vector(K));\n for (int i = 0; i < N; i++) for (int k = 0; k < K; k++) cin >> d[i][k];\n succs.assign(N, {}); task_pre.assign(N, 0);\n for (int r = 0; r < R; r++) { int u, v; cin >> u >> v; u--; v--; succs[u].push_back(v); task_pre[v]++; }\n task_st.assign(N, 0); task_w.assign(N, -1); worker_t.assign(M, -1); task_sd.assign(N, 0);\n prior_sk = 40.0 / sqrt((double)K);\n sk.assign(M, vector(K, prior_sk)); lb.assign(M, vector(K, 0)); obs.resize(M);\n et.assign(N, vector(M));\n for (int j = 0; j < M; j++) upd_et(j);\n set avail, idle;\n for (int i = 0; i < N; i++) if (!task_pre[i]) avail.insert(i);\n for (int j = 0; j < M; j++) idle.insert(j);\n cur_day = 0;\n while (true) {\n cur_day++; calc_cp();\n vector av(avail.begin(), avail.end());\n sort(av.begin(), av.end(), [](int a, int b){ return cp[a] > cp[b]; });\n vector> asgn; set id = idle;\n for (int t : av) {\n if (id.empty()) break;\n int bw = -1; double bt = 1e18;\n for (int j : id) if (et[t][j] < bt) { bt = et[t][j]; bw = j; }\n asgn.push_back({bw, t}); id.erase(bw);\n }\n cout << asgn.size();\n for (auto [w, t] : asgn) {\n cout << ' ' << w+1 << ' ' << t+1;\n task_w[t] = w; worker_t[w] = t; task_sd[t] = cur_day;\n task_st[t] = 1; avail.erase(t); idle.erase(w);\n }\n cout << '\\n'; cout.flush();\n int nc; cin >> nc;\n if (nc == -1) break;\n for (int i = 0; i < nc; i++) {\n int w; cin >> w; w--;\n int t = worker_t[w], tk = cur_day - task_sd[t] + 1;\n obs[w].push_back({t, tk});\n if (tk == 1) for (int k = 0; k < K; k++) lb[w][k] = max(lb[w][k], d[t][k]);\n refit(w);\n task_st[t] = 2; task_w[t] = -1; worker_t[w] = -1; idle.insert(w);\n for (int v : succs[t]) if (!--task_pre[v]) avail.insert(v);\n }\n }\n}","ahc006":"#include \nusing namespace std;\n\nconst int OX=400,OY=400,TOT=1000,K=50,NN=2*K+1;\nint A[TOT],B[TOT],C[TOT],D[TOT];\nint sel[K];\nint NX[NN],NY[NN];\n\nint md(int x1,int y1,int x2,int y2){return abs(x1-x2)+abs(y1-y2);}\nint ec(int u,int v){return md(NX[u],NY[u],NX[v],NY[v]);}\n\nvoid refresh(){\n NX[0]=OX;NY[0]=OY;\n for(int i=0;i&r){\n int s=0;\n for(int i=0;i+1<(int)r.size();i++) s+=ec(r[i],r[i+1]);\n return s;\n}\n\nbool feasible(const vector&r){\n bool p[K+1]={};\n for(int v:r){\n if(v>=1&&v<=K) p[v]=true;\n else if(v>K&&!p[v-K]) return false;\n }\n return true;\n}\n\nvector build_nn(){\n bool vis[NN]={},has[K+1]={};\n vector r={0};vis[0]=true;\n for(int s=0;s<2*K;s++){\n int cur=r.back(),bv=-1,bd=INT_MAX;\n for(int v=1;vK&&!has[v-K])) continue;\n int dd=ec(cur,v);\n if(dd&r){\n int n=r.size();bool any=false;\n for(int i=1;i&r){\n int n=r.size();bool any=false;\n for(int i=1;ibd){bd=rem-ins;bj=j;}\n }\n if(bj<0) continue;\n vector nr;nr.reserve(n);\n for(int k=0;k&r){\n for(;;){bool a=two_opt_pass(r),b=or1_pass(r);if(!a&&!b)break;}\n}\nvoid quick_search(vector&r,int it=5){\n for(int i=0;i build_perturbed(const vector&base,int si){\n int pi=si+1,di=K+si+1;\n vector r;r.reserve(base.size()-2);\n for(int v:base) if(v!=pi&&v!=di) r.push_back(v);\n int n=r.size();\n int bc=INT_MAX,bp=0,bd2=1;\n for(int p=0;p res=r;\n res.insert(res.begin()+bp+1,pi);\n res.insert(res.begin()+bd2+1,di);\n return res;\n}\n\nvoid emit(const vector&r){\n cout<(Clk::now()-T0).count();}\n\nint bcost=INT_MAX;\nvector broute;\nint bsel[K];\nbool inS[TOT]={};\n\nvoid trysel(){\n refresh();\n auto r=build_nn();full_search(r);\n int c=tcost(r);\n if(c pos(NN,-1);\n for(int i=0;i rem(K);\n for(int i=0;ibg){bg=g;bsi=si;bj=j;}\n }\n }\n if(bsi<0) return false;\n int old=sel[bsi];\n sel[bsi]=bj;refresh();\n auto nr=build_perturbed(broute,bsi);\n quick_search(nr,10);\n int nc=tcost(nr);\n if(nc>A[i]>>B[i]>>C[i]>>D[i];\n\n // Strategy 1: isolated tour cost\n {\n vector> sc(TOT);\n for(int i=0;i> sc(TOT);\n for(int i=0;i> sc(TOT);\n for(int i=0;i1.95) break;\n bool a=two_opt_pass(broute),b=or1_pass(broute);\n if(!a&&!b) break;\n }\n emit(broute);\n return 0;\n}","ahc007":"#include \nusing namespace std;\nconst int N = 400, M = 1995;\nint px[N], py[N];\nint eu[M], ev[M];\nlong long ed[M];\nstruct UF {\n int p[N], r[N];\n void init() { for(int i=0;i>px[i]>>py[i];\n for(int i=0;i>eu[i]>>ev[i];\n double dx=px[eu[i]]-px[ev[i]], dy=py[eu[i]]-py[ev[i]];\n ed[i]=llround(sqrt(dx*dx+dy*dy));\n }\n uf.init();\n for(int i=0;i>l;\n if(uf.same(eu[i],ev[i])){ cout<<0<1){ cout<<1<0){ threshold=(double)min_d*(1.0+2.0/(k+1.0)); }\n else {\n int comp_id[N]; fill(comp_id,comp_id+N,-1); int nc=0;\n for(int v=0;v>> cadj(nc);\n for(int j=i+1;j dist(nc,1e18);\n priority_queue,vector>,greater<>> pq;\n dist[src]=0; pq.push({0.0,src});\n while(!pq.empty()){\n auto [dv,u]=pq.top(); pq.pop();\n if(dv>dist[u]+1e-9) continue; if(u==dst) break;\n for(auto [v,w]:cadj[u]){ double nd=dist[u]+w; if(nd1e17)?2.0*ed[i]:dist[dst];\n }\n if((double)l<=threshold){ cout<<1<\nusing namespace std;\nconst int G=30;\nint N,M,px[20],py[20],hx[10],hy[10];\nbool wall[G+2][G+2];\nint spx[20],spy[20],shx[10],shy[10];\nconst int ddx[]={-1,1,0,0},ddy[]={0,0,-1,1};\nconst char DIRS[]=\"UDLR\",WDIRS[]=\"udlr\";\nbool inb(int x,int y){return x>=1&&x<=G&&y>=1&&y<=G;}\nint dbuf[G+2][G+2];\nvoid bfs(int tx,int ty){\n for(int i=0;i<=G+1;i++)fill(dbuf[i],dbuf[i]+G+2,-1);\n dbuf[tx][ty]=0;queue>q;q.push({tx,ty});\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int d=0;d<4;d++){int nx=x+ddx[d],ny=y+ddy[d];if(!inb(nx,ny)||wall[nx][ny]||dbuf[nx][ny]!=-1)continue;dbuf[nx][ny]=dbuf[x][y]+1;q.push({nx,ny});}}\n}\nchar gmv(int sx,int sy,int tx,int ty){if(sx==tx&&sy==ty)return '.';bfs(tx,ty);if(dbuf[sx][sy]==-1)return '.';for(int d=0;d<4;d++){int nx=sx+ddx[d],ny=sy+ddy[d];if(!inb(nx,ny)||wall[nx][ny])continue;if(dbuf[nx][ny]==dbuf[sx][sy]-1)return DIRS[d];}return '.';}\nbool cpl(int wx,int wy){if(!inb(wx,wy)||wall[wx][wy])return false;for(int i=0;i>N;for(int i=0;i>px[i]>>py[i]>>t;}cin>>M;for(int i=0;i>hx[i]>>hy[i];\n double bv=-1e18;int wt=0,wp=16;bool hp=true;\n auto ch=[&](int wtype,int wpos,bool hpos)->int{int c=0;for(int i=0;i=wpos):(hpos?hx[i]=wpos);if(ok)c++;}return c;};\n auto ev=[&](int area,int pets,int wtype,int wpos,bool hpos)->double{return (double)area/900.0*pow(2.0,-(double)pets)*(0.7+0.3*ch(wtype,wpos,hpos)/M);};\n for(int c=2;c<=G;c++){int lp=0,rp=0;for(int i=0;ibv){bv=vl;wt=0;wp=c;hp=true;}if(vr>bv){bv=vr;wt=0;wp=c;hp=false;}}\n for(int r=2;r<=G;r++){int tp=0,bp=0;for(int i=0;ibv){bv=vt;wt=1;wp=r;hp=true;}if(vb>bv){bv=vb;wt=1;wp=r;hp=false;}}\n struct Task{int wx,wy,sx,sy,wd;};vector tasks(G);\n if(wt==0){if(hp)for(int r=1;r<=G;r++)tasks[r-1]={r,wp,r,wp-1,3};else for(int r=1;r<=G;r++)tasks[r-1]={r,wp-1,r,wp,2};}\n else{if(hp)for(int c=1;c<=G;c++)tasks[c-1]={wp,c,wp-1,c,1};else for(int c=1;c<=G;c++)tasks[c-1]={wp-1,c,wp,c,0};}\n vector hord(M);iota(hord.begin(),hord.end(),0);\n if(wt==0)sort(hord.begin(),hord.end(),[&](int a,int b){return hx[a] te(M),ct(M);for(int i=0;ibool{return wt==0?(hp?hy[h]=wp):(hp?hx[h]=wp);};\n for(int turn=0;turn<300;turn++){\n for(int i=0;i> pl;\n for(int h=0;h=te[h]){acts[h]='.';continue;}\n Task&t=tasks[ct[h]];bool ig=(ct[h]==G-1)&&!all_safe;\n if(hx[h]==t.sx&&hy[h]==t.sy){if(!ig&&cpl(t.wx,t.wy)&&!pl.count({t.wx,t.wy})){acts[h]=WDIRS[t.wd];pl.insert({t.wx,t.wy});wall[t.wx][t.wy]=true;ct[h]++;}}\n else{char mv=gmv(hx[h],hy[h],t.sx,t.sy);acts[h]=mv;if(mv!='.')for(int d=0;d<4;d++)if(DIRS[d]==mv){hx[h]+=ddx[d];hy[h]+=ddy[d];break;}}\n }\n cout<>s;for(char c:s){if(c=='U')px[i]--;else if(c=='D')px[i]++;else if(c=='L')py[i]--;else if(c=='R')py[i]++;}}\n }\n}","ahc009":"#include \nusing namespace std;\nint si,sj,ti,tj; double pf;\nbool H[20][19],V[19][20];\nint nbr[400][4],G;\nvoid initN(){for(int i=0;i<20;i++)for(int j=0;j<20;j++){int c=i*20+j;nbr[c][0]=(i>0&&!V[i-1][j])?(i-1)*20+j:c;nbr[c][1]=(i<19&&!V[i][j])?(i+1)*20+j:c;nbr[c][2]=(j>0&&!H[i][j-1])?i*20+(j-1):c;nbr[c][3]=(j<19&&!H[i][j])?i*20+(j+1):c;}}\nint dc(char c){return c=='U'?0:c=='D'?1:c=='L'?2:3;}\ndouble PP[201][400],PE[201];\nvoid buildP(const string&s,int fr){for(int t=fr;t<(int)s.size();t++){int d=dc(s[t]);double*a=PP[t],*b=PP[t+1];memset(b,0,400*8);for(int k=0;k<400;k++){double v=a[k];if(v<1e-15)continue;b[k]+=v*pf;b[nbr[k][d]]+=v*(1-pf);}double e=b[G]*(401.0-(t+1));b[G]=0;PE[t+1]=PE[t]+e;}}\ndouble evalF(const string&s,int fr){double prob[400],np[400];memcpy(prob,PP[fr],400*8);double E=PE[fr];for(int t=fr;t<(int)s.size();t++){int d=dc(s[t]);memset(np,0,sizeof(np));for(int k=0;k<400;k++){double v=prob[k];if(v<1e-15)continue;np[k]+=v*pf;np[nbr[k][d]]+=v*(1-pf);}E+=np[G]*(401.0-(t+1));np[G]=0;memcpy(prob,np,sizeof(prob));}return E;}\ndouble fullE(const string&s){memset(PP[0],0,400*8);PP[0][si*20+sj]=1.0;PE[0]=0;buildP(s,0);return PE[s.size()];}\nstring bfsPath(){int d[400];fill(d,d+400,-1);int p[400],pd[400];int src=si*20+sj;queueq;q.push(src);d[src]=0;while(!q.empty()){int k=q.front();q.pop();for(int dd=0;dd<4;dd++){int nk=nbr[k][dd];if(nk==k||d[nk]!=-1)continue;d[nk]=d[k]+1;p[nk]=k;pd[nk]=dd;q.push(nk);}}string r;for(int c=G;c!=src;c=p[c])r+=\"UDLR\"[pd[c]];reverse(r.begin(),r.end());return r;}\nstring greedyPath(){int bd[400];fill(bd,bd+400,-1);queueq;q.push(G);bd[G]=0;while(!q.empty()){int k=q.front();q.pop();for(int d=0;d<4;d++){int nk=nbr[k][d];if(nk==k||bd[nk]!=-1)continue;bd[nk]=bd[k]+1;q.push(nk);}}double prob[400]={},np[400];prob[si*20+sj]=1.0;string s(200,'D');for(int t=0;t<200;t++){double best=-1e18;int bd2=0;for(int d=0;d<4;d++){double g=0;for(int k=0;k<400;k++){if(prob[k]<1e-15)continue;g+=prob[k]*(1-pf)*(bd[k]-bd[nbr[k][d]]);}if(g>best){best=g;bd2=d;}}s[t]=\"UDLR\"[bd2];memset(np,0,sizeof(np));for(int k=0;k<400;k++){if(prob[k]<1e-15)continue;np[k]+=prob[k]*pf;np[nbr[k][bd2]]+=prob[k]*(1-pf);}np[G]=0;memcpy(prob,np,sizeof(prob));}return s;}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n cin>>si>>sj>>ti>>tj>>pf;\n for(int i=0;i<20;i++){string r;cin>>r;for(int j=0;j<19;j++)H[i][j]=(r[j]=='1');}\n for(int i=0;i<19;i++){string r;cin>>r;for(int j=0;j<20;j++)V[i][j]=(r[j]=='1');}\n initN(); G=ti*20+tj;\n string path=bfsPath(); int k=path.size();\n string s1(200,'D'); for(int i=0;i<200;i++)s1[i]=path[i%k];\n string s2=greedyPath();\n double e1=fullE(s1),e2=fullE(s2);\n string best=(e1>=e2)?s1:s2; double bestE=max(e1,e2);\n memset(PP[0],0,400*8); PP[0][si*20+sj]=1.0; PE[0]=0; buildP(best,0);\n auto t0=chrono::steady_clock::now();\n for(;;){\n if(chrono::duration(chrono::steady_clock::now()-t0).count()>1.8)break;\n bool imp=false;\n for(int t=0;t<200;t++){\n int od=dc(best[t]);\n for(int d=0;d<4;d++){\n if(d==od)continue;\n best[t]=\"UDLR\"[d];\n double e=evalF(best,t);\n if(e>bestE+1e-12){bestE=e;od=d;buildP(best,t);imp=true;}\n else best[t]=\"UDLR\"[od];\n }\n }\n if(!imp)break;\n }\n cout<\nusing namespace std;\nconst int N = 30, TOTAL = N * N * 4;\nconst int to_t[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}};\nconst int di[4]={0,-1,0,1}, dj[4]={-1,0,1,0};\nint tiles[N][N], init_t[N][N], rots[N][N], best_rots[N][N];\ninline int apply_rot(int t,int r){\n if(t<=3)return(t+r)&3;\n if(t<=5)return 4+((t-4+r)&1);\n return 6+((t-6+r)&1);}\nint nxt[TOTAL]; uint8_t col[TOTAL];\ninline void update_nxt(int i,int j){\n int base=(i*N+j)*4, t=tiles[i][j];\n for(int d=0;d<4;d++){\n int d2=to_t[t][d];\n if(d2<0){nxt[base+d]=-1;continue;}\n int ni=i+di[d2],nj=j+dj[d2];\n if((unsigned)ni>=N||(unsigned)nj>=N){nxt[base+d]=-1;continue;}\n nxt[base+d]=(ni*N+nj)*4+((d2+2)&3);}}\nlong long evaluate(){\n memset(col,0,TOTAL); int t1=0,t2=0;\n for(int s=0;s=0&&!col[c]){col[c]=1;c=nxt[c];}\n if(c>=0&&col[c]==1){\n int len=0,cc=c;\n do{cc=nxt[cc];len++;}while(cc!=c);\n if(len>t1){t2=t1;t1=len;}else if(len>t2)t2=len;}\n c=s;\n while(c>=0&&col[c]==1){col[c]=2;c=nxt[c];}}\n return(long long)t1*t2;}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n for(int i=0;i>s;\n for(int j=0;j(chrono::steady_clock::now()-ts).count();\n cnt++;\n double T=T0*exp(lnr*elapsed/TL);\n int i=rng()%N,j=rng()%N;\n int dr=(rng()%3)+1,nr=(rots[i][j]+dr)&3,ot=tiles[i][j];\n tiles[i][j]=apply_rot(init_t[i][j],nr);\n update_nxt(i,j);\n long long ns=evaluate(),delta=ns-cur;\n if(delta>=0||rng()/4294967296.0best){best=ns;memcpy(best_rots,rots,sizeof(rots));}}\n else{tiles[i][j]=ot;update_nxt(i,j);}}\n string out(N*N,'0');\n for(int i=0;i\nusing namespace std;\nint N,T,board[10][10],board_label[10][10],er,ec,tgt[10][10],avail[16];\nbool fixed_cells[10][10];\nstring out;\nvoid read_input(){cin>>N>>T;for(int i=0;i>s;for(int j=0;j='0'&&c<='9')?c-'0':c-'a'+10;if(!board[i][j]){er=i;ec=j;}}}}\nbool valid_pos(int v,int i,int j){return!((v&1)&&!j)&&!((v&2)&&!i)&&!((v&4)&&j==N-1)&&!((v&8)&&i==N-1);}\nbool is_tree(){bool vis[10][10]={};int sr=-1,sc=0;for(int i=0;i0){sr=i;sc=j;break;}if(sr<0)return false;queue>q;q.push({sr,sc});vis[sr][sc]=true;int cnt=1,ed=0;int dr[]={0,1,0,-1},dc[]={1,0,-1,0},cb[]={4,8,1,2},nb[]={1,2,4,8};while(!q.empty()){auto[r,c]=q.front();q.pop();for(int d=0;d<4;d++){int nr=r+dr[d],nc=c+dc[d];if(nr<0||nr>=N||nc<0||nc>=N||tgt[nr][nc]<=0)continue;if((tgt[r][c]&cb[d])&&(tgt[nr][nc]&nb[d])){ed++;if(!vis[nr][nc]){vis[nr][nc]=true;cnt++;q.push({nr,nc});}}}}return cnt==N*N-1&&ed==2*(N*N-2);}\nbool find_target(int pos){if(pos==N*N)return is_tree();int i=pos/N,j=pos%N;if(i==N-1&&j==N-1){tgt[i][j]=0;return find_target(pos+1);}bool fl=(j>0),nl=fl&&(tgt[i][j-1]&4);bool fu=(i>0),nu=fu&&(tgt[i-1][j]&8);for(int v=1;v<=15;v++){if(!avail[v]||!valid_pos(v,i,j))continue;if(fl&&!!(v&1)!=nl)continue;if(fu&&!!(v&2)!=nu)continue;avail[v]--;tgt[i][j]=v;if(find_target(pos+1))return true;avail[v]++;}tgt[i][j]=-1;return false;}\nvoid init_labels(){vector>cp[16],tp[16];for(int i=0;i0)cp[board[i][j]].push_back({i,j});if(tgt[i][j]>0)tp[tgt[i][j]].push_back({i,j});}for(int v=1;v<=15;v++){sort(cp[v].begin(),cp[v].end());sort(tp[v].begin(),tp[v].end());for(int k=0;k<(int)cp[v].size();k++){auto[cr,cc]=cp[v][k];auto[tr,tc]=tp[v][k];board_label[cr][cc]=tr*N+tc;}}}\nbool check_solvable(){vectors;for(int i=0;i=0)s.push_back(board_label[i][j]);int inv=0;for(int a=0;a<(int)s.size();a++)for(int b=a+1;b<(int)s.size();b++)if(s[a]>s[b])inv++;if(N%2)return!(inv%2);return(inv+er)%2==1;}\nvoid fix_parity(){if(check_solvable())return;for(int v=1;v<=15;v++){vector>cp;for(int i=0;i=2){swap(board_label[cp[0].first][cp[0].second],board_label[cp[1].first][cp[1].second]);if(check_solvable())return;swap(board_label[cp[0].first][cp[0].second],board_label[cp[1].first][cp[1].second]);}}}\nvoid do_move(char m){int tr=er,tc=ec;if(m=='U')tr--;else if(m=='D')tr++;else if(m=='L')tc--;else tc++;board[er][ec]=board[tr][tc];board_label[er][ec]=board_label[tr][tc];board[tr][tc]=0;board_label[tr][tc]=-1;er=tr;ec=tc;out+=m;}\nbool move_empty(int gr,int gc){if(er==gr&&ec==gc)return true;if((int)out.size()>=T||fixed_cells[gr][gc])return false;int NN=N*N;vectorprv(NN,-2);int s=er*N+ec,g=gr*N+gc;prv[s]=-1;queueq;q.push(s);int dr[]={-1,1,0,0},dcc[]={0,0,-1,1};while(!q.empty()){int cur=q.front();q.pop();if(cur==g)break;int r=cur/N,c=cur%N;for(int d=0;d<4;d++){int nr=r+dr[d],nc=c+dcc[d];if(nr<0||nr>=N||nc<0||nc>=N||fixed_cells[nr][nc])continue;int nxt=nr*N+nc;if(prv[nxt]!=-2)continue;prv[nxt]=cur;q.push(nxt);}}if(prv[g]==-2)return false;vectorpath;int cur=g;while(cur!=s){path.push_back(cur);cur=prv[cur];}reverse(path.begin(),path.end());for(int nxt:path){if((int)out.size()>=T)return false;int nr=nxt/N,nc=nxt%N;char m;if(nr==er-1)m='U';else if(nr==er+1)m='D';else if(nc==ec-1)m='L';else m='R';do_move(m);}return true;}\nbool bfs_tile(int&tr,int&tc,int dr,int dc){if(tr==dr&&tc==dc)return true;if((int)out.size()>=T)return false;int NN=N*N,t0=tr*N+tc,e0=er*N+ec,tg=dr*N+dc,tot=NN*NN;vectorprv(tot,-2);vectormv(tot,0);prv[t0*NN+e0]=-1;queueq;q.push(t0*NN+e0);int ddr[]={-1,1,0,0},ddc[]={0,0,-1,1};const char dch[]={'U','D','L','R'};int goal=-1;while(!q.empty()){int cur=q.front();q.pop();int ct=cur/NN,ce=cur%NN;if(ct==tg){goal=cur;break;}int er_=ce/N,ec_=ce%N;for(int d=0;d<4;d++){int nr=er_+ddr[d],nc=ec_+ddc[d];if(nr<0||nr>=N||nc<0||nc>=N||fixed_cells[nr][nc])continue;int np=nr*N+nc,nt=(np==ct)?ce:ct,ne=np;if(nt==ne)continue;int nst=nt*NN+ne;if(nst<0||nst>=tot||prv[nst]!=-2)continue;prv[nst]=cur;mv[nst]=dch[d];q.push(nst);}}if(goal<0){for(int e=0;epath;int cur=goal;while(cur!=t0*NN+e0){path.push_back(mv[cur]);cur=prv[cur];}reverse(path.begin(),path.end());for(char m:path){if((int)out.size()>=T)return false;do_move(m);}tr=dr;tc=dc;return true;}\npairfind_lbl(int lbl){for(int i=0;i=T)return;for(int col=0;col<=N-3&&(int)out.size()=T)return;auto[ar,ac]=find_lbl(row*N+(N-2));auto[br,bc]=find_lbl(row*N+(N-1));if(ar<0||br<0)return;if(ar==row&&ac==N-2&&br==row&&bc==N-1){fixed_cells[row][N-2]=fixed_cells[row][N-1]=true;return;}bfs_tile(ar,ac,row,N-1);if((int)out.size()>=T)return;auto[br2,bc2]=find_lbl(row*N+(N-1));if(br2<0)return;fixed_cells[row][N-1]=true;bfs_tile(br2,bc2,row+1,N-1);fixed_cells[row][N-1]=false;if((int)out.size()>=T)return;fixed_cells[row][N-1]=fixed_cells[row+1][N-1]=true;move_empty(row,N-2);fixed_cells[row][N-1]=fixed_cells[row+1][N-1]=false;if((int)out.size()=T)return;auto[ar,ac]=find_lbl((N-2)*N+col);auto[br,bc]=find_lbl((N-1)*N+col);if(ar<0||br<0)return;if(ar==N-2&&ac==col&&br==N-1&&bc==col){fixed_cells[N-2][col]=fixed_cells[N-1][col]=true;return;}bfs_tile(ar,ac,N-1,col);if((int)out.size()>=T)return;auto[br2,bc2]=find_lbl((N-1)*N+col);if(br2<0)return;fixed_cells[N-1][col]=true;bfs_tile(br2,bc2,N-1,col+1);fixed_cells[N-1][col]=false;if((int)out.size()>=T)return;fixed_cells[N-1][col]=fixed_cells[N-1][col+1]=true;move_empty(N-2,col);fixed_cells[N-1][col]=fixed_cells[N-1][col+1]=false;if((int)out.size()=T)return;int p0=(N-2)*N+(N-2),p1=(N-2)*N+(N-1),p2=(N-1)*N+(N-2);int a=board_label[N-2][N-2],b=board_label[N-2][N-1],c=board_label[N-1][N-2],d=board_label[N-1][N-1];if(a==p0&&b==p1&&c==p2&&d==-1)return;auto el=[&](int l)->int{if(l==p0)return 0;if(l==p1)return 1;if(l==p2)return 2;return 3;};auto enc=[](int v0,int v1,int v2,int v3){return v0*64+v1*16+v2*4+v3;};int gs=enc(0,1,2,3),ss=enc(el(a),el(b),el(c),el(d));if(ss==gs)return;arraypar;par.fill(-2);arraymfr;mfr.fill(0);queueq;q.push(ss);par[ss]=-1;static const int adj[4][2]={{1,2},{0,3},{0,3},{1,2}};static const char amv[4][2]={{'R','D'},{'L','D'},{'U','R'},{'U','L'}};while(!q.empty()){int cur=q.front();q.pop();if(cur==gs)break;int v[4]={(cur>>6)&3,(cur>>4)&3,(cur>>2)&3,cur&3};int ep=-1;for(int p=0;p<4;p++)if(v[p]==3){ep=p;break;}if(ep<0)continue;for(int k=0;k<2;k++){int np=adj[ep][k];char m=amv[ep][k];int nv[4]={v[0],v[1],v[2],v[3]};nv[ep]=nv[np];nv[np]=3;int nst=enc(nv[0],nv[1],nv[2],nv[3]);if(par[nst]==-2){par[nst]=cur;mfr[nst]=m;q.push(nst);}}}if(par[gs]==-2)return;vectorpath;int cur=gs;while(cur!=ss){path.push_back(mfr[cur]);cur=par[cur];}reverse(path.begin(),path.end());for(char m:path){if((int)out.size()>=T)break;do_move(m);}}\nvoid solve(){for(int row=0;row<=N-3&&(int)out.size()0)avail[board[i][j]]++;memset(tgt,-1,sizeof(tgt));memset(fixed_cells,0,sizeof(fixed_cells));memset(board_label,-1,sizeof(board_label));if(!find_target(0)){cout<<\"\\n\";return 0;}init_labels();fix_parity();solve();cout<\nusing namespace std;\ntypedef long long ll;\ntypedef unsigned long long ull;\ntypedef pair puu;\nstruct PH{size_t operator()(const puu&p)const{size_t h=hash()(p.first);h^=hash()(p.second)+0x9e3779b9ULL+(h<<6)+(h>>2);return h;}};\nmt19937 rng(42);\nint N,K,a[11],stx[5501],sty[5501];\nstruct Line{ll px,py,qx,qy;};\nconst int MK=100;\nLine cur_lines[MK],best_lines[MK];\nint8_t sgn_data[5501][MK];\null slo[5501],shi[5501];\nunordered_mapgrps;\nint b_arr[12],cscore,best_score;\nstruct Change{int idx;puu old_sig,new_sig;int8_t new_sgn;};\nvectorpending;\nvector>dvec;\nll ecross(const Line&l,ll x,ll y){return(l.qx-l.px)*(y-l.py)-(l.qy-l.py)*(x-l.px);}\nvoid upd(int oc,int nc){if(oc>=1&&oc<=10){cscore-=min(a[oc],b_arr[oc]);b_arr[oc]--;cscore+=min(a[oc],b_arr[oc]);}if(nc>=1&&nc<=10){cscore-=min(a[nc],b_arr[nc]);b_arr[nc]++;cscore+=min(a[nc],b_arr[nc]);}}\nvoid build(){grps.clear();grps.reserve(32768);grps.max_load_factor(0.3f);memset(b_arr,0,sizeof(b_arr));cscore=0;for(int i=0;i=0)?1:-1;sgn_data[i][j]=s;if(s==1){if(j<64)slo[i]|=(1ULL<second,it->second+1);it->second++;}}\nint try_ch(int j,const Line&nl){pending.clear();dvec.clear();for(int i=0;i=0)?1:-1;if(ns==sgn_data[i][j])continue;puu os{slo[i],shi[i]};ull nl2=slo[i],nh2=shi[i];if(j<64){if(ns==1)nl2|=(1ULL<second:0,nc=c+d;if(c>=1&&c<=10){nsc-=min(a[c],nb[c]);nb[c]--;nsc+=min(a[c],nb[c]);}if(nc>=1&&nc<=10){nsc-=min(a[nc],nb[nc]);nb[nc]++;nsc+=min(a[nc],nb[nc]);}}i=j2;}return nsc;}\nvoid do_ch(int j,const Line&nl){for(auto&ch:pending){{auto it=grps.find(ch.old_sig);upd(it->second,it->second-1);if(!--it->second)grps.erase(it);}slo[ch.idx]=ch.new_sig.first;shi[ch.idx]=ch.new_sig.second;sgn_data[ch.idx][j]=ch.new_sgn;{auto[it2,ins]=grps.emplace(ch.new_sig,0);upd(it2->second,it2->second+1);it2->second++;}}cur_lines[j]=nl;}\nLine rline(){double th=(rng()%314159)*(M_PI/314159.0);double r=(int)(rng()%18001)-9000;double cx=r*cos(th),cy=r*sin(th),sdx=-sin(th)*9000,sdy=cos(th)*9000;return{llround(cx+sdx),llround(cy+sdy),llround(cx-sdx),llround(cy-sdy)};}\nLine pline(const Line&l,int s){ll dx=(ll)(rng()%(2*s+1))-s,dy=(ll)(rng()%(2*s+1))-s;int t=rng()%3;if(t==0)return{l.px+dx,l.py+dy,l.qx,l.qy};if(t==1)return{l.px,l.py,l.qx+dx,l.qy+dy};return{l.px+dx,l.py+dy,l.qx-dx,l.qy-dy};}\nint main(){ios_base::sync_with_stdio(false);cin.tie(NULL);cin>>N>>K;for(int d=1;d<=10;d++)cin>>a[d];for(int i=0;i>stx[i]>>sty[i];\nfor(int i=0;i<50;i++){ll y=llround(-9000.0+18000.0*i/49.0);cur_lines[i]={-10000,y,10000,y};}\nfor(int i=0;i<50;i++){ll x=llround(-9000.0+18000.0*i/49.0);cur_lines[50+i]={x,-10000,x,10000};}\nbuild();best_score=cscore;memcpy(best_lines,cur_lines,sizeof(cur_lines));pending.reserve(N+10);dvec.reserve(2*N+10);\nauto t0=chrono::steady_clock::now();double T=15.0;int iter=0;\nwhile(true){if(!(++iter&511)){double e=chrono::duration(chrono::steady_clock::now()-t0).count();if(e>2.75)break;T=max(0.05,15.0*pow(0.05/15.0,e/2.75));}\nint j=rng()%MK;Line nl;int sel=rng()%100;\nif(sel<35)nl=pline(cur_lines[j],30);else if(sel<60)nl=pline(cur_lines[j],300);else if(sel<80)nl=pline(cur_lines[j],2000);else nl=rline();\nif(nl.px==nl.qx&&nl.py==nl.qy)continue;\nint ns=try_ch(j,nl);int ds=ns-cscore;bool acc=(ds>=0);\nif(!acc&&T>0.01)acc=((double)(rng()>>8)/(double)(1u<<24))best_score){best_score=cscore;memcpy(best_lines,cur_lines,sizeof(cur_lines));}}}\ncout<\nusing namespace std;\nconst int MAXN=65;\nint N,M;\nbool dots[MAXN][MAXN],h_seg[MAXN][MAXN],v_seg[MAXN][MAXN],d1_seg[MAXN][MAXN],d2_seg[MAXN][MAXN];\nvector row_dots[MAXN],col_dots[MAXN],diag_dots[130],ad_dots[130];\nstruct Op{int x1,y1,x2,y2,x3,y3,x4,y4;};\nvector ops;\nvoid insertSorted(vector&v,int x){v.insert(lower_bound(v.begin(),v.end(),x),x);}\nvoid addDot(int x,int y){dots[x][y]=true;insertSorted(row_dots[y],x);insertSorted(col_dots[x],y);insertSorted(diag_dots[x-y+64],x);insertSorted(ad_dots[x+y],x);}\nbool edgeClear(int x1,int y1,int x2,int y2){\n if(x1==x2){for(int y=min(y1,y2);yx1)==(y2>y1)){int xm=min(x1,x2),ym=min(y1,y2);for(int t=0;tx1)?1:-1,dy=(y2>y1)?1:-1;for(int t=1;tx1)==(y2>y1)){int xm=min(x1,x2),ym=min(y1,y2);for(int t=0;t=N||y2<0||y2>=N||x3<0||x3>=N||y3<0||y3>=N||x4<0||x4>=N||y4<0||y4>=N)return false;\n if(!dots[x2][y2]||!dots[x3][y3]||!dots[x4][y4])return false;\n if(!edgeNoDots(nx,ny,x2,y2)||!edgeNoDots(x2,y2,x3,y3)||!edgeNoDots(x3,y3,x4,y4)||!edgeNoDots(x4,y4,nx,ny))return false;\n if(!edgeClear(nx,ny,x2,y2)||!edgeClear(x2,y2,x3,y3)||!edgeClear(x3,y3,x4,y4)||!edgeClear(x4,y4,nx,ny))return false;\n ops.push_back({nx,ny,x2,y2,x3,y3,x4,y4});addDot(nx,ny);\n drawEdge(nx,ny,x2,y2);drawEdge(x2,y2,x3,y3);drawEdge(x3,y3,x4,y4);drawEdge(x4,y4,nx,ny);return true;}\nbool findAndPlace(int nx,int ny){\n if(dots[nx][ny])return false;\n {vector> cands;\n for(int x2:row_dots[ny]){if(x2==nx)continue;for(int y2:col_dots[nx]){if(y2==ny||!dots[x2][y2])continue;cands.emplace_back(abs(x2-nx)+abs(y2-ny),x2,y2);}}\n sort(cands.begin(),cands.end());\n for(auto&[p,x2,y2]:cands)if(checkAndDo(nx,ny,x2,ny,x2,y2,nx,y2))return true;}\n {vector> cands;\n for(int xa:diag_dots[nx-ny+64]){if(xa==nx)continue;int a=xa-nx;for(int xb:ad_dots[nx+ny]){if(xb==nx)continue;int b=xb-nx,x3=nx+a+b,y3=ny+a-b;if(x3>=0&&x3=0&&y3>N>>M;for(int i=0;i>x>>y;addDot(x,y);}\n int c=(N-1)/2;\n vector>> pts;\n for(int x=0;x(chrono::steady_clock::now()-t0).count()>4000)break;\n changed=false;\n for(auto&[w,pos]:pts){auto[x,y]=pos;if(dots[x][y])continue;if(findAndPlace(x,y))changed=true;}}\n cout<\nusing namespace std;\ntypedef array,10> Grid;\n\nGrid applyTilt(Grid g, char dir) {\n if (dir=='L') { for(int i=0;i<10;i++){int p=0;for(int j=0;j<10;j++)if(g[i][j])g[i][p++]=g[i][j];for(;p<10;p++)g[i][p]=0;} }\n else if(dir=='R'){for(int i=0;i<10;i++){int p=9;for(int j=9;j>=0;j--)if(g[i][j])g[i][p--]=g[i][j];for(;p>=0;p--)g[i][p]=0;}}\n else if(dir=='F'){for(int j=0;j<10;j++){int p=0;for(int i=0;i<10;i++)if(g[i][j])g[p++][j]=g[i][j];for(;p<10;p++)g[p][j]=0;}}\n else{for(int j=0;j<10;j++){int p=9;for(int i=9;i>=0;i--)if(g[i][j])g[p--][j]=g[i][j];for(;p>=0;p--)g[p][j]=0;}}\n return g;\n}\nlong long computeScore(const Grid& g){\n bool vis[10][10]={};long long sum=0;int stk[100][2];\n static const int dx[]={-1,1,0,0},dy[]={0,0,-1,1};\n for(int si=0;si<10;si++)for(int sj=0;sj<10;sj++){\n if(!g[si][sj]||vis[si][sj])continue;\n int f=g[si][sj],sz=0,top=0;stk[top][0]=si;stk[top][1]=sj;top++;vis[si][sj]=true;\n while(top>0){--top;int x=stk[top][0],y=stk[top][1];sz++;\n for(int d=0;d<4;d++){int nx=x+dx[d],ny=y+dy[d];\n if(nx>=0&&nx<10&&ny>=0&&ny<10&&!vis[nx][ny]&&g[nx][ny]==f){vis[nx][ny]=true;stk[top][0]=nx;stk[top][1]=ny;top++;}}}\n sum+=(long long)sz*sz;}\n return sum;\n}\nGrid placeCandy(Grid g,int p,int flav){int cnt=0;for(int i=0;i<10;i++)for(int j=0;j<10;j++)if(!g[i][j]&&++cnt==p){g[i][j]=flav;return g;}return g;}\n\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n int fl[100];for(int t=0;t<100;t++)cin>>fl[t];\n Grid grid={};static const char dirs[]={'F','B','L','R'};\n for(int t=0;t<100;t++){\n int p;cin>>p;grid=placeCandy(grid,p,fl[t]);\n char bestDir='F';\n if(t<99){\n long long best=-1;int nc=99-t;\n for(char d1:dirs){\n Grid g1=applyTilt(grid,d1);long long tot=0;\n for(int p2=1;p2<=nc;p2++){\n Grid g2=placeCandy(g1,p2,fl[t+1]);long long mx=0;\n for(char d2:dirs){long long s=computeScore(applyTilt(g2,d2));if(s>mx)mx=s;}\n tot+=mx;}\n if(tot>best){best=tot;bestDir=d1;}}\n }\n cout<\n#include \nusing namespace std;\nusing namespace Eigen;\nint M, N;\ndouble eps;\nvector getDeg(const string& s, int n) {\n vector d(n,0); int idx=0;\n for(int i=0;i getEig(const string& s, int n) {\n MatrixXd A(n,n); A.setZero(); int idx=0;\n for(int i=0;i sol(A,EigenvaluesOnly);\n vector ev(n); for(int i=0;iint{if(a>b)swap(a,b);return a*(2*n-a-1)/2+(b-a-1);};\n int cnt=0;\n for(int d=1;d>M>>eps;\n N=4; while((long long)N*(N-1)/21e-9){\n double need=9.0*(double)(M-1)*(M-1)*eps*(1.0-eps);\n int N2=4; while((double)N2*(N2-1)/2 G(M);\n for(int k=0;k> C(M,vector(FD,0.0));\n if(eps<1e-9){\n for(int k=0;k u(0.0,1.0);\n for(int k=0;k>h;\n vector hf(FD); auto dh=getDeg(h,N); for(int i=0;i\nusing namespace std;\ntypedef long long ll;\ntypedef pair pli;\nconst ll INF=1e18;\nconst int MXN=1005,MXM=3005,MXD=35;\nint N,M,D,K,EU[MXM],EV[MXM];ll EW[MXM];\nvector> G[MXN];\nll gd[MXN][MXN];double imp[MXM];int aday[MXM];\ndouble ADJ[MXM][MXD];vector ladj[MXM],dayE[MXD];int pos[MXM];\nuint64_t rs=0xbad1dea5ULL;\nuint64_t rng(){rs^=rs<<13;rs^=rs>>7;rs^=rs<<17;return rs;}\nint ri(int n){return(int)(rng()%(unsigned)n);}\ndouble rd(){return(rng()>>11)*(1.0/(1ull<<53));}\nvoid dijk(int s){fill(gd[s]+1,gd[s]+N+1,INF);gd[s][s]=0;priority_queue,greater>pq;pq.push({0,s});while(!pq.empty()){auto[d,u]=pq.top();pq.pop();if(d>gd[s][u])continue;for(auto&[v,e]:G[u]){ll nd=d+EW[e];if(nd,greater>pq;pq.push({0,s});while(!pq.empty()){auto[dd,u]=pq.top();pq.pop();if(dd>d[u])continue;if(u==t)return d[t];for(auto&[v,e]:G[u]){if(e==sk)continue;ll nd=dd+EW[e];if(nd>N>>M>>D>>K;\n for(int i=0;i>EU[i]>>EV[i]>>EW[i];G[EU[i]].push_back({EV[i],i});G[EV[i]].push_back({EU[i],i});}\n for(int i=1;i<=N;i++){int x,y;cin>>x>>y;}\n for(int s=1;s<=N;s++)dijk(s);\n {vectorpar(N+1,-1),sv(N);vectorsz(N+1,1);iota(sv.begin(),sv.end(),1);\n for(int s=1;s<=N;s++){fill(par.begin(),par.end(),-1);fill(sz.begin(),sz.end(),1LL);\n sort(sv.begin(),sv.end(),[s](int a,int b){return gd[s][a]=0;i--){int v=sv[i];if(par[v]<0)continue;int p=(EU[par[v]]==v)?EV[par[v]]:EU[par[v]];sz[p]+=sz[v];}\n for(int v:sv){if(par[v]<0)continue;imp[par[v]]+=(double)sz[v];}}}\n for(int e=0;eeo(M);iota(eo.begin(),eo.end(),0);sort(eo.begin(),eo.end(),[](int a,int b){return imp[a]>imp[b];});\n for(int e:eo){int best=-1;double bs=1e18;for(int d=0;d=K)continue;double cf=0;for(int e2:ladj[e])if(aday[e2]==d)cf+=imp[e2];double sc=cf+1e-12*dc[d];if(best<0||sc0)T=sm/c;if(T<1e-9)T=1.0;}\n double T0=T;\n for(long long step=0;;step++){\n if(step%200000==0){double el=chrono::duration(chrono::steady_clock::now()-tst).count();if(el>5.5)break;T=T0*exp(-10.*el/5.5);}\n int d1=ri(D),d2=ri(D);if(d1==d2||dayE[d1].empty()||dayE[d2].empty())continue;\n int e1=dayE[d1][ri(dayE[d1].size())],e2=dayE[d2][ri(dayE[d2].size())];\n double dl=imp[e1]*(ADJ[e1][d2]-ADJ[e1][d1])+imp[e2]*(ADJ[e2][d1]-ADJ[e2][d2])-2.*isA(e1,e2)*imp[e1]*imp[e2];\n if(dl<=0||(T>1e-9&&rd()\nusing namespace std;\nint D;\nstring Fs[2][14], Rs[2][14];\nint bid;\nint B[2][2744];\nvoid fill_patch(int a,int x0,int y0,int z0,int xl,int yl,int id){\n for(int i=0;i getPatches(int a){\n vector P;\n for(int z=0;z> xr,yr;\n for(int x=0,s=-1;x<=D;x++){bool v=x=0){xr.push_back({s,x-s});s=-1;}}\n for(int y=0,s=-1;y<=D;y++){bool v=y=0){yr.push_back({s,y-s});s=-1;}}\n for(auto[x0,xl]:xr)for(auto[y0,yl]:yr)P.push_back({x0,y0,z,xl,yl});\n }\n return P;\n}\nvector makeLines(const vector& P,const vector& u,int ax){\n vector L;\n for(int i=0;i<(int)P.size();i++)if(!u[i]){\n const auto& p=P[i];\n if(ax==1){for(int dx=0;dx& L0,const vector& L1){\n map c0,c1;\n for(const auto& l:L0)c0[l.len]++;\n for(const auto& l:L1)c1[l.len]++;\n double sc=0;int v0=0,v1=0;\n for(const auto& [l,c]:c0){int cl=c1.count(l)?c1.at(l):0;int mc=min(c,cl);sc+=mc*1.0/l;v0+=(c-mc)*l;}\n for(const auto& [l,c]:c1){int cl=c0.count(l)?c0.at(l):0;if(c>cl)v1+=(c-cl)*l;}\n sc+=max(v0,v1);\n return sc;\n}\nint main(){\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n cin>>D;\n for(int i=0;i<2;i++){for(int z=0;z>Fs[i][z];for(int z=0;z>Rs[i][z];}\n memset(B,0,sizeof(B));\n bid=0;\n auto P0=getPatches(0),P1=getPatches(1);\n map,vector> g0,g1;\n for(int i=0;i<(int)P0.size();i++)g0[{min(P0[i].xl,P0[i].yl),max(P0[i].xl,P0[i].yl)}].push_back(i);\n for(int i=0;i<(int)P1.size();i++)g1[{min(P1[i].xl,P1[i].yl),max(P1[i].xl,P1[i].yl)}].push_back(i);\n vector u0(P0.size(),false),u1(P1.size(),false);\n for(auto& [d,v0]:g0){\n auto it=g1.find(d);if(it==g1.end())continue;\n auto& v1=it->second;\n int mc=min((int)v0.size(),(int)v1.size());\n for(int j=0;j> gl0,gl1;\n for(int i=0;i<(int)L0.size();i++)gl0[L0[i].len].push_back(i);\n for(int i=0;i<(int)L1.size();i++)gl1[L1[i].len].push_back(i);\n vector lu0(L0.size(),false),lu1(L1.size(),false);\n for(auto& [l,v0]:gl0){\n auto it=gl1.find(l);if(it==gl1.end())continue;\n auto& v1=it->second;\n int mc=min((int)v0.size(),(int)v1.size());\n for(int j=0;j> rv0,rv1;\n for(int i=0;i<(int)L0.size();i++)if(!lu0[i])rv0.push_back({L0[i].len,i});\n for(int i=0;i<(int)L1.size();i++)if(!lu1[i])rv1.push_back({L1[i].len,i});\n sort(rv0.rbegin(),rv0.rend());\n sort(rv1.begin(),rv1.end());\n struct SO{int idx,off;};\n deque r0,r1;\n for(auto& [l,i]:rv0)r0.push_back({i,0});\n for(auto& [l,i]:rv1)r1.push_back({i,0});\n auto gpos=[&](const Line& s,int off)->tuple{\n return{s.x+(s.ax==0?off:0),s.y+(s.ax==1?off:0),s.z+(s.ax==2?off:0)};\n };\n while(!r0.empty()&&!r1.empty()){\n auto& [i0,o0]=r0.front();\n auto& [i1,o1]=r1.front();\n int ml=min(L0[i0].len-o0,L1[i1].len-o1);\n bid++;\n auto [x0,y0,z0]=gpos(L0[i0],o0);\n auto [x1,y1,z1]=gpos(L1[i1],o1);\n fill_line(0,x0,y0,z0,ml,L0[i0].ax,bid);\n fill_line(1,x1,y1,z1,ml,L1[i1].ax,bid);\n o0+=ml;o1+=ml;\n if(o0==L0[i0].len)r0.pop_front();\n if(o1==L1[i1].len)r1.pop_front();\n }\n while(!r0.empty()){\n auto [i0,o0]=r0.front();r0.pop_front();\n bid++;\n auto [x,y,z]=gpos(L0[i0],o0);\n fill_line(0,x,y,z,L0[i0].len-o0,L0[i0].ax,bid);\n }\n while(!r1.empty()){\n auto [i1,o1]=r1.front();r1.pop_front();\n bid++;\n auto [x,y,z]=gpos(L1[i1],o1);\n fill_line(1,x,y,z,L1[i1].len-o1,L1[i1].ax,bid);\n }\n cout<\nusing namespace std;\ntypedef long long ll;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n int N, M, K;\n cin >> N >> M >> K;\n vector X(N), Y(N);\n for (int i = 0; i < N; i++) cin >> X[i] >> Y[i];\n vector EU(M), EV(M); vector EW(M);\n for (int j = 0; j < M; j++) { cin >> EU[j] >> EV[j] >> EW[j]; EU[j]--; EV[j]--; }\n vector A(K), B(K);\n for (int k = 0; k < K; k++) cin >> A[k] >> B[k];\n const ll MAXP = 5000, MAXP2 = MAXP * MAXP, INF = (ll)4e18;\n vector> D2(N, vector(K));\n for (int i = 0; i < N; i++)\n for (int k = 0; k < K; k++) {\n ll dx = A[k]-X[i], dy = B[k]-Y[i]; D2[i][k] = dx*dx+dy*dy;\n }\n vector>> adj(N);\n for (int j = 0; j < M; j++) {\n adj[EU[j]].push_back({EV[j],j}); adj[EV[j]].push_back({EU[j],j});\n }\n auto pVal = [&](ll d2) -> ll {\n if (!d2) return 0;\n ll p = (ll)sqrt((double)d2);\n while (p*p < d2) p++;\n return min(p, MAXP);\n };\n // APSP\n vector> spD(N, vector(N, INF));\n vector> spE(N, vector(N,-1)), spPr(N, vector(N,-1));\n for (int s = 0; s < N; s++) {\n spD[s][s] = 0;\n priority_queue,vector>,greater<>> pq;\n pq.push({0,s});\n while (!pq.empty()) {\n auto [d,v] = pq.top(); pq.pop();\n if (d > spD[s][v]) continue;\n for (auto& [u,j] : adj[v]) {\n ll nd = d+EW[j];\n if (nd < spD[s][u]) { spD[s][u]=nd; spPr[s][u]=v; spE[s][u]=j; pq.push({nd,u}); }\n }\n }\n }\n auto buildSteiner = [&](vector term) -> vector {\n term[0] = true;\n vector T;\n for (int i = 0; i < N; i++) if (term[i]) T.push_back(i);\n int TN = T.size();\n vector inST(TN,false); vector key(TN,INF); vector par(TN,-1);\n key[0] = 0;\n for (int it = 0; it < TN; it++) {\n int u = -1;\n for (int i = 0; i < TN; i++) if (!inST[i]&&(u<0||key[i]=INF) break;\n inST[u] = true;\n for (int w = 0; w < TN; w++)\n if (!inST[w]&&spD[T[u]][T[w]] eo(M,false);\n for (int i = 0; i < TN; i++) {\n if (par[i]<0) continue;\n int src=T[par[i]], dst=T[i];\n for (int v=dst; v!=src; v=spPr[src][v]) eo[spE[src][v]]=true;\n }\n return eo;\n };\n auto evalEO = [&](const vector& eo) -> tuple,ll,bool> {\n vector reach(N,false);\n queue q; q.push(0); reach[0]=true;\n while (!q.empty()) {\n int v=q.front(); q.pop();\n for (auto& [u,j]:adj[v]) if(eo[j]&&!reach[u]){reach[u]=true;q.push(u);}\n }\n ll ec=0; for(int j=0;j mxD2(N,0);\n for (int k=0; kMAXP2) return {{},INF,false};\n mxD2[bv]=max(mxD2[bv],best);\n }\n vector P(N,0); ll pc=0;\n for (int i=0;i0){ll p=pVal(mxD2[i]);P[i]=(int)p;pc+=p*p;}\n return {P,ec+pc,true};\n };\n // MST\n vector mstPar(N,-1), mstPE(N,-1); vector> mstCh(N);\n {\n vector vis(N,false); vector key(N,INF); key[0]=0;\n priority_queue,vector>,greater<>> pq; pq.push({0,0});\n while (!pq.empty()) {\n auto [d,v]=pq.top(); pq.pop();\n if (vis[v]) continue; vis[v]=true;\n for (auto& [u,j]:adj[v]) if(!vis[u]&&EW[j] act(N,true); vector> vRes(N); vector vmx(N,0), Pv(N,0);\n for (int k=0;k> bAs; vector> bAf;\n for (int v=1;v tmp; vector> ta; bool ok=true;\n for (int k:vRes[v]) {\n ll best=INF; int bu=-1;\n for (int u=0;uMAXP2){ok=false;break;}\n ta.push_back({k,bu});\n if(!tmp.count(bu)) tmp[bu]=vmx[bu];\n tmp[bu]=max(tmp[bu],best);\n }\n if (!ok) continue;\n for (auto& [u,nd]:tmp){ll np=pVal(nd);delta+=np*np-Pv[u]*Pv[u];}\n if (delta=0) {\n act[bV]=false; ec0-=EW[mstPE[bV]]; pc0-=Pv[bV]*Pv[bV];\n Pv[bV]=0; vmx[bV]=0; vRes[bV].clear();\n for (auto&[k,u]:bAs) vRes[u].push_back(k);\n for (auto&[u,nd]:bAf){pc0-=Pv[u]*Pv[u];vmx[u]=nd;Pv[u]=pVal(nd);pc0+=Pv[u]*Pv[u];}\n imp=true;\n }\n }\n ll bestCost=ec0+pc0;\n vector bestEO(M,false);\n for (int v=1;v bestP(N,0);\n for (int i=0;i& eo,const vector& P,ll cost){\n if(cost term){\n term[0]=true;\n for (int sit=0;sit<20;sit++){\n auto eo=buildSteiner(term);\n auto [sp,sc,sf]=evalEO(eo);\n if (!sf) break;\n updateBest(eo,sp,sc);\n vector nt(N,false); nt[0]=true;\n for (int i=0;i0) nt[i]=true;\n if (nt==term) break;\n term=nt;\n }\n };\n // Steiner from MST-pruned terminals\n { vector t(N,false); for(int i=0;i0) t[i]=true; runSteiner(t); }\n // Steiner from all-vertices terminals\n { vector t(N,true); runSteiner(t); }\n for (int i=0;i\nusing namespace std;\n\nconst int N = 30;\nint board[N][N];\nint pr[N*(N+1)/2], pc[N*(N+1)/2];\nvector> ops;\n\nvoid swap_it(int x1, int y1, int x2, int y2) {\n int v1 = board[x1][y1], v2 = board[x2][y2];\n swap(board[x1][y1], board[x2][y2]);\n pr[v1] = x2; pc[v1] = y2;\n pr[v2] = x1; pc[v2] = y1;\n ops.push_back({x1, y1, x2, y2});\n}\n\nvoid move_to(int v, int tx, int ty) {\n if (pc[v] < ty) {\n while (pc[v] < ty) swap_it(pr[v], pc[v], pr[v], pc[v]+1);\n while (pr[v] > tx) swap_it(pr[v], ty, pr[v]-1, ty);\n } else {\n int extra = (pc[v] - ty) - (pr[v] - tx);\n for (int i = 0; i < extra; i++)\n swap_it(pr[v], pc[v], pr[v], pc[v]-1);\n while (pr[v] > tx) {\n if (pc[v] > ty) swap_it(pr[v], pc[v], pr[v]-1, pc[v]-1);\n else swap_it(pr[v], pc[v], pr[v]-1, pc[v]);\n }\n }\n}\n\nint main() {\n ios::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 >> board[x][y];\n pr[board[x][y]] = x;\n pc[board[x][y]] = y;\n }\n \n for (int x = 0; x < N; x++) {\n int base = x*(x+1)/2;\n \n vector> cv;\n for (int i = 0; i <= x; i++) cv.push_back({pc[base+i], i});\n sort(cv.begin(), cv.end());\n \n vector asgn(x+1);\n for (int i = 0; i <= x; i++) asgn[i] = cv[i].second;\n \n for (int ty = x; ty >= 0; ty--)\n move_to(base + asgn[ty], x, ty);\n }\n \n cout << ops.size() << \"\\n\";\n for (auto& op : ops)\n cout << op[0] << \" \" << op[1] << \" \" << op[2] << \" \" << op[3] << \"\\n\";\n}","toyota2023summer-final":"#include \nusing namespace std;\nconst int D9=9;\nint D,N,M;\nbool obs[D9][D9],hasc[D9][D9];\nint cnum[D9][D9],sr[D9*D9],sc[D9*D9],prank[D9][D9];\nint er,ec;\nconst int dr[4]={-1,1,0,0},dc[4]={0,0,-1,1};\nbool in_(int r,int c){return r>=0&&r=0&&c>q;q.push({er,ec});dist[er][ec]=0;\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+dr[i],ny=y+dc[i];if(!in_(nx,ny)||dist[nx][ny]>=0||obs[nx][ny])continue;dist[nx][ny]=dist[x][y]+1;q.push({nx,ny});}}\n vector>pos;\n for(int r=0;r&a,const pair&b){if(dist[a.first][a.second]!=dist[b.first][b.second])return dist[a.first][a.second]>q;q.push({er,ec});vis[er][ec]=1;\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+dr[i],ny=y+dc[i];if(!in_(nx,ny)||vis[nx][ny]||obs[nx][ny]||hasc[nx][ny])continue;vis[nx][ny]=1;q.push({nx,ny});}}\n}\nbool safe_place(int r,int c,const vector>&reach){\n bool vis[D9][D9];memset(vis,0,sizeof vis);\n queue>q;q.push({er,ec});vis[er][ec]=1;\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+dr[i],ny=y+dc[i];if(!in_(nx,ny)||vis[nx][ny]||obs[nx][ny]||hasc[nx][ny])continue;if(nx==r&&ny==c)continue;vis[nx][ny]=1;q.push({nx,ny});}}\n for(auto[pr,pc]:reach){if(pr==r&&pc==c)continue;if(!vis[pr][pc])return false;}\n return true;\n}\npairpick_place(int t){\n bool vis[D9][D9];bfs_emp(vis);\n int ir=sr[t],ic=sc[t];\n vector>reach;\n for(int r=0;rbest{-1,-1};int bd=INT_MAX,brk=-1;bool gots=false;\n for(auto[r,c]:reach){\n if(r==ir&&c==ic)continue;\n bool s=safe_place(r,c,reach);\n int d=abs(prank[r][c]-t),rk=prank[r][c];\n bool better=(!gots&&s)||(gots==s&&(dbrk)));\n if(better){best={r,c};bd=d;brk=rk;gots=s;}\n }\n return best;\n}\nvector>transport(){\n bool h[D9][D9];memcpy(h,hasc,sizeof h);\n vector>ord;ord.reserve(M);\n for(int s=0;s>q;q.push({er,ec});vis[er][ec]=1;\n int bn=INT_MAX,br=-1,bc=-1;\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+dr[i],ny=y+dc[i];if(!in_(nx,ny)||vis[nx][ny]||obs[nx][ny])continue;vis[nx][ny]=1;if(h[nx][ny]){if(cnum[nx][ny]>D>>N;\n memset(obs,0,sizeof obs);memset(hasc,0,sizeof hasc);memset(cnum,-1,sizeof cnum);\n er=0;ec=(D-1)/2;\n for(int i=0;i>r>>c;obs[r][c]=1;}\n build_sigma();\n for(int d=0;d>t;\n auto[r,c]=pick_place(t);\n hasc[r][c]=1;cnum[r][c]=t;\n cout<\nusing namespace std;\nint n,m,g[50][50];\nbool adj[102][102];\nint acnt[102][102],ccnt[102];\nconst int dr[]={0,0,1,-1},dc[]={1,-1,0,0};\nint gc(int r,int c){return(r<0||r>=n||c<0||c>=n)?0:g[r][c];}\nvoid init(){\n for(int i=0;i>q;q.push({sr,sc_});vis[sr][sc_]=1;int cnt=1;\n while(!q.empty()){\n auto[cr,cc]=q.front();q.pop();\n for(int d=0;d<4;d++){int nr=cr+dr[d],nc=cc+dc[d];\n if(nr>=0&&nr=0&&nc=0&&nr=0&&nc=n||nc<0||nc>=n)continue;\n int ncol=g[nr][nc];if(!ncol)continue;\n bool hz=0;\n for(int d2=0;d2<4;d2++){\n int nr2=nr+dr[d2],nc2=nc+dc[d2];\n if(nr2==r&&nc2==c)continue;\n if(nr2<0||nr2>=n||nc2<0||nc2>=n){hz=1;break;}\n if(!g[nr2][nc2]){hz=1;break;}\n }\n if(!hz)acnt[ncol][0]++;\n if(ncol==col)continue;\n bool sc2=0;\n for(int d2=0;d2<4;d2++){\n int nr2=nr+dr[d2],nc2=nc+dc[d2];\n if(nr2==r&&nc2==c)continue;\n if(nr2>=0&&nr2=0&&nc2>n>>m;\n for(int i=0;i>g[i][j];\n init();\n bool ch=1;\n while(ch){\n ch=0;\n for(int i=0;i\nusing namespace std;\n\nint N, D, Q, q_used = 0;\n\nchar bq(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 q_used++;\n char c; cin >> c; return c;\n}\n\nint slm;\nvector ms(vector a) {\n if ((int)a.size() <= 1 || q_used >= slm) return a;\n int m = a.size() / 2;\n auto L = ms(vector(a.begin(), a.begin() + m));\n auto R = ms(vector(a.begin() + m, a.end()));\n vector r; int i = 0, j = 0;\n while (i < (int)L.size() && j < (int)R.size()) {\n if (q_used >= slm) break;\n if (bq({L[i]}, {R[j]}) != '>') r.push_back(L[i++]);\n else r.push_back(R[j++]);\n }\n while (i < (int)L.size()) r.push_back(L[i++]);\n while (j < (int)R.size()) r.push_back(R[j++]);\n return r;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> D >> Q;\n\n auto t0 = chrono::high_resolution_clock::now();\n auto el = [&]() {\n return chrono::duration(chrono::high_resolution_clock::now() - t0).count();\n };\n\n // Phase 1: Sort\n slm = Q / 2;\n vector ini(N); iota(ini.begin(), ini.end(), 0);\n vector ord = ms(ini);\n\n vector pos(N);\n for (int i = 0; i < N; i++) pos[ord[i]] = i;\n\n // Phase 2: Weight estimation via binary search on prefix sums\n int est_end = Q * 4 / 5;\n vector w(N, 1.0), ps(N + 1, 0.0);\n w[ord[0]] = 1.0; ps[1] = 1.0;\n\n for (int i = 1; i < N; i++) {\n int lo = 0, hi = i;\n while (lo < hi && q_used < est_end) {\n int mid = (lo + hi) / 2;\n if (bq({ord[i]}, vector(ord.begin(), ord.begin() + mid + 1)) == '>')\n lo = mid + 1;\n else hi = mid;\n }\n double wlo = ps[lo];\n double whi = (lo < i) ? ps[lo + 1] : ps[i] * 2.0;\n w[ord[i]] = max(w[ord[i-1]], (wlo + whi) / 2.0);\n ps[i+1] = ps[i] + w[ord[i]];\n }\n\n // Phase 3: LPT partition\n vector oi(N); iota(oi.begin(), oi.end(), 0);\n sort(oi.begin(), oi.end(), [&](int a, int b) {\n if (fabs(w[a]-w[b]) > 1e-12) return w[a] > w[b];\n return pos[a] > pos[b];\n });\n vector gw(D, 0.0);\n vector asgn(N, 0);\n for (int x : oi) {\n int g = (int)(min_element(gw.begin(), gw.end()) - gw.begin());\n asgn[x] = g; gw[g] += w[x];\n }\n\n // Phase 4: Local search with estimated weights\n double total = 0; for (double x : gw) total += x;\n double mean = total / D;\n\n for (int p = 0; p < 5000 && el() < 1.5; p++) {\n bool imp = false;\n // Single moves\n for (int x = 0; x < N; x++) {\n int g0 = asgn[x]; int bg = g0; double bd = 0;\n double d0 = gw[g0] - mean;\n for (int g = 0; g < D; g++) {\n if (g == g0) continue;\n double d1 = gw[g] - mean;\n double dc = d0*d0 + d1*d1 - (d0-w[x])*(d0-w[x]) - (d1+w[x])*(d1+w[x]);\n if (dc > bd) { bd = dc; bg = g; }\n }\n if (bg != g0) { gw[g0] -= w[x]; gw[bg] += w[x]; asgn[x] = bg; imp = true; }\n }\n // Swaps\n for (int i = 0; i < N && el() < 1.4; i++) {\n for (int j = i+1; j < N; j++) {\n if (asgn[i] == asgn[j]) continue;\n int gi = asgn[i], gj = asgn[j];\n double di = gw[gi]-mean, dj = gw[gj]-mean;\n double di2 = di-w[i]+w[j], dj2 = dj+w[i]-w[j];\n if (di*di + dj*dj > di2*di2 + dj2*dj2 + 1e-9) {\n gw[gi] += w[j]-w[i]; gw[gj] += w[i]-w[j];\n asgn[i] = gj; asgn[j] = gi; imp = true;\n }\n }\n }\n if (!imp) break;\n }\n\n // Phase 5: Actual balance improvement using remaining queries\n vector> gi(D);\n for (int x = 0; x < N; x++) gi[asgn[x]].push_back(x);\n for (int g = 0; g < D; g++)\n sort(gi[g].begin(), gi[g].end(), [&](int a, int b){ return pos[a] < pos[b]; });\n\n while (q_used + 2 <= Q && el() < 1.9) {\n int gh = (int)(max_element(gw.begin(), gw.end()) - gw.begin());\n int gl = (int)(min_element(gw.begin(), gw.end()) - gw.begin());\n if (gw[gh] <= gw[gl] + 1e-9 || gi[gh].empty() || gi[gl].empty()) break;\n\n char cmp = bq(gi[gh], gi[gl]);\n if (cmp == '=') { gw[gh] = gw[gl] = (gw[gh]+gw[gl])/2; continue; }\n if (cmp == '<') { swap(gh, gl); swap(gw[gh], gw[gl]); }\n\n auto& hv = gi[gh]; auto& lt = gi[gl];\n if ((int)hv.size() <= 1) continue;\n\n int lo = 0, hi = (int)hv.size() - 1;\n while (lo < hi && q_used + 1 <= Q && el() < 1.85) {\n int mid = (lo + hi) / 2;\n vector L2, R2 = lt;\n for (int k = 0; k < (int)hv.size(); k++) if (k != mid) L2.push_back(hv[k]);\n R2.push_back(hv[mid]);\n char r = bq(L2, R2);\n if (r == '=') { lo = hi = mid; break; }\n else if (r == '>') lo = mid + 1;\n else hi = mid;\n }\n lo = min(lo, (int)hv.size() - 1);\n if (lo > 0) {\n double da = fabs((gw[gh]-w[hv[lo]]) - (gw[gl]+w[hv[lo]]));\n double db = fabs((gw[gh]-w[hv[lo-1]]) - (gw[gl]+w[hv[lo-1]]));\n if (db < da) lo--;\n }\n\n int mv = hv[lo];\n asgn[mv] = gl;\n gw[gh] -= w[mv]; gw[gl] += w[mv];\n hv.erase(hv.begin() + lo);\n lt.insert(lower_bound(lt.begin(), lt.end(), mv,\n [&](int a, int b){ return pos[a] < pos[b]; }), mv);\n }\n\n while (q_used < Q) bq({0}, {1});\n\n for (int i = 0; i < N; i++) cout << asgn[i] << \" \\n\"[i==N-1];\n cout.flush();\n return 0;\n}","ahc026":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n \n int n, m;\n cin >> n >> m;\n \n vector> stacks(m);\n vector stk(n + 1), pidx(n + 1);\n \n int h = n / m;\n for (int i = 0; i < m; i++) {\n stacks[i].resize(h);\n for (int j = 0; j < h; j++) {\n cin >> stacks[i][j];\n stk[stacks[i][j]] = i;\n pidx[stacks[i][j]] = j;\n }\n }\n \n vector> ops;\n \n for (int v = 1; v <= n; v++) {\n int s = stk[v];\n int j = pidx[v];\n \n while ((int)stacks[s].size() > j + 1) {\n int top_pos = (int)stacks[s].size() - 1;\n int run_start = top_pos;\n while (run_start > j + 1 && stacks[s][run_start - 1] > stacks[s][run_start])\n run_start--;\n \n int u1 = stacks[s][run_start];\n int best_t = -1, best_score = INT_MIN;\n \n for (int t = 0; t < m; t++) {\n if (t == s) continue;\n int score;\n if (stacks[t].empty()) score = n;\n else {\n int top_t = stacks[t].back();\n score = (top_t > u1) ? 2*n+1-top_t : top_t-n-1;\n }\n if (score > best_score) { best_score = score; best_t = t; }\n }\n \n int move_box = stacks[s][run_start];\n int new_base = (int)stacks[best_t].size();\n int old_size_s = (int)stacks[s].size();\n \n ops.push_back({move_box, best_t + 1});\n for (int p = run_start; p < old_size_s; p++) {\n int b = stacks[s][p];\n stacks[best_t].push_back(b);\n stk[b] = best_t;\n pidx[b] = new_base + (p - run_start);\n }\n stacks[s].resize(run_start);\n }\n \n ops.push_back({v, 0});\n stacks[s].pop_back();\n }\n \n for (auto& [v, i] : ops)\n cout << v << \" \" << i << \"\\n\";\n \n return 0;\n}","ahc027":"#include \nusing namespace std;\nconst int MAXN=41,MAXC=1601,BUD=100000;\nint N,n;\nbool hw[MAXN][MAXN],vw[MAXN][MAXN];\nint dv[MAXN][MAXN];\nconst int DI[]={0,1,0,-1},DJ[]={1,0,-1,0};\nconst char DC[]=\"RDLU\";\nint C(int i,int j){return i*N+j;}\nint RI(int c){return c/N;}\nint RJ(int c){return c%N;}\nbool OK(int i,int j,int d){\n int ni=i+DI[d],nj=j+DJ[d];\n if(ni<0||ni>=N||nj<0||nj>=N)return false;\n if(d==0)return !vw[i][j];\n if(d==1)return !hw[i][j];\n if(d==2)return !vw[i][nj];\n return !hw[ni][j];\n}\nshort AP[MAXC][MAXC];\nint AF[MAXC][MAXC];\nvoid bfs(int s){\n memset(AP[s],0xFF,n*sizeof(short));\n int fs[MAXC];AP[s][s]=0;fs[s]=s;\n static int q[MAXC];int h=0,tail=0;q[tail++]=s;\n while(h>N;n=N*N;\n for(int i=0;i>s;for(int j=0;j>s;for(int j=0;j>dv[i][j];\n for(int s=0;s lv(n,0);int pos=0,t=0;\n {\n vector vis(n,false);vis[0]=true;\n vector> stk;stk.reserve(n);stk.push_back({0,0});\n while(!stk.empty()){\n int u=stk.back().first;int& nd=stk.back().second;bool found=false;\n while(nd<4){\n int d=nd++;\n if(OK(RI(u),RJ(u),d)){int v=C(RI(u)+DI[d],RJ(u)+DJ[d]);\n if(!vis[v]){route+=DC[d];t++;pos=v;lv[v]=t;vis[v]=true;stk.push_back({v,0});found=true;break;}}\n }\n if(!found){stk.pop_back();\n if(!stk.empty()){int par=stk.back().first;\n for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==par){route+=DC[d];t++;pos=par;lv[par]=t;break;}}}\n }\n }\n for(int c=0;cBUD)continue;\n float u=sqd[c]*(float)(t-lv[c]+1);\n if(u>bu){bu=u;best=c;}\n }\n if(best<0)break;\n int nx=AF[pos][best];\n for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==nx){route+=DC[d];pos=nx;t++;lv[pos]=t;break;}\n }\n while(pos!=0){\n int nx=AF[pos][0];\n for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==nx){route+=DC[d];pos=nx;t++;break;}\n }\n cout<\nusing namespace std;\nint N, M, si, sj;\nvector targets;\nvector> charPos[26];\nint ovM[200][200];\nvoid computeOvMatrix() {\n for(int i=0;i=1;k--){bool ok=true;for(int l=0;l greedyPerm(int start){\n vector used(M,false);vector perm;perm.reserve(M);perm.push_back(start);used[start]=true;\n while((int)perm.size()bov){bov=ovM[last][j];best=j;}perm.push_back(best);used[best]=true;}\n return perm;\n}\nint permOv(const vector&p){int s=0;for(int i=1;i<(int)p.size();i++)s+=ovM[p[i-1]][p[i]];return s;}\nint swapGain(const vector&perm,int i,int j){\n int m=perm.size(),a=perm[i],b=perm[j],og=0,ng=0;\n if(i>0){og+=ovM[perm[i-1]][a];ng+=ovM[perm[i-1]][b];}\n if(j0){og+=ovM[perm[j-1]][b];ng+=ovM[perm[j-1]][a];}}\n return ng-og;\n}\nbool swapOpt(vector&perm){int m=perm.size(),bg=0,bi=-1,bj=-1;for(int i=0;ibg){bg=g;bi=i;bj=j;}}if(bi==-1)return false;swap(perm[bi],perm[bj]);return true;}\nbool orOpt(vector&perm){\n int m=perm.size(),bg=0,bk=-1,bp=-1;\n for(int k=0;k rest;rest.reserve(m-1);for(int i=0;i0)?ovM[perm[k-1]][e]:0,ro=(k0&&k0)?ovM[rest[p-1]][e]:0,nr=(p<(int)rest.size())?ovM[e][rest[p]]:0,nb=(p>0&&p<(int)rest.size())?ovM[rest[p-1]][rest[p]]:0,g=nl+nr-nb-rc;if(g>bg){bg=g;bk=k;bp=p;}}}\n if(bk==-1)return false;\n int e=perm[bk];vector rest;rest.reserve(m-1);for(int i=0;i&perm){\n int m=perm.size();if(m<2)return false;\n vector diff(m-1),pref(m,0);\n for(int k=0;k0)g+=ovM[perm[i-1]][perm[j]]-ovM[perm[i-1]][perm[i]];if(jbg){bg=g;bi=i;bj=j;}}\n if(bi==-1)return false;reverse(perm.begin()+bi,perm.begin()+bj+1);return true;\n}\nvoid localSearch(vector&perm){bool imp=true;while(imp){imp=false;if(swapOpt(perm))imp=true;if(orOpt(perm))imp=true;if(reverseOpt(perm))imp=true;}}\nstring buildString(const vector&perm){string s=targets[perm[0]];for(int i=1;i<(int)perm.size();i++)s+=targets[perm[i]].substr(ovM[perm[i-1]][perm[i]]);return s;}\nvector> findPath(const string&s){\n int L=s.size(),G=N*N;const int INF=1e9;\n vector dp((L+1)*G,INF),prv((L+1)*G,-1);\n dp[si*N+sj]=0;\n for(int i=0;i> path(L);int pos=bp;\n for(int i=L;i>=1;i--){path[i-1]={pos/N,pos%N};pos=prv[i*G+pos];}\n return path;\n}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n auto t0=chrono::steady_clock::now();\n auto ms_el=[&](){return chrono::duration_cast(chrono::steady_clock::now()-t0).count();};\n cin>>N>>M>>si>>sj;\n for(int i=0;i>row;for(int j=0;j>targets[i];\n computeOvMatrix();\n vector best;int bestOv=-1;\n for(int s=0;sbestOv){bestOv=o;best=p;}}\n localSearch(best);bestOv=permOv(best);\n {\n mt19937 rng(42);uniform_real_distribution ud(0.0,1.0);\n vector cur=best;int curOv=bestOv;double T=2.0;\n for(long long it=0;;it++){\n if(it%50000==0&&ms_el()>=1700)break;\n T=max(0.05,T*0.9999998);\n int i=rng()%M,j=rng()%M;if(i==j)continue;if(i>j)swap(i,j);\n int gain=swapGain(cur,i,j);\n if(gain>0||ud(rng)bestOv){bestOv=curOv;best=cur;}}\n }\n }\n if(ms_el()<1850)localSearch(best);\n string ss=buildString(best);\n auto path=findPath(ss);\n for(auto&[r,c]:path)cout<\nusing namespace std;\nint N,M,MAX_OPS;double eps,coef;int ops=0;\nstruct Field{int d,hi,hj;vector>cells;vectorrp,cp;vector>pos;};\nvectorF;vector>drld;vector>prob,ell;\nvectorrobs,cobs;int nrr=0,nrc=0;\ndouble qdiv(const vector>&c){ops++;cout<<\"q \"<>v;return v;}\nint qdrl(int i,int j){ops++;cout<<\"q 1 \"<>v;drld[i][j]=v;return v;}\nbool qans(const vector>&o){ops++;cout<<\"a \"<>r;return r==1;}\nvoid do_row_col(int reps){for(int rep=0;rep>c;for(int j=0;j>c;for(int i=0;itmr(N,0),tmc(N,0);\n for(int k=0;kkmr(N,0),kmc(N,0);\n for(int p=0;p>drow(N,vector(F[k].hi+1)),dcol(N,vector(F[k].hj+1));\n for(int i=0;ill(np,-1e300);double mx=-1e300;\n for(int p=0;p-1e250)?exp(ll[p]-mx):0.0;s+=prob[k][p];}\n if(s>1e-15)for(int p=0;p1e-15){for(auto&pp:prob[k])pp/=s;}\n else{int cnt=0;for(int p=0;p-1e29)cnt++;\n for(int p=0;p-1e29&&cnt>0)?1.0/cnt:0;\n if(cnt==0){fill(ell[k].begin(),ell[k].end(),0);fill(prob[k].begin(),prob[k].end(),1.0/np);}}}\n }\n}\ndouble field_entropy(int k){double H=0;for(double p:prob[k])if(p>1e-12)H-=p*log(p);return H;}\nvoid do_shape_query(int k){\n if(ops>=MAX_OPS-5)return;int np=(int)F[k].pos.size();\n int p1=-1,p2=-1;for(int p=0;pprob[k][p1]){p2=p1;p1=p;}else if(p2<0||prob[k][p]>prob[k][p2])p2=p;}\n if(p1<0||prob[k][p1]>0.98)return;\n auto[di1,dj1]=F[k].pos[p1];\n vector>S;\n if(p2>=0){auto[di2,dj2]=F[k].pos[p2];set>c2;for(auto[ci,cj]:F[k].cells)c2.insert({di2+ci,dj2+cj});for(auto[ci,cj]:F[k].cells){pairc={di1+ci,dj1+cj};if(!c2.count(c))S.push_back(c);}if((int)S.size()<2){S.clear();for(auto[ci,cj]:F[k].cells)S.push_back({di1+ci,dj1+cj});}}\n else{for(auto[ci,cj]:F[k].cells)S.push_back({di1+ci,dj1+cj});}\n if((int)S.size()<2)return;\n vectorSmap(N*N,false);for(auto[i,j]:S)Smap[i*N+j]=true;\n vectorovl(np,0);for(int p=0;p-1e29)for(int p=0;p-1e29)ell[k][p]-=newmax;\n}\nvector>get_oil_prob(){\n vector>noc(N,vector(N,1.0));\n for(int k=0;k>cvk(N,vector(N,0));for(int p=0;p<(int)F[k].pos.size();p++){double pp=prob[k][p];if(pp<1e-12)continue;auto[di,dj]=F[k].pos[p];for(auto[ci,cj]:F[k].cells)cvk[di+ci][dj+cj]+=pp;}for(int i=0;i>op(N,vector(N));for(int i=0;i>make_guess(const vector>&op,double thr=0.5){\n vector>res;for(int i=0;i0)||(drld[i][j]<0&&op[i][j]>thr);if(oil)res.push_back({i,j});}return res;\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>N>>M>>eps;MAX_OPS=2*N*N;coef=1.0-2.0*eps;\n drld.assign(N,vector(N,-1));robs.assign(N,0.0);cobs.assign(N,0.0);\n F.resize(M);\n for(int k=0;k>F[k].d;F[k].cells.resize(F[k].d);F[k].hi=F[k].hj=0;\n for(int t=0;t>F[k].cells[t].first>>F[k].cells[t].second;F[k].hi=max(F[k].hi,F[k].cells[t].first);F[k].hj=max(F[k].hj,F[k].cells[t].second);}\n F[k].rp.assign(F[k].hi+1,0);F[k].cp.assign(F[k].hj+1,0);for(auto[ci,cj]:F[k].cells){F[k].rp[ci]++;F[k].cp[cj]++;}\n for(int di=0;di+F[k].hi=0.15)?3:(eps>=0.08)?2:1;\n do_row_col(n_reps);\n run_mf(200);\n {int qb=min(60,MAX_OPS-ops-20);\n for(int q=0;qbe){be=h;bk=k;}}\n if(be<0.1)break;do_shape_query(bk);run_mf(15);}}\n apply_constraints();run_mf(100);\n while(ops=0)continue;double pu=min(op[i][j],1.0-op[i][j]);if(pu>bunc){bunc=pu;bi=i;bj=j;}}\n if(bunc<0.05||bi<0){for(int i=0;i0.05&&op[i][j]<0.95)qdrl(i,j);break;}\n qdrl(bi,bj);apply_constraints();run_mf(20);}\n {auto op=get_oil_prob();auto g=make_guess(op);if(ops\nusing namespace std;\ntypedef long long ll;\ntypedef tuple T3;\nint W,D,N;\nvector> a;\nvector compute_heights(const vector& days){\n vector h(N,1);\n auto ben=[&](int k,int cur)->ll{ll b=0;for(int d:days){int def=a[d][k]-cur*W;if(def>0)b+=min(W,def);}return b;};\n priority_queue pq;\n for(int k=0;k0)pq.push({b,k,1});}\n for(int rem=W-N;rem>0&&!pq.empty();){auto[b,k,c]=pq.top();pq.pop();if(b<=0)break;h[k]++;rem--;ll nb=ben(k,h[k]);if(nb>0)pq.push({nb,k,h[k]});}\n sort(h.begin(),h.end());return h;}\nll area_cost(int d,const vector& h){ll c=0;for(int k=0;k0)c+=(ll)def*100;}return c;}\nset get_bd(const vector& arr){set S;int y=0;for(int i=0;i<(int)arr.size()-1;i++){y+=arr[i];S.insert(y);}return S;}\nll bdist(const set& A,const set& B){ll c=0;for(int x:A)if(!B.count(x))c++;for(int x:B)if(!A.count(x))c++;return c*W;}\nvector arrange_greedy(const vector& h,const set& targets){\n vector tgt(targets.begin(),targets.end());\n multiset av(h.begin(),h.end());\n vector arr;int S=0,j=0,nt=(int)tgt.size();\n while(!av.empty()){while(j=tgt[j])j++;if(j>=nt){for(int x:av)arr.push_back(x);break;}\n int need=tgt[j]-S;auto it=av.find(need);\n if(it!=av.end()){arr.push_back(need);S+=need;av.erase(it);j++;}\n else{auto ub=av.upper_bound(need);if(ub!=av.begin()){--ub;arr.push_back(*ub);S+=*ub;av.erase(ub);while(j=tgt[j])j++;}\n else{it=av.begin();arr.push_back(*it);S+=*it;av.erase(it);while(j=tgt[j])j++;}}}\n return arr;}\nvoid out(const vector>& arrs){\n for(int d=0;d y(N+1);y[0]=0;for(int i=0;i> s(N);for(int i=0;i>> eval_seq(const vector& seq,const vector>& C){\n vector> arrs(D);ll cost=0;arrs[0]=C[seq[0]];cost+=area_cost(0,arrs[0]);set cur=get_bd(arrs[0]);\n for(int d=1;d ns=get_bd(arrs[d]);cost+=area_cost(d,C[seq[d]])+bdist(cur,ns);cur=ns;}}\n return{cost,arrs};}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>W>>D>>N;a.resize(D,vector(N));\n for(int d=0;d>a[d][k];\n vector> day_h(D);for(int d=0;d aidx(D);iota(aidx.begin(),aidx.end(),0);vector fh=compute_heights(aidx);\n int NC=D+1;vector> C(NC);C[0]=fh;for(int d=0;d> SS(NC);for(int L=0;L> ar(D,vector(NC));for(int d=0;d> pcg(NC,vector(NC,0));\n for(int L1=0;L1> dp(D,vector(NC,INF));vector> from(D,vector(NC,-1));\n for(int L=0;L seq(D);seq[D-1]=bL;for(int d=D-2;d>=0;d--)seq[d]=from[d+1][seq[d+1]];\n auto[dp_cost,dp_arrs]=eval_seq(seq,C);\n ll g_cost=INF;vector> g_arrs;\n {vector> arrs(D);ll cost=0;int cL=1;arrs[0]=C[cL];cost+=ar[0][cL];set cs=get_bd(arrs[0]);\n for(int d=1;d barr=arrs[d-1];set bS=cs;\n for(int L=0;L ag;set Sg;\n if(L==cL){c=ar[d][L];ag=arrs[d-1];Sg=cs;}\n else{ag=arrange_greedy(C[L],cs);Sg=get_bd(ag);c=ar[d][L]+bdist(cs,Sg);}\n if(c\nusing namespace std;\nusing namespace chrono;\nconstexpr long long MOD = 998244353;\nlong long sv[20][3][3];\nlong long b[9][9];\nlong long cur_score;\nint N, M, K;\nvoid apply_stamp(int m, int p, int q) {\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n long long ov = b[p+i][q+j];\n long long nv = (ov + sv[m][i][j]) % MOD;\n cur_score += nv - ov; b[p+i][q+j] = nv;\n }\n}\nvoid undo_stamp(int m, int p, int q) {\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) {\n long long ov = b[p+i][q+j];\n long long nv = (ov - sv[m][i][j] + MOD) % MOD;\n cur_score += nv - ov; b[p+i][q+j] = nv;\n }\n}\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n cin >> N >> M >> K;\n cur_score = 0;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) { cin >> b[i][j]; b[i][j] %= MOD; cur_score += b[i][j]; }\n for (int m = 0; m < M; m++) for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) cin >> sv[m][i][j];\n struct Op { int m, p, q; };\n vector ops; ops.reserve(K);\n for (int iter = 0; iter < K; iter++) {\n long long best_gain = 0; int bm=-1,bp=-1,bq=-1;\n for (int m = 0; m < M; m++) for (int p = 0; p <= N-3; p++) for (int q = 0; q <= N-3; q++) {\n long long gain = 0;\n for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) gain += (b[p+i][q+j]+sv[m][i][j])%MOD - b[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 apply_stamp(bm,bp,bq); ops.push_back({bm,bp,bq});\n }\n long long best_score = cur_score; vector best_ops = ops;\n mt19937 rng(42); auto t_start = steady_clock::now();\n const long long TL = 1850000; double T = 1e7;\n for (long long si = 0; ; si++) {\n if (si % 10000 == 0) {\n long long el = duration_cast(steady_clock::now()-t_start).count();\n if (el >= TL) break;\n T = 1e7 * pow(1e-7, (double)el/TL);\n }\n int L = (int)ops.size();\n int mtype = (L==0)?0:(L==K)?(1+(int)(rng()&1)):(int)(rng()%3);\n Op old_op{0,0,0}, new_op{0,0,0}; int old_idx=-1;\n if (mtype==0) new_op={( int)(rng()%M),(int)(rng()%(N-2)),(int)(rng()%(N-2))};\n else if (mtype==1) { old_idx=(int)(rng()%L); old_op=ops[old_idx]; }\n else { old_idx=(int)(rng()%L); old_op=ops[old_idx]; new_op={(int)(rng()%M),(int)(rng()%(N-2)),(int)(rng()%(N-2))}; }\n long long s0 = cur_score;\n if (mtype==0) apply_stamp(new_op.m,new_op.p,new_op.q);\n else if (mtype==1) undo_stamp(old_op.m,old_op.p,old_op.q);\n else { undo_stamp(old_op.m,old_op.p,old_op.q); apply_stamp(new_op.m,new_op.p,new_op.q); }\n long long delta = cur_score - s0;\n bool accept = (delta>=0) || (((double)(rng()%1000000)) < exp((double)delta/T)*1000000.0);\n if (accept) {\n if (mtype==0) ops.push_back(new_op);\n else if (mtype==1) { ops[old_idx]=ops.back(); ops.pop_back(); }\n else ops[old_idx]=new_op;\n if (cur_score > best_score) { best_score=cur_score; best_ops=ops; }\n } else {\n if (mtype==0) undo_stamp(new_op.m,new_op.p,new_op.q);\n else if (mtype==1) apply_stamp(old_op.m,old_op.p,old_op.q);\n else { undo_stamp(new_op.m,new_op.p,new_op.q); apply_stamp(old_op.m,old_op.p,old_op.q); }\n }\n }\n cout << best_ops.size() << \"\\n\";\n for (auto& op : best_ops) cout << op.m << \" \" << op.p << \" \" << op.q << \"\\n\";\n return 0;\n}","ahc033":"#include \nusing namespace std;\n\nconst int N = 5;\nint A[N][N];\nint posR[N*N], posP[N*N];\nint grid[N][N];\nint craneR, craneC;\nbool craneHolding;\nint craneContainer;\nint recvSent[N];\nint recvPickedUp[N];\nint dispatchCount[N];\nmap> bufPos;\nset> usedBufs;\nbool done_[N*N];\nstring result;\n\nvoid sRecv(){\n for(int r=0;rtr) turn_('U');\n else if(craneC freeBuf(){\n for(int c=1;c=0){\n bool isGate=!bestIsBuf;\n deliver_(bestSrcR,bestSrcC,bestIsBuf,isGate,bestK/N);\n } else {\n bool cleared=false;\n for(int gate=0;gate>n;\n for(int r=0;r>A[r][p];\n solve();\n cout<\nusing namespace std;\n\nint N;\nint h[20][20];\nint curR, curC, curLoad;\nvector ops;\n\nvoid doLoad(int d) {\n if (d <= 0) return;\n ops.push_back(\"+\" + to_string(d));\n h[curR][curC] -= d; curLoad += d;\n}\n\nvoid doUnload(int d) {\n d = min(d, curLoad);\n if (d <= 0) return;\n ops.push_back(\"-\" + to_string(d));\n h[curR][curC] += d; curLoad -= d;\n}\n\nvoid doStep(char dir, int dr, int dc) {\n curR += dr; curC += dc;\n ops.push_back(string(1, dir));\n if (h[curR][curC] > 0) doLoad(h[curR][curC]);\n else if (h[curR][curC] < 0 && curLoad > 0) doUnload(min(curLoad, -h[curR][curC]));\n}\n\nvoid moveRowFirst(int tr, int tc) {\n while (curR < tr) doStep('D', 1, 0); while (curR > tr) doStep('U', -1, 0);\n while (curC < tc) doStep('R', 0, 1); while (curC > tc) doStep('L', 0, -1);\n}\n\nvoid moveColFirst(int tr, int tc) {\n while (curC < tc) doStep('R', 0, 1); while (curC > tc) doStep('L', 0, -1);\n while (curR < tr) doStep('D', 1, 0); while (curR > tr) doStep('U', -1, 0);\n}\n\nvoid moveTo(int tr, int tc) {\n if (curR == tr || curC == tc) { moveRowFirst(tr, tc); return; }\n int drSign = (curR < tr) ? 1 : -1, dcSign = (curC < tc) ? 1 : -1;\n int bA = 0, bB = 0;\n for (int r = curR + drSign; r != tr + drSign; r += drSign) bA += abs(h[r][curC]);\n for (int c = curC + dcSign; c != tc + dcSign; c += dcSign) bA += abs(h[tr][c]);\n for (int c = curC + dcSign; c != tc + dcSign; c += dcSign) bB += abs(h[curR][c]);\n for (int r = curR + drSign; r != tr + drSign; r += drSign) bB += abs(h[r][tc]);\n if (bB > bA) moveColFirst(tr, tc); else moveRowFirst(tr, tc);\n}\n\nbool allZero() {\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (h[i][j] != 0) return false;\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(0);\n cin >> N;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cin >> h[i][j];\n curR = curC = curLoad = 0;\n if (h[0][0] > 0) doLoad(h[0][0]);\n while (!allZero() && (int)ops.size() < 95000) {\n auto dist = [&](int i, int j) { return abs(i-curR)+abs(j-curC); };\n if (curLoad > 0) {\n int best = INT_MAX, bi = -1, bj = -1;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++)\n if (h[i][j] < 0) { int d = dist(i,j); if (d < best) { best=d; bi=i; bj=j; } }\n if (bi < 0) break;\n moveTo(bi, bj);\n if (h[bi][bj] < 0 && curLoad > 0) doUnload(min(curLoad, -h[bi][bj]));\n } else {\n int best = INT_MAX, bi = -1, bj = -1;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++)\n if (h[i][j] > 0) { int d = dist(i,j); if (d < best) { best=d; bi=i; bj=j; } }\n if (bi < 0) break;\n moveTo(bi, bj);\n if (h[bi][bj] > 0) doLoad(h[bi][bj]);\n }\n }\n for (const auto& op : ops) cout << op << \"\\n\";\n return 0;\n}","ahc035":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n int N, M, T;\n cin >> N >> M >> T;\n const int SC = 2*N*(N-1), nn = N*N;\n vector> X(SC, vector(M));\n for(int i=0;i>X[i][j];\n mt19937 rng(42);\n for(int t=0;t vals(SC,0);\n for(int k=0;k in_sel(SC,false);\n vector sel;\n for(int l=0;lX[bk][l]) bk=k;\n if(!in_sel[bk]){in_sel[bk]=true;sel.push_back(bk);}\n }\n vector ord(SC); iota(ord.begin(),ord.end(),0);\n sort(ord.begin(),ord.end(),[&](int a,int b){return vals[a]>vals[b];});\n for(int k:ord){\n if((int)sel.size()>=nn) break;\n if(!in_sel[k]){in_sel[k]=true;sel.push_back(k);}\n }\n vector> pst(nn,vector(nn));\n for(int i=0;i grid(nn); iota(grid.begin(),grid.end(),0);\n shuffle(grid.begin(),grid.end(),rng);\n auto contrib=[&](int p)->int{\n int r=p/N,c=p%N,v=0;\n if(r>0) v+=pst[grid[p]][grid[(r-1)*N+c]];\n if(r0) v+=pst[grid[p]][grid[r*N+c-1]];\n if(c bg=grid;\n double temp=1000.0; const double TL=0.18;\n for(int it=0;;it++){\n if((it&0x7FF)==0){\n double e=chrono::duration(chrono::steady_clock::now()-ts).count();\n if(e>=TL) break;\n temp=1000.0*pow(1e-4,e/TL);\n }\n int p1=rng()%nn,p2=rng()%nn;\n if(p1==p2) continue;\n int bef=contrib(p1)+contrib(p2);\n swap(grid[p1],grid[p2]);\n int aft=contrib(p1)+contrib(p2);\n int d=aft-bef;\n if(d>=0||(rng()%1000000)<(int)(1e6*exp((double)d/temp))){\n cur+=d; if(cur>best){best=cur;bg=grid;}\n } else swap(grid[p1],grid[p2]);\n }\n for(int i=0;i>X[i][j];\n }\n return 0;\n}","ahc038":"#include \nusing namespace std;\nint N,M,V;\nconst int DR[]={0,1,0,-1},DC[]={1,0,-1,0};\nint rx,ry,fd;\nvector ops;\nbool nav(int tr,int tc,int td){\n while(rx!=tr||ry!=tc||fd!=td){\n if((int)ops.size()>=99990)return false;\n char mv='.',rot='.';\n if(rx!=tr||ry!=tc){if(rxtr){rx--;mv='U';}else if(ry>&g,int val){\n int br=-1,bc=-1,bdir=-1,bv=INT_MAX;\n for(int d=0;d<4;d++){int ar=r-DR[d],ac=c-DC[d];if(ar<0||ar>=N||ac<0||ac>=N)continue;int v=abs(rx-ar)+abs(ry-ac);if(v=99990)return false;ops.push_back(\"...P\");g[r][c]=val;return true;\n}\nint main(){\n ios::sync_with_stdio(false);cin.tie(0);\n cin>>N>>M>>V;\n vectorsg(N),tg(N);for(auto&s:sg)cin>>s;for(auto&s:tg)cin>>s;\n vector>S,T;vector>g(N,vector(N,0));\n for(int i=0;imt(m,-1);\n {vectorsu(m,false),tu(m,false);\n for(int i=0;iP;\n for(int i=0;i0&&(int)ops.size()<97000){\n int fi=-1,bd=INT_MAX;\n for(int i=0;i=0){if(!do_act(P[fi].sr,P[fi].sc,g,0))break;if(!do_act(P[fi].tr,P[fi].tc,g,1))break;P[fi].done=true;rem--;}\n else{fi=-1;bd=INT_MAX;for(int i=0;itmp={-1,-1};\n {set>ts;for(auto&d:P)if(!d.done)ts.insert({d.tr,d.tc});\n for(int i=0;i\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n using Clock = chrono::steady_clock;\n auto t0 = Clock::now();\n auto elapsedMs = [&]() -> long long {\n return chrono::duration_cast(Clock::now()-t0).count();\n };\n int N; cin >> N;\n int M = 2*N;\n vector X(M), Y(M), W(M);\n for (int i = 0; i < M; i++) {\n cin >> X[i] >> Y[i];\n W[i] = (i < N) ? 1 : -1;\n }\n const int CMAX = 100000;\n // Trivial initial output\n {\n int tx1=X[0], ty1=Y[0];\n int tx2=(tx1tx2) swap(tx1,tx2);\n if(ty1>ty2) swap(ty1,ty2);\n cout<<4<<\"\\n\"< bx(M), by(M);\n {\n vector idx(M);\n iota(idx.begin(),idx.end(),0);\n sort(idx.begin(),idx.end(),[&](int a,int b){return X[a]& fish,int lo,int hi)->pair{\n int cur=0,cs=-1,mx=0,blo=-1,bhi=-1; bool in_run=false;\n for(int i=0,n=(int)fish.size();i=lo&&fish[i].other<=hi) gsum+=fish[i].w;\n i++;\n }\n if(!in_run){\n if(gsum>0){cs=xval;cur=gsum;in_run=true;if(cur>mx){mx=cur;blo=cs;bhi=xval;}}\n } else {\n cur+=gsum;\n if(cur>mx){mx=cur;blo=cs;bhi=xval;}\n if(cur<0){cur=0;in_run=false;}\n }\n }\n return {blo,bhi};\n };\n auto evalRect=[&](int x1,int x2,int y1,int y2){\n int s=0;\n for(int i=0;i=x1&&X[i]<=x2&&Y[i]>=y1&&Y[i]<=y2) s+=W[i];\n return s;\n };\n auto coordDescent=[&](int x1,int x2,int y1,int y2)->tuple{\n x1=max(0,min(CMAX,x1));x2=max(0,min(CMAX,x2));\n y1=max(0,min(CMAX,y1));y2=max(0,min(CMAX,y2));\n if(x1>x2) swap(x1,x2); if(y1>y2) swap(y1,y2);\n int px1=-1,px2=-1,py1=-1,py2=-1;\n for(int it=0;it<20;it++){\n if(x1==px1&&x2==px2&&y1==py1&&y2==py2) break;\n px1=x1;px2=x2;py1=y1;py2=y2;\n auto [nx1,nx2]=kadane(bx,y1,y2); if(nx1>=0){x1=nx1;x2=nx2;}\n auto [ny1,ny2]=kadane(by,x1,x2); if(ny1>=0){y1=ny1;y2=ny2;}\n }\n return make_tuple(evalRect(x1,x2,y1,y2),x1,x2,y1,y2);\n };\n // Grid Kadane's\n const int G=200, step=CMAX/G;\n vector> grid(G,vector(G,0));\n for(int i=0;i cs(G,0);\n for(int gx2=gx1;gx2mx){mx=cur;ms=cst;me=gy;}\n if(cur<0){cur=0;cst=gy+1;}\n }\n if(me>=0&&mx>bgs){bgs=mx;bgx1=gx1;bgx2=gx2;bgy1=ms;bgy2=me;}\n }\n }\n int ix1=bgx1*step, ix2=min((bgx2+1)*step,CMAX);\n int iy1=bgy1*step, iy2=min((bgy2+1)*step,CMAX);\n int gscore=-1,rx1=0,rx2=1,ry1=0,ry2=1;\n auto tryRun=[&](int x1,int x2,int y1,int y2){\n auto [s,a,b,c,d]=coordDescent(x1,x2,y1,y2);\n if(s>gscore){gscore=s;rx1=a;rx2=b;ry1=c;ry2=d;}\n };\n tryRun(ix1,ix2,iy1,iy2);\n tryRun(0,CMAX,0,CMAX);\n // Centroid start\n {\n long long cx=0,cy=0;\n for(int i=0;i1700) break;\n int seed=rng()%N;\n int cx=X[seed],cy=Y[seed];\n int half;\n switch(rng()%4){\n case 0: half=200+rng()%800; break;\n case 1: half=1000+rng()%9000; break;\n case 2: half=10000+rng()%20000; break;\n default: half=30000+rng()%20000; break;\n }\n tryRun(cx-half,cx+half,cy-half,cy+half);\n }\n if(gscore>=1){\n rx1=max(0,rx1);rx2=min(CMAX,rx2);\n ry1=max(0,ry1);ry2=min(CMAX,ry2);\n if(rx1>=rx2){if(rx2=ry2){if(ry2\nusing namespace std;\ntypedef long long ll;\n\nint N, T;\nvector W, H;\ndouble sW, sH, mxW, mxH, totA;\n\nstruct Op { int p, r; char d; int b; };\n\npair simulate(const vector& ops) {\n vector x0(N,0),y0(N,0),x1(N,0),y1(N,0);\n vector pl(N,false);\n for (const auto& o : ops) {\n int p = o.p;\n ll w = max(1LL, llround(o.r ? H[p] : W[p]));\n ll h = max(1LL, llround(o.r ? W[p] : H[p]));\n if (o.d == 'U') {\n ll xl = o.b >= 0 ? x1[o.b] : 0LL;\n ll yt = 0;\n for (int i = 0; i < N; i++)\n if (pl[i] && x0[i] < xl+w && x1[i] > xl)\n yt = max(yt, y1[i]);\n x0[p]=xl; y0[p]=yt; x1[p]=xl+w; y1[p]=yt+h;\n } else {\n ll yt = o.b >= 0 ? y1[o.b] : 0LL;\n ll xl = 0;\n for (int i = 0; i < N; i++)\n if (pl[i] && y0[i] < yt+h && y1[i] > yt)\n xl = max(xl, x1[i]);\n x0[p]=xl; y0[p]=yt; x1[p]=xl+w; y1[p]=yt+h;\n }\n pl[p] = true;\n }\n ll rW=0, rH=0;\n for (int i = 0; i < N; i++)\n if (pl[i]) { rW=max(rW,x1[i]); rH=max(rH,y1[i]); }\n return {rW, rH};\n}\n\n// col=false: shelf packing (rows); col=true: column packing\n// For col=false, line0 uses U, rest use L\n// For col=true, line0 uses L, rest use U\nvector make_pack(const vector& rot, double tgt, bool col) {\n vector ops; ops.reserve(N);\n int cl = -1; double cm = 0;\n vector lr; vector lc;\n int p0 = -1;\n for (int i = 0; i < N; i++) {\n double m = col ? (rot[i] ? W[i] : H[i]) : (rot[i] ? H[i] : W[i]);\n double c = col ? (rot[i] ? H[i] : W[i]) : (rot[i] ? W[i] : H[i]);\n if (cl < 0 || cm + m > tgt) {\n cl++; cm = m;\n lr.push_back(i); lc.push_back(c);\n if (cl == 0) {\n ops.push_back({i, rot[i], col?'L':'U', -1});\n p0 = i;\n } else {\n ops.push_back({i, rot[i], col?'U':'L', lr[cl-1]});\n }\n } else {\n cm += m;\n if (c > lc[cl]) { lc[cl]=c; lr[cl]=i; }\n if (cl == 0) {\n ops.push_back({i, rot[i], col?'L':'U', p0});\n p0 = i;\n } else {\n ops.push_back({i, rot[i], col?'U':'L', lr[cl-1]});\n }\n }\n }\n return ops;\n}\n\ndouble calc_score(const vector& rot, double tgt, bool col) {\n auto [a,b] = simulate(make_pack(rot, tgt, col));\n return (double)(a+b);\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n\n double sigma;\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 sW=sH=mxW=mxH=totA=0;\n for (int i = 0; i < N; i++) {\n sW+=W[i]; sH+=H[i];\n mxW=max(mxW,W[i]); mxH=max(mxH,H[i]);\n totA+=W[i]*H[i];\n }\n\n const double BUDGET = 2600.0;\n auto t0 = chrono::steady_clock::now();\n auto now = [&]() {\n return chrono::duration(chrono::steady_clock::now()-t0).count();\n };\n\n vector g_rot;\n double g_tgt=0, g_score=1e18;\n bool g_col=false;\n\n for (int t = 0; t < T; t++) {\n double ts = now();\n double per = max(1.0, (BUDGET - ts) / (T - t));\n double dl = ts + per * 0.95;\n\n mt19937 rng(t * 1234567891u ^ 987654321u);\n uniform_real_distribution uni(0,1);\n\n bool col;\n double lo, hi, tgt;\n vector rot(N);\n\n if (t < (T+1)/2) {\n col = (t & 1);\n lo = col ? mxH : mxW;\n hi = col ? sH : sW;\n tgt = max(lo, min(hi, sqrt(totA)));\n // Init rotation: minimize cross-dim\n for (int i = 0; i < N; i++)\n rot[i] = col ? (H[i] br=rot;\n double bt=tgt;\n bool bc=col;\n double bs=cur;\n\n double Th = cur*0.05+1.0;\n double Tl = max(1.0, cur*1e-5);\n\n // Simulated Annealing\n for (int it=0; ; it++) {\n if ((it&63)==0 && now()>=dl) break;\n double frac = max(0.0, min(1.0, (now()-ts)/per));\n double Tc = max(Tl, Th * pow(Tl/Th, frac));\n\n int mv = rng()%10, fi=-1;\n double ot=tgt;\n bool oc=col;\n double olo=lo, ohi=hi;\n\n if (mv < 7) {\n fi = rng()%N;\n rot[fi] ^= 1;\n } else if (mv < 9) {\n tgt = max(lo, min(hi, tgt * exp((uni(rng)*2-1)*0.35)));\n } else {\n col ^= 1;\n lo = col ? mxH : mxW;\n hi = col ? sH : sW;\n tgt = max(lo, min(hi, ot));\n }\n\n double ns = calc_score(rot, tgt, col);\n double d = ns - cur;\n if (d <= 0 || uni(rng) < exp(-d/Tc)) {\n cur = ns;\n if (ns < bs) { bs=ns; br=rot; bt=tgt; bc=col; }\n } else {\n if (fi >= 0) rot[fi] ^= 1;\n else if (mv < 9) tgt = ot;\n else { col=oc; lo=olo; hi=ohi; tgt=ot; }\n }\n }\n\n // Final greedy passes\n for (int pass=0; pass<3; pass++) {\n bool imp=false;\n for (int i=0; i> Wf >> Hf;\n }\n\n return 0;\n}","ahc041":"#include \nusing namespace std;\ntypedef long long ll;\nint N, M, H, A[1000];\nvector G[1000];\nint par[1000], dep[1000], ssm[1000], mdn[1000];\nvector ch[1000];\nvoid dfs_init(int v){ssm[v]=A[v];mdn[v]=0;for(int c:ch[v]){dfs_init(c);ssm[v]+=ssm[c];mdn[v]=max(mdn[v],mdn[c]+1);}}\nvoid push_dep(int v,int d){dep[v]=d;for(int c:ch[v])push_dep(c,d+1);}\nbool in_sub(int w,int v){for(;w!=-1;w=par[w])if(w==v)return true;return false;}\nvoid pull_ssm(int v){for(;v!=-1;v=par[v]){int s=A[v];for(int c:ch[v])s+=ssm[c];ssm[v]=s;}}\nvoid pull_mdn(int v){for(;v!=-1;v=par[v]){int m=0;for(int c:ch[v])m=max(m,mdn[c]+1);mdn[v]=m;}}\nvoid do_move(int v,int np){\n int op=par[v];\n if(op!=-1){auto&c=ch[op];c.erase(find(c.begin(),c.end(),v));}\n par[v]=np;\n if(np!=-1){ch[np].push_back(v);push_dep(v,dep[np]+1);}else push_dep(v,0);\n if(op!=-1){pull_ssm(op);pull_mdn(op);}\n if(np!=-1){pull_ssm(np);pull_mdn(np);}\n}\nint main(){\n ios::sync_with_stdio(false);cin.tie(0);\n cin>>N>>M>>H;\n for(int i=0;i>A[i];\n for(int i=0;i>u>>v;G[u].push_back(v);G[v].push_back(u);}\n for(int i=0;i>x>>y;}\n fill(par,par+N,-1);fill(dep,dep+N,0);\n for(int i=0;ivis(N,false);\n vectorord(N);iota(ord.begin(),ord.end(),0);\n sort(ord.begin(),ord.end(),[](int a,int b){return A[a]q;q.push(s);vis[s]=true;\n while(!q.empty()){\n int v=q.front();q.pop();\n if(dep[v]>=H)continue;\n for(int u:G[v])if(!vis[u]){vis[u]=true;par[u]=v;dep[u]=dep[v]+1;ch[v].push_back(u);q.push(u);}\n }\n }\n for(int v=0;v(chrono::steady_clock::now()-t0).count()>1800)break;\n bool impr=false;\n vectorperm(N);iota(perm.begin(),perm.end(),0);\n shuffle(perm.begin(),perm.end(),rng);\n for(int v:perm){\n int lim=H-1-mdn[v];\n if(lim<0)continue;\n int bp=par[v];ll bg=0;\n for(int w:G[v]){\n if(dep[w]>lim)continue;\n if(in_sub(w,v))continue;\n ll g=(ll)(dep[w]+1-dep[v])*ssm[v];\n if(g>bg){bg=g;bp=w;}\n }\n if(bg>0){do_move(v,bp);impr=true;}\n }\n if(!impr)break;\n }\n for(int v=0;v\nusing namespace std;\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int N; cin >> N;\n vector board(N);\n for (int i = 0; i < N; i++) cin >> board[i];\n vector> oni;\n for (int i = 0; i < N; i++)\n for (int j = 0; j < N; j++)\n if (board[i][j] == 'x') oni.push_back({i, j});\n int M = (int)oni.size();\n if (M == 0) return 0;\n vector ctop(N,N),cbot(N,-1),rleft(N,N),rright(N,-1);\n for (int i=0;ilong long {\n long long mask=0;\n for (int k=0;k=depth) mask|=1LL<=depth) mask|=1LL<int { return (dir=='U'||dir=='L')?2*(depth+1):2*(N-depth); };\n struct Cand{char dir;int idx,depth,cost;long long mask;};\n vector cands;\n for (int k=0;kcbot[c]) cands.push_back({'D',c,r,get_cost('D',r),get_mask('D',c,r)});\n if(crright[r]) cands.push_back({'R',r,c,get_cost('R',c),get_mask('R',r,c)}); }\n long long remaining=(1LL<,int> sel;\n while (remaining) {\n double best=1e18; int bi=-1;\n for (int i=0;i<(int)cands.size();i++) {\n long long nm=cands[i].mask&remaining; if(!nm) continue;\n auto key=make_pair(cands[i].dir,cands[i].idx);\n int ac=cands[i].cost; auto it=sel.find(key);\n if (it!=sel.end()) { char d=cands[i].dir; int cur=it->second;\n bool up=(d=='U'||d=='L')?cands[i].depth>cur:cands[i].depth,long long> smask;\n for (auto&[key,d]:sel) smask[key]=get_mask(key.first,key.second,d);\n bool changed=true;\n while (changed) { changed=false;\n for (auto it=sel.begin();it!=sel.end();) {\n auto&[key,d]=*it; char dir=key.first; int idx=key.second;\n long long others=0;\n for (auto&[k2,m]:smask) if(k2!=key) others|=m;\n long long uniq=smask[key]&~others;\n if(!uniq){smask.erase(key);it=sel.erase(it);changed=true;break;}\n int nd;\n if(dir=='U'){nd=0;for(int k=0;k>k)&1)nd=max(nd,oni[k].first);}\n else if(dir=='D'){nd=N-1;for(int k=0;k>k)&1)nd=min(nd,oni[k].first);}\n else if(dir=='L'){nd=0;for(int k=0;k>k)&1)nd=max(nd,oni[k].second);}\n else{nd=N-1;for(int k=0;k>k)&1)nd=min(nd,oni[k].second);}\n if(nd!=d){d=nd;smask[key]=get_mask(dir,idx,nd);changed=true;break;}\n else ++it; } }\n for (auto&[key,d]:sel) {\n char dir=key.first,rev; int idx=key.second;\n int s=(dir=='U'||dir=='L')?d+1:N-d;\n if(dir=='U')rev='D';else if(dir=='D')rev='U';else if(dir=='L')rev='R';else rev='L';\n for(int k=0;k\nusing namespace std;\nconst int MAXN = 100;\nint N, L, T[MAXN], a[MAXN], b[MAXN], cv[MAXN], fv[MAXN], flow[MAXN];\nvoid computeFlow(){fill(flow,flow+N,0);for(int i=0;iq;vis[0]=true;q.push(0);while(!q.empty()){int x=q.front();q.pop();if(!vis[a[x]]){vis[a[x]]=true;q.push(a[x]);}if(!vis[b[x]]){vis[b[x]]=true;q.push(b[x]);}}for(int j=0;j0&&!vis[j])return false;return true;}\nvoid fixConn(){for(int pass=0;passq;vis[0]=true;q.push(0);while(!q.empty()){int x=q.front();q.pop();if(!vis[a[x]]){vis[a[x]]=true;q.push(a[x]);}if(!vis[b[x]]){vis[b[x]]=true;q.push(b[x]);}}int u=-1;for(int j=0;j0&&!vis[j]){u=j;break;}if(u<0)break;long long bestD=(long long)4e18;int besti=-1;bool bestA=false;for(int i=0;i0)?((long long)(abs(flow[old]-w-T[old])-abs(flow[old]-T[old]))+(long long)(abs(flow[u]+w-T[u])-abs(flow[u]-T[u]))):0LL;if(d0)?((long long)(abs(flow[old]-w-T[old])-abs(flow[old]-T[old]))+(long long)(abs(flow[u]+w-T[u])-abs(flow[u]-T[u]))):0LL;if(d0){flow[a[besti]]-=cv[besti];flow[u]+=cv[besti];}a[besti]=u;}else{if(fv[besti]>0){flow[b[besti]]-=fv[besti];flow[u]+=fv[besti];}b[besti]=u;}}}\nvoid flowSearch(){long long curErr=flowErr();bool improved=true;while(improved){improved=false;for(int i=0;i0)?((long long)(abs(flow[old]-w-T[old])-abs(flow[old]-T[old]))+(long long)(abs(flow[j]+w-T[j])-abs(flow[j]-T[j]))):0LL;if(d=0){if(w>0){flow[old]-=w;flow[bestJ]+=w;}curErr+=bestD;if(t2)b[i]=bestJ;else a[i]=bestJ;improved=true;}}}}}\nlong long simulate(){int cnt[MAXN]={},vc[MAXN]={};int cur=0;cnt[0]++;vc[0]++;for(int w=2;w<=L;w++){int nxt=(vc[cur]&1)?a[cur]:b[cur];cur=nxt;cnt[cur]++;vc[cur]++;}long long e=0;for(int j=0;j>N>>L;for(int i=0;i>T[i];\n for(int i=0;i>items;\n for(int i=0;i0)rem[0]--;\n priority_queue>pq;for(int j=0;j(chrono::steady_clock::now()-t0).count();\n if(el>1800000LL)break;\n int i=rng()%N,type=rng()%2,jNew=(int)(rng()%N);\n int&ptr=type?b[i]:a[i];int old=ptr;\n if(jNew==old)continue;\n ptr=jNew;\n if(!checkConn()){ptr=old;continue;}\n long long err=simulate();\n if(err<=curErr){curErr=err;if(err\nusing namespace std;\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n int N, M, Q, L, W;\n cin >> N >> M >> Q >> L >> W;\n vector G(M);\n for (int& g : G) cin >> g;\n vector lx(N),rx(N),ly(N),ry(N);\n vector cx(N),cy(N);\n for (int i=0;i>lx[i]>>rx[i]>>ly[i]>>ry[i];cx[i]=(lx[i]+rx[i])/2.0;cy[i]=(ly[i]+ry[i])/2.0;}\n auto edist2=[&](int a,int b)->double{double dx=cx[a]-cx[b],dy=cy[a]-cy[b];return dx*dx+dy*dy;};\n auto expand_bits=[](uint32_t x)->uint64_t{uint64_t r=0;for(int i=0;i<16;i++)r|=((uint64_t)((x>>i)&1))<<(2*i);return r;};\n vector city_order(N);iota(city_order.begin(),city_order.end(),0);\n sort(city_order.begin(),city_order.end(),[&](int a,int b)->bool{uint64_t ma=expand_bits((uint32_t)cx[a])|(expand_bits((uint32_t)cy[a])<<1);uint64_t mb=expand_bits((uint32_t)cx[b])|(expand_bits((uint32_t)cy[b])<<1);return ma> groups(M);{int pos=0;for(int i=0;i> sc(M);\n for(int i=0;i used(g,false);int start=0;for(int k=1;k>>> all_edges(M);\n auto do_query=[&](const vector& qc,int gi){if((int)qc.size()<2||qrem<=0)return;qrem--;cout<<\"? \"<>a>>b;all_edges[gi].push_back({edist2(a,b),{a,b}});}};\n auto nwindows=[&](int g)->int{if(g<=1)return 0;if(g<=L)return 1;return(g-2)/(L-1)+1;};\n int total_mandatory=0;for(int i=0;i=g);if(is_last&&end-start(sc[i].begin()+start,sc[i].begin()+end),i);if(is_last)break;start+=L-1;}}}\n {vector large;for(int i=0;iL)large.push_back(i);\n if(!large.empty()&&extra_budget>0)for(int qi=0;qi0;qi++){int gi=large[qi%(int)large.size()];int g=G[gi];int stride=max(1,g/L);int offset=(qi/(int)large.size())%stride;vector window;for(int k=offset;k=2)do_query(window,gi);}}\n vector par(N);auto find_uf=[&](int x)->int{while(par[x]!=x){par[x]=par[par[x]];x=par[x];}return x;};\n vector>> ans(M);\n for(int i=0;i0)cout<<\" \";cout<\nusing namespace std;\nconst int N=20;\nbool grid[N][N];\nconst int DR[]={-1,1,0,0},DC[]={0,0,-1,1};\nconst int NS=N*N*21*21;\nstatic int bdist[NS],bprev[NS],bq[NS];\nstatic uint8_t bact[NS];\nvector> findPath(int r0,int c0,int tr,int tc){\n memset(bdist,-1,sizeof(bdist));\n int start=(r0*N+c0)*441,goal=(tr*N+tc)*441;\n bdist[start]=0;int qh=0,qt=0;bq[qt++]=start;\n while(qhbool{return(unsigned)br>=(unsigned)N||(unsigned)bc>=(unsigned)N||grid[br][bc]||(br==ebr&&bc==ebc);};\n if(!isB(nr,nc)){int ns=(nr*N+nc)*441+(ebr+1)*21+(ebc+1);if(bdist[ns]==-1){bdist[ns]=d1;bprev[ns]=s;bact[ns]=(0<<2)|d;bq[qt++]=ns;}}\n {int sr=r,sc=c;while(!isB(sr+DR[d],sc+DC[d])){sr+=DR[d];sc+=DC[d];}if(sr!=r||sc!=c){int ns=(sr*N+sc)*441+(ebr+1)*21+(ebc+1);if(bdist[ns]==-1){bdist[ns]=d1;bprev[ns]=s;bact[ns]=(1<<2)|d;bq[qt++]=ns;}}}\n if((unsigned)nr<(unsigned)N&&(unsigned)nc<(unsigned)N){if(nr==ebr&&nc==ebc){int ns=(r*N+c)*441;if(bdist[ns]==-1){bdist[ns]=d1;bprev[ns]=s;bact[ns]=(2<<2)|d;bq[qt++]=ns;}}else if(ebr==-1&&!grid[nr][nc]){int ns=(r*N+c)*441+(nr+1)*21+(nc+1);if(bdist[ns]==-1){bdist[ns]=d1;bprev[ns]=s;bact[ns]=(2<<2)|d;bq[qt++]=ns;}}}\n }\n }\n if(bdist[goal]==-1){vector> res;int r=r0,c=c0;while(r!=tr){res.push_back({'M',r> path;\n for(int cur=goal;cur!=start;cur=bprev[cur])path.push_back({\"MSA\"[bact[cur]>>2],\"UDLR\"[bact[cur]&3]});\n reverse(path.begin(),path.end());return path;\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n int Nin,M;cin>>Nin>>M;\n vector> pts(M);for(int i=0;i>pts[i].first>>pts[i].second;\n memset(grid,0,sizeof(grid));int cr=pts[0].first,cc=pts[0].second;\n for(int i=1;i\nusing namespace std;\nconst int MAXN=205;\nint n,px[MAXN],py[MAXN];\nlong long pr[MAXN];\ndouble score_pi(double si,long long ri){\n if(si<=0)return 0.0;\n double ratio=(si<=(double)ri)?si/ri:(double)ri/si;\n return 1.0-(1.0-ratio)*(1.0-ratio);\n}\nstruct Split{int x1,y1,x2,y2,dir,sp,lo,hi;vectorL,R;};\nvectorsplits;\nint rx1[MAXN],ry1[MAXN],rx2[MAXN],ry2[MAXN];\nvoid recompute(){\n for(int i=0;icomp,int x1,int y1,int x2,int y2){\n int nc=comp.size();\n if(nc==1)return;\n long long tr=0;for(int i:comp)tr+=pr[i];\n vectorbx(comp),by(comp);\n sort(bx.begin(),bx.end(),[](int a,int b){return px[a]=px[bx[k]])continue;int lo=max(px[bx[k-1]]+1,x1+1),hi=min(px[bx[k]],x2-1);if(lo>hi)continue;int sx=(int)round(x1+(double)(x2-x1)*pf/tr);sx=max(lo,min(hi,sx));double e=fabs((double)pf/tr-(double)(sx-x1)/(x2-x1));if(e=py[by[k]])continue;int lo=max(py[by[k-1]]+1,y1+1),hi=min(py[by[k]],y2-1);if(lo>hi)continue;int sy=(int)round(y1+(double)(y2-y1)*pf/tr);sy=max(lo,min(hi,sy));double e=fabs((double)pf/tr-(double)(sy-y1)/(y2-y1));if(e=s.hi)continue;\n int bsp=s.sp;double bs=evalAt(s,s.sp);\n int lo=s.lo,hi=s.hi;\n while(hi-lo>=3){\n int m1=lo+(hi-lo)/3,m2=hi-(hi-lo)/3;\n double s1=evalAt(s,m1),s2=evalAt(s,m2);\n if(s1bs){bs=sc;bsp=sp;}}\n if(bsp!=s.sp){s.sp=bsp;recompute();imp=true;}\n }\n return imp;\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>n;for(int i=0;i>px[i]>>py[i]>>pr[i];\n vectorall(n);iota(all.begin(),all.end(),0);\n build(all,0,0,10000,10000);\n recompute();\n auto t0=chrono::steady_clock::now();\n for(;;){\n if(chrono::duration_cast(chrono::steady_clock::now()-t0).count()>4000)break;\n if(!lsPass())break;\n }\n for(int i=0;i(long long)H)continue;\n long long area=(long long)w*hh;\n double ratio=area<=(long long)ri?(double)area/ri:(double)ri/area;\n if(ratio>br){br=ratio;bw=w;bh=(int)hh;if(br>=1-1e-9){done=true;break;}}\n }\n }\n int a=max(x1,xi+1-bw),b=max(y1,yi+1-bh);\n cout<\nusing namespace std;\ntypedef chrono::steady_clock Clock;\nconst int N=50, MAXM=N*N+1;\nint si,sj,M,tid[N][N],pval[N][N];\nconst int dx[]={-1,1,0,0},dy[]={0,0,-1,1};\nconst char dc[]={'U','D','L','R'};\nmt19937 rng;\nbool tu[MAXM],btu[MAXM];\nint pi_[MAXM],pj_[MAXM],pt_[MAXM],bpi[MAXM],bpj[MAXM],bpt[MAXM];\nchar pmv[MAXM],bpmv[MAXM];\nint plen,blen;long long cscore,bscore;int ci,cj;\nvoid save_best(){if(cscore<=bscore)return;bscore=cscore;blen=plen;memcpy(btu,tu,M);memcpy(bpi,pi_,plen*4);memcpy(bpj,pj_,plen*4);memcpy(bpt,pt_,plen*4);if(plen>1)memcpy(bpmv,pmv,plen-1);}\nvoid restore_best(){cscore=bscore;plen=blen;memcpy(tu,btu,M);memcpy(pi_,bpi,plen*4);memcpy(pj_,bpj,plen*4);memcpy(pt_,bpt,plen*4);if(plen>1)memcpy(pmv,bpmv,plen-1);ci=pi_[plen-1];cj=pj_[plen-1];}\nvoid walk_init(){fill(tu,tu+M,false);plen=1;ci=si;cj=sj;pi_[0]=si;pj_[0]=sj;pt_[0]=tid[si][sj];tu[tid[si][sj]]=true;cscore=pval[si][sj];}\nbool walk_step(double a,double b,double g){int bd=-1;double bh=-1e18;for(int d=0;d<4;d++){int ni=ci+dx[d],nj=cj+dy[d];if((unsigned)ni>=(unsigned)N||(unsigned)nj>=(unsigned)N)continue;int t=tid[ni][nj];if(tu[t])continue;tu[t]=true;int deg=0;double nv=0;for(int d2=0;d2<4;d2++){int nni=ni+dx[d2],nnj=nj+dy[d2];if((unsigned)nni>=(unsigned)N||(unsigned)nnj>=(unsigned)N)continue;if(!tu[tid[nni][nnj]]){deg++;nv+=pval[nni][nnj];}}tu[t]=false;double h=a*pval[ni][nj]+g*nv-b*deg+uniform_real_distribution(-0.5,0.5)(rng);if(h>bh){bh=h;bd=d;}}if(bd==-1)return false;int ni=ci+dx[bd],nj=cj+dy[bd];tu[tid[ni][nj]]=true;cscore+=pval[ni][nj];pmv[plen-1]=dc[bd];pi_[plen]=ni;pj_[plen]=nj;pt_[plen]=tid[ni][nj];plen++;ci=ni;cj=nj;return true;}\nvoid walk_extend(double a,double b,double g){while(walk_step(a,b,g));}\nvoid walk_undo(int steps){steps=min(steps,plen-1);while(steps-->0){plen--;tu[pt_[plen]]=false;cscore-=pval[pi_[plen]][pj_[plen]];}ci=pi_[plen-1];cj=pj_[plen-1];}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n rng.seed(chrono::steady_clock::now().time_since_epoch().count());\n cin>>si>>sj;\n for(int i=0;i>tid[i][j];\n for(int i=0;i>pval[i][j];\n M=0;for(int i=0;i(0.5,2.0)(rng);\n double b=uniform_real_distribution(0,25)(rng);\n double g=uniform_real_distribution(0,0.5)(rng);\n if(iter%4==0||blen<=1){walk_init();}\n else{restore_best();walk_undo(uniform_int_distribution(1,blen-1)(rng));}\n walk_extend(a,b,g);save_best();iter++;\n }\n cout<\nusing namespace std;\nconst int N=30;\nconst double DELTA_VAR=1e6,INIT_SIG2_R=1e8,INIT_SIG2_E=1e7,MIN_SIG2=1e4;\ndouble mu_row[N],sig2_row[N],mu_col[N],sig2_col[N];\ndouble mu_h[N][N-1],sig2_h[N][N-1],mu_v[N-1][N],sig2_v[N-1][N];\nbool obs_h[N][N-1],obs_v[N-1][N];\ndouble wh(int i,int j){return obs_h[i][j]?mu_h[i][j]:mu_row[i];}\ndouble wv(int i,int j){return obs_v[i][j]?mu_v[i][j]:mu_col[j];}\nstring dijkstra(int sr,int sc,int tr,int tc){\n static double dist[N*N];static int par[N*N];static char pdir[N*N];\n fill(dist,dist+N*N,1e18);\n priority_queue,vector>,greater<>> pq;\n int src=sr*N+sc,dst=tr*N+tc;dist[src]=0;pq.push({0.0,src});\n while(!pq.empty()){\n auto[d,u]=pq.top();pq.pop();\n if(d>dist[u]+1e-9)continue;if(u==dst)break;\n int r=u/N,c=u%N;\n if(r>0){int nv=(r-1)*N+c;double nd=d+wv(r-1,c);if(nd0){int nv=r*N+(c-1);double nd=d+wh(r,c-1);if(nd>sr>>sc>>tr>>tc;\n string path=dijkstra(sr,sc,tr,tc);cout<>obs;\n double noise_var=(double)obs*obs/300.0;\n int kh[N]={},lv[N]={};\n struct E{bool is_h;int i,j;};vector edges;\n int r=sr,c=sc;\n for(char ch:path){\n if(ch=='U'){edges.push_back({false,r-1,c});lv[c]++;r--;}\n else if(ch=='D'){edges.push_back({false,r,c});lv[c]++;r++;}\n else if(ch=='L'){edges.push_back({true,r,c-1});kh[r]++;c--;}\n else{edges.push_back({true,r,c});kh[r]++;c++;}\n }\n double pred_r=0,pvar_r=0;\n for(int i=0;i0){pred_r+=kh[i]*mu_row[i];pvar_r+=(double)kh[i]*kh[i]*sig2_row[i]+kh[i]*DELTA_VAR;}\n for(int j=0;j0){pred_r+=lv[j]*mu_col[j];pvar_r+=(double)lv[j]*lv[j]*sig2_col[j]+lv[j]*DELTA_VAR;}\n double tvr=pvar_r+noise_var,resr=(double)obs-pred_r;\n for(int i=0;i0){double K=sig2_row[i]*kh[i]/tvr;mu_row[i]=clamp(mu_row[i]+K*resr,1000.0,9000.0);sig2_row[i]=max(sig2_row[i]*(1.0-K*kh[i]),MIN_SIG2);}\n for(int j=0;j0){double K=sig2_col[j]*lv[j]/tvr;mu_col[j]=clamp(mu_col[j]+K*resr,1000.0,9000.0);sig2_col[j]=max(sig2_col[j]*(1.0-K*lv[j]),MIN_SIG2);}\n for(auto& e:edges){\n if(e.is_h&&!obs_h[e.i][e.j]){obs_h[e.i][e.j]=true;mu_h[e.i][e.j]=mu_row[e.i];sig2_h[e.i][e.j]=INIT_SIG2_E;}\n else if(!e.is_h&&!obs_v[e.i][e.j]){obs_v[e.i][e.j]=true;mu_v[e.i][e.j]=mu_col[e.j];sig2_v[e.i][e.j]=INIT_SIG2_E;}\n }\n double pred_e=0,pvar_e=0;\n for(auto& e:edges){pred_e+=(e.is_h?mu_h[e.i][e.j]:mu_v[e.i][e.j]);pvar_e+=(e.is_h?sig2_h[e.i][e.j]:sig2_v[e.i][e.j]);}\n double tve=pvar_e+noise_var,rese=(double)obs-pred_e;\n for(auto& e:edges){\n double& mu=e.is_h?mu_h[e.i][e.j]:mu_v[e.i][e.j];\n double& s2=e.is_h?sig2_h[e.i][e.j]:sig2_v[e.i][e.j];\n double K=s2/tve;mu=clamp(mu+K*rese,1000.0,9000.0);s2=max(s2*(1.0-K),MIN_SIG2);\n }\n }\n return 0;\n}","ahc004":"#include \nusing namespace std;\nconst int N=20,MAXM=800,MAXL=12;\nint M;int8_t grid[N][N],h_mm[N][MAXM][N],v_mm[N][MAXM][N];\nint match_count[MAXM];int8_t S[MAXM][MAXL];int slen[MAXM];\nint8_t char_pos[MAXM][8][MAXL],char_pos_cnt[MAXM][8];uint8_t char_appears[MAXM];int score;\nint unsat_arr[MAXM],unsat_cnt,unsat_pos[MAXM];\nvoid unsat_remove(int k){int pos=unsat_pos[k];if(pos<0)return;int last=unsat_arr[--unsat_cnt];unsat_arr[pos]=last;unsat_pos[last]=pos;unsat_pos[k]=-1;}\nvoid unsat_add(int k){if(unsat_pos[k]>=0)return;unsat_pos[k]=unsat_cnt;unsat_arr[unsat_cnt++]=k;}\nvoid apply_cell(int r,int c,int oc,int nc){\n uint8_t mask=(1u<0&&nm==0){unsat_add(k);score--;}else if(om==0&&nm>0){unsat_remove(k);score++;}}grid[r][c]=nc;}\nint compute_delta(int r,int c,int oc,int nc){\n uint8_t mask=(1u<0)-(match_count[k]>0);}return d;}\nvoid recompute(){score=0;unsat_cnt=0;fill(unsat_pos,unsat_pos+M,-1);\n for(int r=0;r0)score++;else unsat_add(k);}}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n int n;cin>>n>>M;\n for(int k=0;k>s;slen[k]=s.size();char_appears[k]=0;memset(char_pos_cnt[k],0,8);\n for(int p=0;p0){\n double el=chrono::duration(chrono::steady_clock::now()-t0).count();\n if(el>=0.15||score>=M*2/5)break;\n int k=unsat_arr[rng()%(uint32_t)unsat_cnt];\n int bm=INT_MAX,br=0,bj=0,bd=0;\n for(int r=0;rbs){bs=score;memcpy(bg,grid,sizeof(grid));}}\n if(score!=bs){memcpy(grid,bg,sizeof(grid));recompute();}}\n double sa0=chrono::duration(chrono::steady_clock::now()-t0).count();\n double sad=max(0.1,TL-sa0);double T=5.0;\n for(int iter=0;;iter++){\n if((iter&0xFFF)==0){double el=chrono::duration(chrono::steady_clock::now()-t0).count();if(el>=TL)break;T=5.0*pow(0.001/5.0,min(1.0,max(0.0,(el-sa0)/sad)));}\n bool guided=false;int r,c,nc,oc;\n if(unsat_cnt>0&&rng()%(uint32_t)M<(uint32_t)unsat_cnt){\n int k=unsat_arr[rng()%(uint32_t)unsat_cnt];\n int bm=INT_MAX,br=0,bj=0,bd=0;\n for(int rr=0;rr=1&&bm<=thr){for(int p=0;p=0||(double)rng()bs){bs=score;memcpy(bg,grid,sizeof(grid));}}\n }\n for(int i=0;i\nusing namespace std;\nint N, si, sj;\nvector grid;\nbool isRoad(int r, int c) { return r>=0&&r=0&&c,vector> dijkstra(int src) {\n vector dist(N*N,INF),par(N*N,-1);\n priority_queue,vector>,greater<>> pq;\n dist[src]=0; pq.push({0,src});\n const int DR[]={-1,1,0,0},DC[]={0,0,-1,1};\n while(!pq.empty()){auto[dd,u]=pq.top();pq.pop();if(dd>dist[u])continue;int r=u/N,c=u%N;for(int i=0;i<4;i++){int nr=r+DR[i],nc=c+DC[i];if(!isRoad(nr,nc))continue;int v=nr*N+nc,nd=dd+(grid[nr][nc]-'0');if(nd>N>>si>>sj;grid.resize(N);for(int i=0;i>grid[i];\n vector roads;vector rIdx(N*N,-1);\n for(int r=0;r> vis(R);\n for(int i=0;i=0&&isRoad(r,c-dd);dd++)vis[i].push_back(rIdx[r*N+(c-dd)]);for(int dd=1;r+dd=0&&isRoad(r-dd,c);dd++)vis[i].push_back(rIdx[(r-dd)*N+c]);}\n vector covered(R,false);int uncov=R;vector cnt(R);for(int i=0;i> pqsc;for(int i=0;i sents;\n while(uncov>0){int best=-1;while(!pqsc.empty()){auto[cv,id]=pqsc.top();pqsc.pop();if(cv==cnt[id]){best=id;break;}}if(best<0)break;sents.push_back(roads[best]);for(int j:vis[best])if(!covered[j]){covered[j]=true;uncov--;for(int k:vis[j]){cnt[k]--;pqsc.push({cnt[k],k});}}}\n int stSq=si*N+sj;{auto it=find(sents.begin(),sents.end(),stSq);if(it==sents.end())sents.insert(sents.begin(),stSq);else swap(*it,sents[0]);}\n int S=sents.size();\n {vector covCnt(R,0);for(int sq:sents)for(int j:vis[rIdx[sq]])covCnt[j]++;bool changed=true;while(changed){changed=false;for(int i=S-1;i>=1;i--){if(sents[i]<0)continue;int ridx=rIdx[sents[i]];bool red=true;for(int j:vis[ridx])if(covCnt[j]<=1){red=false;break;}if(red){for(int j:vis[ridx])covCnt[j]--;sents[i]=-1;changed=true;}}}sents.erase(remove(sents.begin(),sents.end(),-1),sents.end());S=sents.size();}\n vector> allDist(S),allPar(S);\n for(int i=0;i> dm(S,vector(S,INF));for(int i=0;i tvis(S,false);vector tour={0};tvis[0]=true;\n for(int s=1;s path;for(int cur=toSq;cur!=srcSq;cur=allPar[fi][cur])path.push_back(cur);reverse(path.begin(),path.end());int pp=srcSq;for(int nx:path){int pr=pp/N,pc=pp%N,nr=nx/N,nc=nx%N;if(nrpr)res+='D';else if(nc\nusing namespace std;\n\nint N, M, K, R;\nvector> d, succs;\nvector task_st, task_pre, task_w, worker_t, task_sd;\nvector> sk;\nvector> lb;\nvector>> obs;\nvector cp;\nvector> et;\nint cur_day;\ndouble prior_sk;\n\nvoid upd_et(int w) {\n for (int i = 0; i < N; i++) {\n double ww = 0;\n for (int k = 0; k < K; k++) { double df = d[i][k] - sk[w][k]; if (df > 0) ww += df; }\n et[i][w] = ww < 0.5 ? 1.0 : ww;\n }\n}\n\nvoid calc_cp() {\n cp.assign(N, 0.0);\n for (int i = N-1; i >= 0; i--) {\n if (task_st[i] == 2) continue;\n double mn;\n if (task_st[i] == 1) { double rem = task_sd[i] + et[i][task_w[i]] - cur_day; mn = max(1.0, rem); }\n else { mn = et[i][0]; for (int j = 1; j < M; j++) mn = min(mn, et[i][j]); }\n double mx = 0;\n for (int v : succs[i]) mx = max(mx, cp[v]);\n cp[i] = mn + mx;\n }\n}\n\nvoid refit(int w) {\n int n = (int)obs[w].size();\n double decay = exp(-0.1 * n);\n for (int k = 0; k < K; k++) sk[w][k] = max((double)lb[w][k], prior_sk * decay);\n double lr = 1.0;\n for (int it = 0; it < 200; it++) {\n double delta[20] = {}; double loss = 0;\n for (auto& [ti, to] : obs[w]) {\n double wh = 0;\n for (int k = 0; k < K; k++) { double df = d[ti][k] - sk[w][k]; if (df > 0) wh += df; }\n double tgt = to == 1 ? 0.0 : (double)to, err = wh - tgt;\n loss += err * err;\n for (int k = 0; k < K; k++) {\n if (d[ti][k] > sk[w][k]) delta[k] += err;\n else if (err < -0.5 && d[ti][k] > 0) delta[k] += 0.3 * err;\n }\n }\n bool ch = false;\n for (int k = 0; k < K; k++) {\n double ns = max((double)lb[w][k], max(0.0, sk[w][k] + lr * delta[k] / n));\n if (ns != sk[w][k]) { sk[w][k] = ns; ch = true; }\n }\n if (!ch || loss / n < 0.1) break;\n lr *= 0.95;\n }\n upd_et(w);\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> M >> K >> R;\n d.assign(N, vector(K));\n for (int i = 0; i < N; i++) for (int k = 0; k < K; k++) cin >> d[i][k];\n succs.assign(N, {}); task_pre.assign(N, 0);\n for (int r = 0; r < R; r++) { int u, v; cin >> u >> v; u--; v--; succs[u].push_back(v); task_pre[v]++; }\n task_st.assign(N, 0); task_w.assign(N, -1); worker_t.assign(M, -1); task_sd.assign(N, 0);\n prior_sk = 40.0 / sqrt((double)K);\n sk.assign(M, vector(K, prior_sk)); lb.assign(M, vector(K, 0)); obs.resize(M);\n et.assign(N, vector(M));\n for (int j = 0; j < M; j++) upd_et(j);\n set avail, idle;\n for (int i = 0; i < N; i++) if (!task_pre[i]) avail.insert(i);\n for (int j = 0; j < M; j++) idle.insert(j);\n cur_day = 0;\n while (true) {\n cur_day++; calc_cp();\n vector av(avail.begin(), avail.end());\n sort(av.begin(), av.end(), [](int a, int b){ return cp[a] > cp[b]; });\n vector> asgn; set id = idle;\n for (int t : av) {\n if (id.empty()) break;\n int bw = -1; double bt = 1e18;\n for (int j : id) if (et[t][j] < bt) { bt = et[t][j]; bw = j; }\n asgn.push_back({bw, t}); id.erase(bw);\n }\n cout << asgn.size();\n for (auto [w, t] : asgn) {\n cout << ' ' << w+1 << ' ' << t+1;\n task_w[t] = w; worker_t[w] = t; task_sd[t] = cur_day;\n task_st[t] = 1; avail.erase(t); idle.erase(w);\n }\n cout << '\\n'; cout.flush();\n int nc; cin >> nc;\n if (nc == -1) break;\n for (int i = 0; i < nc; i++) {\n int w; cin >> w; w--;\n int t = worker_t[w], tk = cur_day - task_sd[t] + 1;\n obs[w].push_back({t, tk});\n if (tk == 1) for (int k = 0; k < K; k++) lb[w][k] = max(lb[w][k], d[t][k]);\n refit(w);\n task_st[t] = 2; task_w[t] = -1; worker_t[w] = -1; idle.insert(w);\n for (int v : succs[t]) if (!--task_pre[v]) avail.insert(v);\n }\n }\n}","ahc006":"#include \nusing namespace std;\nconst int OX=400,OY=400,TOT=1000,K=50,NN=2*K+1;\nint A[TOT],B[TOT],C[TOT],D[TOT],sel[K],NX[NN],NY[NN];\nint md(int x1,int y1,int x2,int y2){return abs(x1-x2)+abs(y1-y2);}\nint ec(int u,int v){return md(NX[u],NY[u],NX[v],NY[v]);}\nvoid refresh(){NX[0]=OX;NY[0]=OY;for(int i=0;i&r){int s=0;for(int i=0;i+1<(int)r.size();i++)s+=ec(r[i],r[i+1]);return s;}\nbool feasible(const vector&r){bool p[K+1]={};for(int v:r){if(v>=1&&v<=K)p[v]=true;else if(v>K&&!p[v-K])return false;}return true;}\nvector build_nn(){bool vis[NN]={},has[K+1]={};vector r={0};vis[0]=true;for(int s=0;s<2*K;s++){int cur=r.back(),bv=-1,bd=INT_MAX;for(int v=1;vK&&!has[v-K]))continue;int dd=ec(cur,v);if(dd&r){int n=r.size();bool any=false;for(int i=1;i&r){int n=r.size();bool any=false;for(int i=1;ibd){bd=rem-ins;bj=j;}}if(bj<0)continue;vector nr;nr.reserve(n);for(int k=0;k&r){int n=r.size();bool any=false;for(int i=1;ibd){bd=rem-ins;bj=j;}}if(bj<0)continue;vector nr;nr.reserve(n);for(int k=0;k&r){for(;;){bool a=two_opt_pass(r),b=or1_pass(r),c=or2_pass(r);if(!a&&!b&&!c)break;}}\nvoid quick_search(vector&r,int it=5){for(int i=0;i build_perturbed(const vector&base,int si){int pi=si+1,di=K+si+1;vector r;r.reserve(base.size()-2);for(int v:base)if(v!=pi&&v!=di)r.push_back(v);int n=r.size();int bc=INT_MAX,bp=0,bd2=1;for(int p=0;p res=r;res.insert(res.begin()+bp+1,pi);res.insert(res.begin()+bd2+1,di);return res;}\nvector double_bridge(const vector&r,mt19937&rng){int n=r.size();if(n<8)return r;int pos[4];do{for(int i=0;i<4;i++)pos[i]=1+rng()%(n-2);}while(pos[0]==pos[1]||pos[0]==pos[2]||pos[0]==pos[3]||pos[1]==pos[2]||pos[1]==pos[3]||pos[2]==pos[3]);sort(pos,pos+4);int a=pos[0],b=pos[1],c=pos[2],d=pos[3];vector nr;nr.reserve(n);for(int i=0;i&r){cout<(Clk::now()-T0).count();}\nint bcost=INT_MAX;vector broute;int bsel[K];bool inS[TOT]={};\nvoid trysel(){refresh();auto r=build_nn();full_search(r);int c=tcost(r);if(c pos(NN,-1);for(int i=0;i rem(K);for(int i=0;i> cands;for(int j=0;j0)cands.emplace_back(g,si,j);}}\nif(cands.empty())return false;int tk=min(10,(int)cands.size());partial_sort(cands.begin(),cands.begin()+tk,cands.end(),greater>());for(int ci=0;ci>A[i]>>B[i]>>C[i]>>D[i];\n {vector> sc(TOT);for(int i=0;i> sc(TOT);for(int i=0;i> sc(TOT);for(int i=0;i1.95)break;bool a=two_opt_pass(broute),b=or1_pass(broute),c=or2_pass(broute);if(!a&&!b&&!c)break;}\n emit(broute);\n return 0;\n}","ahc007":"#include \nusing namespace std;\nconst int N = 400, M = 1995;\nint px[N], py[N];\nint eu[M], ev[M];\nlong long ed[M];\nstruct UF {\n int p[N], r[N];\n void init() { for(int i=0;i>px[i]>>py[i];\n for(int i=0;i>eu[i]>>ev[i];\n double dx=px[eu[i]]-px[ev[i]], dy=py[eu[i]]-py[ev[i]];\n ed[i]=llround(sqrt(dx*dx+dy*dy));\n }\n uf.init();\n for(int i=0;i>l;\n if(uf.same(eu[i],ev[i])){ cout<<0<1){ cout<<1<0){ threshold=(double)min_d*(1.0+2.0/(k+1.0)); }\n else {\n int comp_id[N]; fill(comp_id,comp_id+N,-1); int nc=0;\n for(int v=0;v>> cadj(nc);\n for(int j=i+1;j dist(nc,1e18);\n priority_queue,vector>,greater<>> pq;\n dist[src]=0; pq.push({0.0,src});\n while(!pq.empty()){\n auto [dv,u]=pq.top(); pq.pop();\n if(dv>dist[u]+1e-9) continue; if(u==dst) break;\n for(auto [v,w]:cadj[u]){ double nd=dist[u]+w; if(nd1e17)?2.0*ed[i]:dist[dst];\n }\n if((double)l<=threshold){ cout<<1<\nusing namespace std;\nconst int G=30;\nint N,M,px[20],py[20],hx[10],hy[10];\nbool wall[G+2][G+2];\nint spx[20],spy[20],shx[10],shy[10];\nconst int ddx[]={-1,1,0,0},ddy[]={0,0,-1,1};\nconst char DIRS[]=\"UDLR\",WDIRS[]=\"udlr\";\nbool inb(int x,int y){return x>=1&&x<=G&&y>=1&&y<=G;}\nint dbuf[G+2][G+2];\nvoid bfs(int tx,int ty){\n for(int i=0;i<=G+1;i++)fill(dbuf[i],dbuf[i]+G+2,-1);\n dbuf[tx][ty]=0;queue>q;q.push({tx,ty});\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int d=0;d<4;d++){int nx=x+ddx[d],ny=y+ddy[d];if(!inb(nx,ny)||wall[nx][ny]||dbuf[nx][ny]!=-1)continue;dbuf[nx][ny]=dbuf[x][y]+1;q.push({nx,ny});}}\n}\nchar gmv(int sx,int sy,int tx,int ty){\n if(sx==tx&&sy==ty)return '.';bfs(tx,ty);if(dbuf[sx][sy]==-1)return '.';\n for(int d=0;d<4;d++){int nx=sx+ddx[d],ny=sy+ddy[d];if(!inb(nx,ny)||wall[nx][ny])continue;if(dbuf[nx][ny]==dbuf[sx][sy]-1)return DIRS[d];}return '.';\n}\nbool cpl(int wx,int wy){\n if(!inb(wx,wy)||wall[wx][wy])return false;\n for(int i=0;i>N;for(int i=0;i>px[i]>>py[i]>>t;}cin>>M;for(int i=0;i>hx[i]>>hy[i];\n double bv=-1e18;int wt=0,wp=16;bool hp=true;\n auto ch_cnt=[&](int wtype,int wpos,bool hpos)->int{int c=0;for(int i=0;i=wpos):(hpos?hx[i]=wpos);if(ok)c++;}return c;};\n auto ev=[&](int area,int pets,int wtype,int wpos,bool hpos)->double{return (double)area/900.0*pow(2.0,-(double)pets)*(0.7+0.3*ch_cnt(wtype,wpos,hpos)/M);};\n for(int c=2;c<=G;c++){int lp=0,rp=0;for(int i=0;ibv){bv=vl;wt=0;wp=c;hp=true;}if(vr>bv){bv=vr;wt=0;wp=c;hp=false;}}\n for(int r=2;r<=G;r++){int tp=0,bp=0;for(int i=0;ibv){bv=vt;wt=1;wp=r;hp=true;}if(vb>bv){bv=vb;wt=1;wp=r;hp=false;}}\n struct Task{int wx,wy,sx,sy,wd;};vector tasks(G);\n if(wt==0){if(hp)for(int r=1;r<=G;r++)tasks[r-1]={r,wp,r,wp-1,3};else for(int r=1;r<=G;r++)tasks[r-1]={r,wp-1,r,wp,2};}\n else{if(hp)for(int c=1;c<=G;c++)tasks[c-1]={wp,c,wp-1,c,1};else for(int c=1;c<=G;c++)tasks[c-1]={wp-1,c,wp,c,0};}\n vector hord(M);iota(hord.begin(),hord.end(),0);\n if(wt==0)sort(hord.begin(),hord.end(),[&](int a,int b){return hx[a] te(M),ct(M);for(int i=0;ibool{return wt==0?(hp?hy[h]=wp):(hp?hx[h]=wp);};\n for(int turn=0;turn<300;turn++){\n for(int i=0;i> pw;vector isp(M,false);\n // PASS 1: Wall placements first\n for(int h=0;h=te[h])continue;\n Task&t=tasks[ct[h]];bool ig=(ct[h]==G-1)&&!all_safe;\n if(hx[h]==t.sx&&hy[h]==t.sy&&!ig&&cpl(t.wx,t.wy)&&!pw.count({t.wx,t.wy})){\n acts[h]=WDIRS[t.wd];pw.insert({t.wx,t.wy});wall[t.wx][t.wy]=true;ct[h]++;isp[h]=true;\n }\n }\n // PASS 2: Movements using updated wall state\n for(int h=0;h=te[h]){acts[h]='.';continue;}\n Task&t=tasks[ct[h]];\n if(hx[h]==t.sx&&hy[h]==t.sy){acts[h]='.';continue;}\n char mv=gmv(hx[h],hy[h],t.sx,t.sy);\n acts[h]=mv;if(mv!='.')for(int d=0;d<4;d++)if(DIRS[d]==mv){hx[h]+=ddx[d];hy[h]+=ddy[d];break;}\n }\n cout<>s;for(char c:s){if(c=='U')px[i]--;else if(c=='D')px[i]++;else if(c=='L')py[i]--;else if(c=='R')py[i]++;}}\n }\n}","ahc009":"#include \nusing namespace std;\nint si,sj,ti,tj; double pf;\nbool H[20][19],V[19][20];\nint nb[400][4],G;\nvoid initNb(){for(int i=0;i<20;i++)for(int j=0;j<20;j++){int c=i*20+j;nb[c][0]=(i>0&&!V[i-1][j])?(i-1)*20+j:c;nb[c][1]=(i<19&&!V[i][j])?(i+1)*20+j:c;nb[c][2]=(j>0&&!H[i][j-1])?i*20+(j-1):c;nb[c][3]=(j<19&&!H[i][j])?i*20+(j+1):c;}}\nint dc(char c){return c=='U'?0:c=='D'?1:c=='L'?2:3;}\ndouble PP[201][400],PE[201];\nvoid buildP(const string&s,int fr){for(int t=fr;t<200;t++){int d=dc(s[t]);double*a=PP[t],*b=PP[t+1];memset(b,0,3200);for(int k=0;k<400;k++){double v=a[k];if(v<1e-15)continue;b[k]+=v*pf;b[nb[k][d]]+=v*(1-pf);}double e=b[G]*(401.-(t+1));b[G]=0;PE[t+1]=PE[t]+e;}}\ndouble evalF(const string&s,int fr){double p[400],q[400];memcpy(p,PP[fr],3200);double E=PE[fr];for(int t=fr;t<200;t++){int d=dc(s[t]);memset(q,0,3200);for(int k=0;k<400;k++){double v=p[k];if(v<1e-15)continue;q[k]+=v*pf;q[nb[k][d]]+=v*(1-pf);}E+=q[G]*(401.-(t+1));q[G]=0;memcpy(p,q,3200);}return E;}\nvoid setP(const string&s){memset(PP[0],0,3200);PP[0][si*20+sj]=1;PE[0]=0;buildP(s,0);}\nchrono::time_pointT0;\ndouble el(){return chrono::duration(chrono::steady_clock::now()-T0).count();}\ndouble hc(string&s,double E0,double tl){double be=E0;for(;;){if(el()>tl)break;bool imp=false;for(int t=0;t<200;t++){int od=dc(s[t]);for(int d=0;d<4;d++){if(d==od)continue;s[t]=\"UDLR\"[d];double e=evalF(s,t);if(e>be+1e-12){be=e;od=d;buildP(s,t);imp=true;}else s[t]=\"UDLR\"[od];}}if(!imp)break;}return be;}\nstring bfsPath(){int ds[400];fill(ds,ds+400,-1);int pr[400],pd[400];int src=si*20+sj;queueq;q.push(src);ds[src]=0;while(!q.empty()){int k=q.front();q.pop();for(int d=0;d<4;d++){int nk=nb[k][d];if(nk==k||ds[nk]!=-1)continue;ds[nk]=ds[k]+1;pr[nk]=k;pd[nk]=d;q.push(nk);}}string r;for(int c=G;c!=src;c=pr[c])r+=\"UDLR\"[pd[c]];reverse(r.begin(),r.end());return r;}\nstring greedyPath(){int bd[400];fill(bd,bd+400,-1);queueq;q.push(G);bd[G]=0;while(!q.empty()){int k=q.front();q.pop();for(int d=0;d<4;d++){int nk=nb[k][d];if(nk==k||bd[nk]!=-1)continue;bd[nk]=bd[k]+1;q.push(nk);}}double p[400]={},np[400];p[si*20+sj]=1;string s(200,'D');for(int t=0;t<200;t++){double bst=-1e18;int bd2=0;for(int d=0;d<4;d++){double g=0;for(int k=0;k<400;k++){if(p[k]<1e-15)continue;g+=p[k]*(1-pf)*(bd[k]-bd[nb[k][d]]);}if(g>bst){bst=g;bd2=d;}}s[t]=\"UDLR\"[bd2];memset(np,0,3200);for(int k=0;k<400;k++){if(p[k]<1e-15)continue;np[k]+=p[k]*pf;np[nb[k][bd2]]+=p[k]*(1-pf);}np[G]=0;memcpy(p,np,3200);}return s;}\nint main(){\n ios::sync_with_stdio(0);cin.tie(0);\n cin>>si>>sj>>ti>>tj>>pf;\n for(int i=0;i<20;i++){string r;cin>>r;for(int j=0;j<19;j++)H[i][j]=(r[j]=='1');}\n for(int i=0;i<19;i++){string r;cin>>r;for(int j=0;j<20;j++)V[i][j]=(r[j]=='1');}\n initNb();G=ti*20+tj;T0=chrono::steady_clock::now();\n string path=bfsPath();int K=(int)path.size();\n string s1(200,'D');for(int i=0;i<200;i++)s1[i]=path[i%K];\n string s2=greedyPath();\n setP(s1);double e1=hc(s1,PE[200],0.2);\n setP(s2);double e2=hc(s2,PE[200],0.4);\n string gb=(e1>=e2)?s1:s2;double gbE=max(e1,e2);\n setP(gb);\n mt19937 rng(42);uniform_real_distributionud(0,1);\n {\n string sc=gb;double scE=gbE;double T=2.0;int stp=0;double sa0=el();\n while(el()<1.2){\n int t=rng()%200,od=dc(sc[t]),nd=(od+1+(int)(rng()%3))%4;\n sc[t]=\"UDLR\"[nd];double e=evalF(sc,t),dlt=e-scE;\n if(dlt>0||ud(rng)gbE){gbE=e;gb=sc;}}\n else sc[t]=\"UDLR\"[od];\n if(++stp%500==0){double f=min(1.,max(0.,(el()-sa0)/(1.2-sa0)));T=2.*exp(-7.*f);if(scEgbE+1e-12){gbE=e;gb=p2;}\n }\n cout<\nusing namespace std;\nconst int N = 30, TOTAL = N * N * 4;\nconst int to_t[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}};\nconst int di[4]={0,-1,0,1}, dj[4]={-1,0,1,0};\nint tiles[N][N], init_t[N][N], rots[N][N], best_rots[N][N];\ninline int apply_rot(int t,int r){\n if(t<=3)return(t+r)&3;\n if(t<=5)return 4+((t-4+r)&1);\n return 6+((t-6+r)&1);}\nint nxt[TOTAL]; uint8_t col[TOTAL];\ninline void update_nxt(int i,int j){\n int base=(i*N+j)*4, t=tiles[i][j];\n for(int d=0;d<4;d++){\n int d2=to_t[t][d];\n if(d2<0){nxt[base+d]=-1;continue;}\n int ni=i+di[d2],nj=j+dj[d2];\n if((unsigned)ni>=N||(unsigned)nj>=N){nxt[base+d]=-1;continue;}\n nxt[base+d]=(ni*N+nj)*4+((d2+2)&3);}}\nlong long evaluate(){\n memset(col,0,TOTAL); int t1=0,t2=0;\n for(int s=0;s=0&&!col[c]){col[c]=1;c=nxt[c];}\n if(c>=0&&col[c]==1){\n int len=0,cc=c;\n do{cc=nxt[cc];len++;}while(cc!=c);\n if(len>t1){t2=t1;t1=len;}else if(len>t2)t2=len;}\n c=s;\n while(c>=0&&col[c]==1){col[c]=2;c=nxt[c];}}\n return(long long)t1*t2;}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n for(int i=0;i>s;\n for(int j=0;j(chrono::steady_clock::now()-ts).count();\n cnt++;\n double T=T0*exp(lnr*elapsed/TL);\n int i=rng()%N,j=rng()%N;\n int dr=(rng()%3)+1,nr=(rots[i][j]+dr)&3,ot=tiles[i][j];\n tiles[i][j]=apply_rot(init_t[i][j],nr);\n update_nxt(i,j);\n long long ns=evaluate(),delta=ns-cur;\n if(delta>=0||rng()/4294967296.0best){best=ns;memcpy(best_rots,rots,sizeof(rots));}}\n else{tiles[i][j]=ot;update_nxt(i,j);}}\n string out(N*N,'0');\n for(int i=0;i\nusing namespace std;\nint N,T,board[10][10],board_label[10][10],er,ec,tgt[10][10],avail[16];\nbool fixed_cells[10][10];\nstring out;\nvoid read_input(){cin>>N>>T;for(int i=0;i>s;for(int j=0;j='0'&&c<='9')?c-'0':c-'a'+10;if(!board[i][j]){er=i;ec=j;}}}}\nbool valid_pos(int v,int i,int j){return!((v&1)&&!j)&&!((v&2)&&!i)&&!((v&4)&&j==N-1)&&!((v&8)&&i==N-1);}\nbool is_tree(){bool vis[10][10]={};int sr=-1,sc=0;for(int i=0;i0){sr=i;sc=j;break;}if(sr<0)return false;queue>q;q.push({sr,sc});vis[sr][sc]=true;int cnt=1,ed=0;int dr[]={0,1,0,-1},dc[]={1,0,-1,0},cb[]={4,8,1,2},nb[]={1,2,4,8};while(!q.empty()){auto[r,c]=q.front();q.pop();for(int d=0;d<4;d++){int nr=r+dr[d],nc=c+dc[d];if(nr<0||nr>=N||nc<0||nc>=N||tgt[nr][nc]<=0)continue;if((tgt[r][c]&cb[d])&&(tgt[nr][nc]&nb[d])){ed++;if(!vis[nr][nc]){vis[nr][nc]=true;cnt++;q.push({nr,nc});}}}}return cnt==N*N-1&&ed==2*(N*N-2);}\nbool find_target(int pos){if(pos==N*N)return is_tree();int i=pos/N,j=pos%N;if(i==N-1&&j==N-1){tgt[i][j]=0;return find_target(pos+1);}bool fl=(j>0),nl=fl&&(tgt[i][j-1]&4);bool fu=(i>0),nu=fu&&(tgt[i-1][j]&8);for(int v=1;v<=15;v++){if(!avail[v]||!valid_pos(v,i,j))continue;if(fl&&!!(v&1)!=nl)continue;if(fu&&!!(v&2)!=nu)continue;avail[v]--;tgt[i][j]=v;if(find_target(pos+1))return true;avail[v]++;}tgt[i][j]=-1;return false;}\nvoid init_labels(){vector>cp[16],tp[16];for(int i=0;i0)cp[board[i][j]].push_back({i,j});if(tgt[i][j]>0)tp[tgt[i][j]].push_back({i,j});}for(int v=1;v<=15;v++){sort(cp[v].begin(),cp[v].end());sort(tp[v].begin(),tp[v].end());for(int k=0;k<(int)cp[v].size();k++){auto[cr,cc]=cp[v][k];auto[tr,tc]=tp[v][k];board_label[cr][cc]=tr*N+tc;}}}\nbool check_solvable(){vectors;for(int i=0;i=0)s.push_back(board_label[i][j]);int inv=0;for(int a=0;a<(int)s.size();a++)for(int b=a+1;b<(int)s.size();b++)if(s[a]>s[b])inv++;if(N%2)return!(inv%2);return(inv+er)%2==1;}\nvoid fix_parity(){if(check_solvable())return;for(int v=1;v<=15;v++){vector>cp;for(int i=0;i=2){swap(board_label[cp[0].first][cp[0].second],board_label[cp[1].first][cp[1].second]);if(check_solvable())return;swap(board_label[cp[0].first][cp[0].second],board_label[cp[1].first][cp[1].second]);}}}\nvoid do_move(char m){int tr=er,tc=ec;if(m=='U')tr--;else if(m=='D')tr++;else if(m=='L')tc--;else tc++;board[er][ec]=board[tr][tc];board_label[er][ec]=board_label[tr][tc];board[tr][tc]=0;board_label[tr][tc]=-1;er=tr;ec=tc;out+=m;}\nbool move_empty(int gr,int gc){if(er==gr&&ec==gc)return true;if((int)out.size()>=T||fixed_cells[gr][gc])return false;int NN=N*N;vectorprv(NN,-2);int s=er*N+ec,g=gr*N+gc;prv[s]=-1;queueq;q.push(s);int dr[]={-1,1,0,0},dcc[]={0,0,-1,1};while(!q.empty()){int cur=q.front();q.pop();if(cur==g)break;int r=cur/N,c=cur%N;for(int d=0;d<4;d++){int nr=r+dr[d],nc=c+dcc[d];if(nr<0||nr>=N||nc<0||nc>=N||fixed_cells[nr][nc])continue;int nxt=nr*N+nc;if(prv[nxt]!=-2)continue;prv[nxt]=cur;q.push(nxt);}}if(prv[g]==-2)return false;vectorpath;int cur=g;while(cur!=s){path.push_back(cur);cur=prv[cur];}reverse(path.begin(),path.end());for(int nxt:path){if((int)out.size()>=T)return false;int nr=nxt/N,nc=nxt%N;char m;if(nr==er-1)m='U';else if(nr==er+1)m='D';else if(nc==ec-1)m='L';else m='R';do_move(m);}return true;}\nbool bfs_tile(int&tr,int&tc,int dr,int dc){if(tr==dr&&tc==dc)return true;if((int)out.size()>=T)return false;int NN=N*N,t0=tr*N+tc,e0=er*N+ec,tg=dr*N+dc,tot=NN*NN;vectorprv(tot,-2);vectormv(tot,0);prv[t0*NN+e0]=-1;queueq;q.push(t0*NN+e0);int ddr[]={-1,1,0,0},ddc[]={0,0,-1,1};const char dch[]={'U','D','L','R'};int goal=-1;while(!q.empty()){int cur=q.front();q.pop();int ct=cur/NN,ce=cur%NN;if(ct==tg){goal=cur;break;}int er_=ce/N,ec_=ce%N;for(int d=0;d<4;d++){int nr=er_+ddr[d],nc=ec_+ddc[d];if(nr<0||nr>=N||nc<0||nc>=N||fixed_cells[nr][nc])continue;int np=nr*N+nc,nt=(np==ct)?ce:ct,ne=np;if(nt==ne)continue;int nst=nt*NN+ne;if(nst<0||nst>=tot||prv[nst]!=-2)continue;prv[nst]=cur;mv[nst]=dch[d];q.push(nst);}}if(goal<0){for(int e=0;epath;int cur=goal;while(cur!=t0*NN+e0){path.push_back(mv[cur]);cur=prv[cur];}reverse(path.begin(),path.end());for(char m:path){if((int)out.size()>=T)return false;do_move(m);}tr=dr;tc=dc;return true;}\npairfind_lbl(int lbl){for(int i=0;i=T)return;for(int col=0;col<=N-3&&(int)out.size()=T)return;auto[ar,ac]=find_lbl(row*N+(N-2));auto[br,bc]=find_lbl(row*N+(N-1));if(ar<0||br<0)return;if(ar==row&&ac==N-2&&br==row&&bc==N-1){fixed_cells[row][N-2]=fixed_cells[row][N-1]=true;return;}bfs_tile(ar,ac,row,N-1);if((int)out.size()>=T)return;auto[br2,bc2]=find_lbl(row*N+(N-1));if(br2<0)return;fixed_cells[row][N-1]=true;bfs_tile(br2,bc2,row+1,N-1);fixed_cells[row][N-1]=false;if((int)out.size()>=T)return;fixed_cells[row][N-1]=fixed_cells[row+1][N-1]=true;move_empty(row,N-2);fixed_cells[row][N-1]=fixed_cells[row+1][N-1]=false;if((int)out.size()=T)return;auto[ar,ac]=find_lbl((N-2)*N+col);auto[br,bc]=find_lbl((N-1)*N+col);if(ar<0||br<0)return;if(ar==N-2&&ac==col&&br==N-1&&bc==col){fixed_cells[N-2][col]=fixed_cells[N-1][col]=true;return;}bfs_tile(ar,ac,N-1,col);if((int)out.size()>=T)return;auto[br2,bc2]=find_lbl((N-1)*N+col);if(br2<0)return;fixed_cells[N-1][col]=true;bfs_tile(br2,bc2,N-1,col+1);fixed_cells[N-1][col]=false;if((int)out.size()>=T)return;fixed_cells[N-1][col]=fixed_cells[N-1][col+1]=true;move_empty(N-2,col);fixed_cells[N-1][col]=fixed_cells[N-1][col+1]=false;if((int)out.size()=T)return;int p0=(N-2)*N+(N-2),p1=(N-2)*N+(N-1),p2=(N-1)*N+(N-2);int a=board_label[N-2][N-2],b=board_label[N-2][N-1],c=board_label[N-1][N-2],d=board_label[N-1][N-1];if(a==p0&&b==p1&&c==p2&&d==-1)return;auto el=[&](int l)->int{if(l==p0)return 0;if(l==p1)return 1;if(l==p2)return 2;return 3;};auto enc=[](int v0,int v1,int v2,int v3){return v0*64+v1*16+v2*4+v3;};int gs=enc(0,1,2,3),ss=enc(el(a),el(b),el(c),el(d));if(ss==gs)return;arraypar;par.fill(-2);arraymfr;mfr.fill(0);queueq;q.push(ss);par[ss]=-1;static const int adj[4][2]={{1,2},{0,3},{0,3},{1,2}};static const char amv[4][2]={{'R','D'},{'L','D'},{'U','R'},{'U','L'}};while(!q.empty()){int cur=q.front();q.pop();if(cur==gs)break;int v[4]={(cur>>6)&3,(cur>>4)&3,(cur>>2)&3,cur&3};int ep=-1;for(int p=0;p<4;p++)if(v[p]==3){ep=p;break;}if(ep<0)continue;for(int k=0;k<2;k++){int np=adj[ep][k];char m=amv[ep][k];int nv[4]={v[0],v[1],v[2],v[3]};nv[ep]=nv[np];nv[np]=3;int nst=enc(nv[0],nv[1],nv[2],nv[3]);if(par[nst]==-2){par[nst]=cur;mfr[nst]=m;q.push(nst);}}}if(par[gs]==-2)return;vectorpath;int cur=gs;while(cur!=ss){path.push_back(mfr[cur]);cur=par[cur];}reverse(path.begin(),path.end());for(char m:path){if((int)out.size()>=T)break;do_move(m);}}\nvoid solve(){for(int row=0;row<=N-3&&(int)out.size()0)avail[board[i][j]]++;memset(tgt,-1,sizeof(tgt));memset(fixed_cells,0,sizeof(fixed_cells));memset(board_label,-1,sizeof(board_label));if(!find_target(0)){cout<<\"\\n\";return 0;}init_labels();fix_parity();solve();cout<\nusing namespace std;\ntypedef long long ll;\ntypedef unsigned long long ull;\ntypedef pair puu;\nstruct PH{size_t operator()(const puu&p)const{size_t h=hash()(p.first);h^=hash()(p.second)+0x9e3779b9ULL+(h<<6)+(h>>2);return h;}};\nmt19937 rng(42);\nint N,K,a[11],stx[5501],sty[5501];\nstruct Line{ll px,py,qx,qy;};\nconst int MK=100;\nLine cur_lines[MK],best_lines[MK];\nint8_t sgn_data[5501][MK];\null slo[5501],shi[5501];\nunordered_mapgrps;\nint b_arr[12],cscore,best_score;\nstruct Change{int idx;puu old_sig,new_sig;int8_t new_sgn;};\nvectorpending;\nvector>dvec;\nll ecross(const Line&l,ll x,ll y){return(l.qx-l.px)*(y-l.py)-(l.qy-l.py)*(x-l.px);}\nvoid upd(int oc,int nc){if(oc>=1&&oc<=10){cscore-=min(a[oc],b_arr[oc]);b_arr[oc]--;cscore+=min(a[oc],b_arr[oc]);}if(nc>=1&&nc<=10){cscore-=min(a[nc],b_arr[nc]);b_arr[nc]++;cscore+=min(a[nc],b_arr[nc]);}}\nvoid build(){grps.clear();grps.reserve(32768);grps.max_load_factor(0.3f);memset(b_arr,0,sizeof(b_arr));cscore=0;for(int i=0;i=0)?1:-1;sgn_data[i][j]=s;if(s==1){if(j<64)slo[i]|=(1ULL<second,it->second+1);it->second++;}}\nint try_ch(int j,const Line&nl){pending.clear();dvec.clear();for(int i=0;i=0)?1:-1;if(ns==sgn_data[i][j])continue;puu os{slo[i],shi[i]};ull nl2=slo[i],nh2=shi[i];if(j<64){if(ns==1)nl2|=(1ULL<second:0,nc=c+d;if(c>=1&&c<=10){nsc-=min(a[c],nb[c]);nb[c]--;nsc+=min(a[c],nb[c]);}if(nc>=1&&nc<=10){nsc-=min(a[nc],nb[nc]);nb[nc]++;nsc+=min(a[nc],nb[nc]);}}i=j2;}return nsc;}\nvoid do_ch(int j,const Line&nl){for(auto&ch:pending){{auto it=grps.find(ch.old_sig);upd(it->second,it->second-1);if(!--it->second)grps.erase(it);}slo[ch.idx]=ch.new_sig.first;shi[ch.idx]=ch.new_sig.second;sgn_data[ch.idx][j]=ch.new_sgn;{auto[it2,ins]=grps.emplace(ch.new_sig,0);upd(it2->second,it2->second+1);it2->second++;}}cur_lines[j]=nl;}\nLine rline(){double th=(rng()%314159)*(M_PI/314159.0);double r=(int)(rng()%18001)-9000;double cx=r*cos(th),cy=r*sin(th),sdx=-sin(th)*9000,sdy=cos(th)*9000;return{llround(cx+sdx),llround(cy+sdy),llround(cx-sdx),llround(cy-sdy)};}\nLine pline(const Line&l,int s){ll dx=(ll)(rng()%(2*s+1))-s,dy=(ll)(rng()%(2*s+1))-s;int t=rng()%3;if(t==0)return{l.px+dx,l.py+dy,l.qx,l.qy};if(t==1)return{l.px,l.py,l.qx+dx,l.qy+dy};return{l.px+dx,l.py+dy,l.qx-dx,l.qy-dy};}\nint main(){ios_base::sync_with_stdio(false);cin.tie(NULL);cin>>N>>K;for(int d=1;d<=10;d++)cin>>a[d];for(int i=0;i>stx[i]>>sty[i];\nfor(int i=0;i<50;i++){ll y=llround(-9000.0+18000.0*i/49.0);cur_lines[i]={-10000,y,10000,y};}\nfor(int i=0;i<50;i++){ll x=llround(-9000.0+18000.0*i/49.0);cur_lines[50+i]={x,-10000,x,10000};}\nbuild();best_score=cscore;memcpy(best_lines,cur_lines,sizeof(cur_lines));pending.reserve(N+10);dvec.reserve(2*N+10);\nauto t0=chrono::steady_clock::now();double T=15.0;int iter=0;\nwhile(true){if(!(++iter&511)){double e=chrono::duration(chrono::steady_clock::now()-t0).count();if(e>2.75)break;T=max(0.05,15.0*pow(0.05/15.0,e/2.75));}\nint j=rng()%MK;Line nl;int sel=rng()%100;\nif(sel<35)nl=pline(cur_lines[j],30);else if(sel<60)nl=pline(cur_lines[j],300);else if(sel<80)nl=pline(cur_lines[j],2000);else nl=rline();\nif(nl.px==nl.qx&&nl.py==nl.qy)continue;\nint ns=try_ch(j,nl);int ds=ns-cscore;bool acc=(ds>=0);\nif(!acc&&T>0.01)acc=((double)(rng()>>8)/(double)(1u<<24))best_score){best_score=cscore;memcpy(best_lines,cur_lines,sizeof(cur_lines));}}}\ncout<\nusing namespace std;\n\nconst int MAXN = 65;\nint N, M;\nbool dots[MAXN][MAXN];\nbool h_seg[MAXN][MAXN], v_seg[MAXN][MAXN], d1_seg[MAXN][MAXN], d2_seg[MAXN][MAXN];\nbool inPQ[MAXN][MAXN];\n\nvector row_dots[MAXN], col_dots[MAXN];\nvector diag_dots[130], ad_dots[130];\n\nstruct Op { int x1,y1,x2,y2,x3,y3,x4,y4; };\nvector ops;\n\nint cc;\n\nvoid insertSorted(vector& v, int x) {\n v.insert(lower_bound(v.begin(),v.end(),x),x);\n}\nvoid addDot(int x, int y) {\n dots[x][y]=true;\n insertSorted(row_dots[y],x);\n insertSorted(col_dots[x],y);\n insertSorted(diag_dots[x-y+64],x);\n insertSorted(ad_dots[x+y],x);\n}\n\nbool edgeClear(int x1,int y1,int x2,int y2) {\n if(x1==x2){for(int y=min(y1,y2);yx1)==(y2>y1)){int xm=min(x1,x2),ym=min(y1,y2);for(int t=0;tx1)?1:-1,dy=(y2>y1)?1:-1;for(int t=1;tx1)==(y2>y1)){int xm=min(x1,x2),ym=min(y1,y2);for(int t=0;t=N||y2<0||y2>=N||x3<0||x3>=N||y3<0||y3>=N||x4<0||x4>=N||y4<0||y4>=N)return false;\n if(!dots[x2][y2]||!dots[x3][y3]||!dots[x4][y4])return false;\n if(!edgeNoDots(nx,ny,x2,y2)||!edgeNoDots(x2,y2,x3,y3)||!edgeNoDots(x3,y3,x4,y4)||!edgeNoDots(x4,y4,nx,ny))return false;\n if(!edgeClear(nx,ny,x2,y2)||!edgeClear(x2,y2,x3,y3)||!edgeClear(x3,y3,x4,y4)||!edgeClear(x4,y4,nx,ny))return false;\n ops.push_back({nx,ny,x2,y2,x3,y3,x4,y4});\n addDot(nx,ny);\n drawEdge(nx,ny,x2,y2);drawEdge(x2,y2,x3,y3);drawEdge(x3,y3,x4,y4);drawEdge(x4,y4,nx,ny);\n return true;\n}\n\nbool findAndPlace(int nx, int ny) {\n if(dots[nx][ny])return false;\n \n // Gather all candidates (axis-parallel + 45-degree), sorted by perimeter\n vector> cands;\n \n // Axis-parallel\n for(int x2:row_dots[ny]){\n if(x2==nx)continue;\n for(int y2:col_dots[nx]){\n if(y2==ny||!dots[x2][y2])continue;\n cands.emplace_back(abs(x2-nx)+abs(y2-ny),x2,ny,x2,y2,nx,y2);\n }\n }\n // 45-degree\n for(int xa:diag_dots[nx-ny+64]){\n if(xa==nx)continue;\n int a=xa-nx;\n for(int xb:ad_dots[nx+ny]){\n if(xb==nx)continue;\n int b=xb-nx;\n int x3=nx+a+b,y3=ny+a-b;\n if(x3>=0&&x3=0&&y3>> work_pq;\n\nvoid addWork(int x,int y){\n if(x<0||x>=N||y<0||y>=N||dots[x][y]||inPQ[x][y])return;\n inPQ[x][y]=true;\n work_pq.push({(x-cc)*(x-cc)+(y-cc)*(y-cc)+1,{x,y}});\n}\n\nvoid afterPlace(int x,int y){\n // Row and column\n for(int i=0;i>N>>M;\n for(int i=0;i>x>>y;addDot(x,y);}\n cc=(N-1)/2;\n \n memset(inPQ,0,sizeof(inPQ));\n for(int x=0;x(chrono::steady_clock::now()-t0).count();\n };\n \n // Event-driven phase\n while(!work_pq.empty()&&elapsed()<4000){\n auto[w,pos]=work_pq.top();work_pq.pop();\n auto[x,y]=pos;\n inPQ[x][y]=false;\n if(dots[x][y])continue;\n if(findAndPlace(x,y))afterPlace(x,y);\n }\n \n // Fallback: full scan passes to catch missed positions\n {\n vector>> pts;\n for(int x=0;x\nusing namespace std;\ntypedef array,10> Grid;\n\nGrid applyTilt(Grid g, char dir) {\n if (dir=='L') { for(int i=0;i<10;i++){int p=0;for(int j=0;j<10;j++)if(g[i][j])g[i][p++]=g[i][j];for(;p<10;p++)g[i][p]=0;} }\n else if(dir=='R'){for(int i=0;i<10;i++){int p=9;for(int j=9;j>=0;j--)if(g[i][j])g[i][p--]=g[i][j];for(;p>=0;p--)g[i][p]=0;}}\n else if(dir=='F'){for(int j=0;j<10;j++){int p=0;for(int i=0;i<10;i++)if(g[i][j])g[p++][j]=g[i][j];for(;p<10;p++)g[p][j]=0;}}\n else{for(int j=0;j<10;j++){int p=9;for(int i=9;i>=0;i--)if(g[i][j])g[p--][j]=g[i][j];for(;p>=0;p--)g[p][j]=0;}}\n return g;\n}\nlong long computeScore(const Grid& g){\n bool vis[10][10]={};long long sum=0;int stk[100][2];\n static const int dx[]={-1,1,0,0},dy[]={0,0,-1,1};\n for(int si=0;si<10;si++)for(int sj=0;sj<10;sj++){\n if(!g[si][sj]||vis[si][sj])continue;\n int f=g[si][sj],sz=0,top=0;stk[top][0]=si;stk[top][1]=sj;top++;vis[si][sj]=true;\n while(top>0){--top;int x=stk[top][0],y=stk[top][1];sz++;\n for(int d=0;d<4;d++){int nx=x+dx[d],ny=y+dy[d];\n if(nx>=0&&nx<10&&ny>=0&&ny<10&&!vis[nx][ny]&&g[nx][ny]==f){vis[nx][ny]=true;stk[top][0]=nx;stk[top][1]=ny;top++;}}}\n sum+=(long long)sz*sz;}\n return sum;\n}\nGrid placeCandy(Grid g,int p,int flav){int cnt=0;for(int i=0;i<10;i++)for(int j=0;j<10;j++)if(!g[i][j]&&++cnt==p){g[i][j]=flav;return g;}return g;}\n\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n int fl[100];for(int t=0;t<100;t++)cin>>fl[t];\n Grid grid={};static const char dirs[]={'F','B','L','R'};\n for(int t=0;t<100;t++){\n int p;cin>>p;grid=placeCandy(grid,p,fl[t]);\n char bestDir='F';\n if(t<99){\n long long best=-1;int nc=99-t;\n for(char d1:dirs){\n Grid g1=applyTilt(grid,d1);long long tot=0;\n for(int p2=1;p2<=nc;p2++){\n Grid g2=placeCandy(g1,p2,fl[t+1]);long long mx=0;\n for(char d2:dirs){long long s=computeScore(applyTilt(g2,d2));if(s>mx)mx=s;}\n tot+=mx;}\n if(tot>best){best=tot;bestDir=d1;}}\n }\n cout<\n#include \nusing namespace std;\nusing namespace Eigen;\nint M, N;\ndouble eps;\nvector getDeg(const string& s, int n) {\n vector d(n,0); int idx=0;\n for(int i=0;i getEig(const string& s, int n) {\n MatrixXd A(n,n); A.setZero(); int idx=0;\n for(int i=0;i sol(A,EigenvaluesOnly);\n vector ev(n); for(int i=0;iint{if(a>b)swap(a,b);return a*(2*n-a-1)/2+(b-a-1);};\n int cnt=0;\n for(int d=1;d>M>>eps;\n N=4; while((long long)N*(N-1)/21e-9){\n double need=9.0*(double)(M-1)*(M-1)*eps*(1.0-eps);\n int N2=4; while((double)N2*(N2-1)/2 G(M);\n for(int k=0;k> C(M,vector(FD,0.0));\n if(eps<1e-9){\n for(int k=0;k u(0.0,1.0);\n for(int k=0;k>h;\n vector hf(FD); auto dh=getDeg(h,N); for(int i=0;i\nusing namespace std;\ntypedef long long ll;\ntypedef pair pli;\nconst ll INF=1e18;\nconst int MXN=1005,MXM=3005,MXD=35,MAXCP=10;\nint N,M,D,K,EU[MXM],EV[MXM];ll EW[MXM];\nvector> G[MXN];\nll gd[MXN][MXN];double imp[MXM];int aday[MXM];\ndouble ADJ[MXM][MXD];int cutD[MXM][MXD];\nvector ladj[MXM],cpairs[MXM],dayE[MXD];int dpos[MXM];\nuint64_t rs=0xdeadbeef123ULL;\nuint64_t rng(){rs^=rs<<13;rs^=rs>>7;rs^=rs<<17;return rs;}\nint ri(int n){return(int)(rng()%(unsigned)n);}\ndouble rd(){return(rng()>>11)*(1.0/(1ull<<53));}\nvoid dijk(int s){fill(gd[s]+1,gd[s]+N+1,INF);gd[s][s]=0;priority_queue,greater>pq;pq.push({0,s});while(!pq.empty()){auto[d,u]=pq.top();pq.pop();if(d>gd[s][u])continue;for(auto&[v,e]:G[u]){ll nd=d+EW[e];if(nd,greater>pq;pq.push({0,s});while(!pq.empty()){auto[dd,u]=pq.top();pq.pop();if(dd>d[u])continue;if(u==t)return d[t];for(auto&[v,e]:G[u]){if(e==sk)continue;ll nd=dd+EW[e];if(nd bstk;\nvoid findBr(int sk,vector&br){fill(bdt+1,bdt+N+1,-1);int tm=0;bstk.clear();if((int)bstk.capacity()bdt[p.u])br.push_back({pe,sz});}}}}\nbool cvis[MXN];int cq[MXN];\nint main(){\n ios_base::sync_with_stdio(0);cin.tie(0);auto tst=chrono::steady_clock::now();\n cin>>N>>M>>D>>K;for(int i=0;i>EU[i]>>EV[i]>>EW[i];G[EU[i]].push_back({EV[i],i});G[EV[i]].push_back({EU[i],i});}\n for(int i=1;i<=N;i++){int x,y;cin>>x>>y;}\n for(int s=1;s<=N;s++)dijk(s);\n {vectorpar(N+1,-1),sv(N);vectorsz(N+1,1);iota(sv.begin(),sv.end(),1);for(int s=1;s<=N;s++){fill(par.begin(),par.end(),-1);fill(sz.begin(),sz.end(),1LL);sort(sv.begin(),sv.end(),[s](int a,int b){return gd[s][a]=0;i--){int v=sv[i];if(par[v]<0)continue;int p=(EU[par[v]]==v)?EV[par[v]]:EU[par[v]];sz[p]+=sz[v];}for(int v:sv){if(par[v]<0)continue;imp[par[v]]+=(double)sz[v];}}}\n for(int e=0;ebr;for(int e=0;emin(b.sz,N-b.sz);});for(auto&bi:br){if((int)cpairs[e].size()>=MAXCP)break;auto it=lower_bound(cpairs[e].begin(),cpairs[e].end(),bi.e);if(it==cpairs[e].end()||*it!=bi.e)cpairs[e].insert(it,bi.e);}}}\n for(int u=1;u<=N;u++){int dg=G[u].size();for(int i=0;ieo(M);iota(eo.begin(),eo.end(),0);sort(eo.begin(),eo.end(),[](int a,int b){return imp[a]>imp[b];});for(int e:eo){int best=-1;double bs=1e18;int bc=INT_MAX;for(int d=0;d=K)continue;int cuts=0;for(int f:cpairs[e])if(aday[f]==d)cuts++;double cf=0;for(int e2:ladj[e])if(aday[e2]==d)cf+=imp[e2];double sc=cf+1e-12*dc[d];if(cuts0)continue;double dl=imp[e1]*(ADJ[e1][d2]-ADJ[e1][d1])+imp[e2]*(ADJ[e2][d1]-ADJ[e2][d2])-2.*isAdj(e1,e2)*imp[e1]*imp[e2];sm+=fabs(dl);c++;}if(c>0)T=sm/c;if(T<1e-9)T=1.0;}\n double T0=T;\n for(long long step=0;;step++){\n if(step%200000==0){double el=chrono::duration(chrono::steady_clock::now()-tst).count();if(el>5.3)break;T=T0*exp(-10.*el/5.3);}\n int d1=ri(D),d2=ri(D);if(d1==d2||dayE[d1].empty()||dayE[d2].empty())continue;\n int e1=dayE[d1][ri(dayE[d1].size())],e2=dayE[d2][ri(dayE[d2].size())];\n int ic=isCut(e1,e2)?1:0;\n double dl=imp[e1]*(ADJ[e1][d2]-ADJ[e1][d1])+imp[e2]*(ADJ[e2][d1]-ADJ[e2][d2])-2.*isAdj(e1,e2)*imp[e1]*imp[e2];\n int dlc=(cutD[e1][d2]-ic)+(cutD[e2][d1]-ic)-cutD[e1][d1]-cutD[e2][d2];\n double dtot=dl+BIG*dlc;\n if(dtot<=0||(T>1e-9&&rd()0){fill(cvis+1,cvis+N+1,false);int h=0,t=0;cvis[1]=true;cq[t++]=1;while(h=K)continue;for(int ef:ladj[e]){ADJ[ef][d]-=imp[e];ADJ[ef][dd]+=imp[e];}for(int f:cpairs[e]){cutD[f][d]--;cutD[f][dd]++;}int p=dpos[e],L=dayE[d].back();dayE[d][p]=L;dpos[L]=p;dayE[d].pop_back();dpos[e]=dayE[dd].size();dayE[dd].push_back(e);aday[e]=dd;fx=true;}}if(!fx)break;}}\n for(int i=0;i\nusing namespace std;\nint D;\nstring Fs[2][14],Rs[2][14];\nint bid,B[2][2744];bool occ[2][2744];\nbool boxFits(int r,int x0,int y0,int z0,int a,int b,int c){for(int i=0;i enumBoxes(int arr){\n vector boxes;uint16_t fz[14]={},rz[14]={};\n for(int z=0;z getRemLines(int arr,int ax){\n vectorL;\n if(ax==0){for(int y=0;y=0){L.push_back({s,y,z,x-s,0});s=-1;}}}}\n else if(ax==1){for(int x=0;x=0){L.push_back({x,s,z,y-s,1});s=-1;}}}}\n else{for(int x=0;x=0){L.push_back({x,y,s,z-s,2});s=-1;}}}}\n return L;}\ndouble matchScore(const vector&L0,const vector&L1){\n mapc0,c1;for(auto&l:L0)c0[l.len]++;for(auto&l:L1)c1[l.len]++;\n double sc=0;int v0=0,v1=0;\n for(auto&[l,c]:c0){int cl=c1.count(l)?c1[l]:0;int mc=min(c,cl);sc+=mc*1.0/l;v0+=(c-mc)*l;}\n for(auto&[l,c]:c1){int cl=c0.count(l)?c0[l]:0;if(c>cl)v1+=(c-cl)*l;}\n sc+=max(v0,v1);return sc;}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>D;for(int i=0;i<2;i++){for(int z=0;z>Fs[i][z];for(int z=0;z>Rs[i][z];}\n memset(B,0,sizeof(B));memset(occ,0,sizeof(occ));bid=0;\n auto bx0=enumBoxes(0),bx1=enumBoxes(1);\n typedef array Key;\n auto gk=[](const Box&bx)->Key{Key k={bx.a,bx.b,bx.c};sort(k.begin(),k.end());return k;};\n map>g0,g1;\n for(int i=0;i<(int)bx0.size();i++)g0[gk(bx0[i])].push_back(i);\n for(int i=0;i<(int)bx1.size();i++)g1[gk(bx1[i])].push_back(i);\n vector>grps;\n for(auto&[k,v]:g0)if(g1.count(k))grps.push_back({k[0]*k[1]*k[2],k});\n sort(grps.rbegin(),grps.rend());\n for(auto&[vol,key]:grps){\n auto&v0=g0[key];auto&v1=g1[key];int p1=0;\n for(int i0:v0){\n auto&B0=bx0[i0];if(!boxFits(0,B0.x,B0.y,B0.z,B0.a,B0.b,B0.c))continue;\n while(p1<(int)v1.size()&&!boxFits(1,bx1[v1[p1]].x,bx1[v1[p1]].y,bx1[v1[p1]].z,bx1[v1[p1]].a,bx1[v1[p1]].b,bx1[v1[p1]].c))p1++;\n if(p1>=(int)v1.size())break;\n auto&B1=bx1[v1[p1++]];bid++;\n fillBox(0,B0.x,B0.y,B0.z,B0.a,B0.b,B0.c,bid);fillBox(1,B1.x,B1.y,B1.z,B1.a,B1.b,B1.c,bid);}}\n int bax0=1,bax1=1;double bsc=1e18;\n for(int ax0=0;ax0<3;ax0++){auto Lt0=getRemLines(0,ax0);for(int ax1=0;ax1<3;ax1++){auto Lt1=getRemLines(1,ax1);double sc=matchScore(Lt0,Lt1);if(sc>gl0,gl1;\n for(int i=0;i<(int)L0.size();i++)gl0[L0[i].len].push_back(i);\n for(int i=0;i<(int)L1.size();i++)gl1[L1[i].len].push_back(i);\n vectorlu0(L0.size(),false),lu1(L1.size(),false);\n for(auto&[l,v0]:gl0){auto it=gl1.find(l);if(it==gl1.end())continue;auto&v1=it->second;int mc=min((int)v0.size(),(int)v1.size());for(int j=0;j>rv0,rv1;\n for(int i=0;i<(int)L0.size();i++)if(!lu0[i])rv0.push_back({L0[i].len,i});\n for(int i=0;i<(int)L1.size();i++)if(!lu1[i])rv1.push_back({L1[i].len,i});\n sort(rv0.rbegin(),rv0.rend());sort(rv1.begin(),rv1.end());\n struct SO{int idx,off;};dequer0,r1;\n for(auto&[l,i]:rv0)r0.push_back({i,0});for(auto&[l,i]:rv1)r1.push_back({i,0});\n auto gpos=[&](const Line&s,int off)->tuple{return{s.x+(s.ax==0?off:0),s.y+(s.ax==1?off:0),s.z+(s.ax==2?off:0)};};\n while(!r0.empty()&&!r1.empty()){\n auto&[i0,o0]=r0.front();auto&[i1,o1]=r1.front();\n int ml=min(L0[i0].len-o0,L1[i1].len-o1);bid++;\n auto[x0,y0,z0]=gpos(L0[i0],o0);auto[x1,y1,z1]=gpos(L1[i1],o1);\n fillLine(0,x0,y0,z0,ml,L0[i0].ax,bid);fillLine(1,x1,y1,z1,ml,L1[i1].ax,bid);\n o0+=ml;o1+=ml;if(o0==L0[i0].len)r0.pop_front();if(o1==L1[i1].len)r1.pop_front();}\n while(!r0.empty()){auto[i0,o0]=r0.front();r0.pop_front();bid++;auto[x,y,z]=gpos(L0[i0],o0);fillLine(0,x,y,z,L0[i0].len-o0,L0[i0].ax,bid);}\n while(!r1.empty()){auto[i1,o1]=r1.front();r1.pop_front();bid++;auto[x,y,z]=gpos(L1[i1],o1);fillLine(1,x,y,z,L1[i1].len-o1,L1[i1].ax,bid);}\n cout<\nusing namespace std;\ntypedef long long ll;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n int N, M, K;\n cin >> N >> M >> K;\n vector X(N), Y(N);\n for (int i = 0; i < N; i++) cin >> X[i] >> Y[i];\n vector EU(M), EV(M); vector EW(M);\n for (int j = 0; j < M; j++) { cin >> EU[j] >> EV[j] >> EW[j]; EU[j]--; EV[j]--; }\n vector A(K), B(K);\n for (int k = 0; k < K; k++) cin >> A[k] >> B[k];\n const ll MAXP = 5000, MAXP2 = MAXP*MAXP, INF = (ll)4e18;\n vector> D2(N, vector(K));\n for (int i = 0; i < N; i++)\n for (int k = 0; k < K; k++) { ll dx=A[k]-X[i],dy=B[k]-Y[i]; D2[i][k]=dx*dx+dy*dy; }\n vector>> adj(N);\n for (int j = 0; j < M; j++) { adj[EU[j]].push_back({EV[j],j}); adj[EV[j]].push_back({EU[j],j}); }\n auto pVal = [&](ll d2) -> ll {\n if (!d2) return 0; ll p=(ll)sqrt((double)d2); while(p*p> spD(N, vector(N, INF));\n vector> spE(N, vector(N,-1)), spPr(N, vector(N,-1));\n for (int s = 0; s < N; s++) {\n spD[s][s]=0;\n priority_queue,vector>,greater<>> pq; pq.push({0,s});\n while (!pq.empty()) {\n auto [d,v]=pq.top(); pq.pop(); if(d>spD[s][v]) continue;\n for (auto& [u,j]:adj[v]) { ll nd=d+EW[j]; if(nd term) -> vector {\n term[0]=true; vector T; for(int i=0;i in(TN,false); vector key(TN,INF); vector par(TN,-1); key[0]=0;\n for (int it=0;it=INF) break; in[u]=true;\n for(int w=0;w eo(M,false);\n for(int i=0;i& reach) -> pair,ll> {\n vector> vR(N); vector vMx(N,0);\n for (int k=0;kMAXP2) return {{},INF};\n vR[bv].push_back(k); vMx[bv]=max(vMx[bv],best);\n }\n vector Pv(N,0); for(int i=0;imxD2u){mxD2u=D2[u][k];kFar=k;}\n ll secMx=0;\n for(int k:vR[u]) if(k!=kFar&&D2[u][k]>secMx) secMx=D2[u][k];\n ll newPu=pVal(secMx); if(newPu==Pv[u]) continue;\n ll bDelta=0; int bV=-1;\n for(int v=0;vMAXP2) continue;\n ll newMxv=max(vMx[v],dkv), newPv=pVal(newMxv);\n ll delta=newPu*newPu+newPv*newPv-Pv[u]*Pv[u]-Pv[v]*Pv[v];\n if(delta=0){\n auto& ru=vR[u]; ru.erase(find(ru.begin(),ru.end(),kFar));\n vMx[u]=secMx; Pv[u]=newPu;\n vR[bV].push_back(kFar);\n vMx[bV]=max(vMx[bV],D2[bV][kFar]); Pv[bV]=pVal(vMx[bV]);\n imp=true;\n }\n }\n }\n vector P(N,0); ll pc=0;\n for(int i=0;i& eo) -> tuple,ll,bool> {\n vector reach(N,false); queue q; q.push(0); reach[0]=true;\n while(!q.empty()){int v=q.front();q.pop();for(auto&[u,j]:adj[v])if(eo[j]&&!reach[u]){reach[u]=true;q.push(u);}}\n ll ec=0; for(int j=0;j mstPar(N,-1),mstPE(N,-1); vector> mstCh(N);\n {\n vector vis(N,false); vector key(N,INF); key[0]=0;\n priority_queue,vector>,greater<>> pq; pq.push({0,0});\n while(!pq.empty()){auto[d,v]=pq.top();pq.pop();if(vis[v])continue;vis[v]=true;for(auto&[u,j]:adj[v])if(!vis[u]&&EW[j] act(N,true); vector> vRes(N); vector vmx(N,0),Pv(N,0);\n for(int k=0;k> bAs; vector> bAf;\n for(int v=1;v tmp; vector> ta; bool ok=true;\n for(int k:vRes[v]){\n ll best=INF;int bu=-1;for(int u=0;uMAXP2){ok=false;break;}\n ta.push_back({k,bu}); if(!tmp.count(bu))tmp[bu]=vmx[bu]; tmp[bu]=max(tmp[bu],best);\n }\n if(!ok) continue;\n for(auto&[u,nd]:tmp){ll np=pVal(nd);delta+=np*np-Pv[u]*Pv[u];}\n if(delta=0){\n act[bV]=false;ec0-=EW[mstPE[bV]];pc0-=Pv[bV]*Pv[bV];Pv[bV]=0;vmx[bV]=0;vRes[bV].clear();\n for(auto&[k,u]:bAs)vRes[u].push_back(k);\n for(auto&[u,nd]:bAf){pc0-=Pv[u]*Pv[u];vmx[u]=nd;Pv[u]=pVal(nd);pc0+=Pv[u]*Pv[u];}\n imp=true;\n }\n }\n ll bestCost=INF; vector bestEO(M,false); vector bestP(N,0);\n auto updateBest=[&](const vector&eo,const vector&P,ll cost){if(cost eo(M,false); for(int v=1;v term){\n term[0]=true;\n for(int sit=0;sit<15;sit++){\n auto eo=buildSteiner(term);\n auto[sp,sc,sf]=evalEO(eo); if(!sf) break;\n updateBest(eo,sp,sc);\n vector nt(N,false); nt[0]=true;\n for(int i=0;i0) nt[i]=true;\n if(nt==term) break; term=nt;\n }\n };\n {vector t(N,false);for(int i=0;i0)t[i]=true;runSteiner(t);}\n {vector t(N,true);runSteiner(t);}\n for(int i=0;i\nusing namespace std;\n\nconst int N = 30;\nint board[N][N];\nvector> ops;\n\nvoid do_swap(int x1, int y1, int x2, int y2) {\n swap(board[x1][y1], board[x2][y2]);\n ops.push_back({x1, y1, x2, y2});\n}\n\nvoid sift_down(int x, int y) {\n while (x < N-1) {\n int ny = (board[x+1][y] <= board[x+1][y+1]) ? y : y+1;\n if (board[x][y] <= board[x+1][ny]) break;\n do_swap(x, y, x+1, ny);\n y = ny;\n x++;\n }\n}\n\nint main() {\n ios::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 >> board[x][y];\n \n // Bottom-up heapify: one pass is sufficient to produce a valid heap\n for (int x = N-2; x >= 0; x--)\n for (int y = 0; y <= x; y++)\n sift_down(x, y);\n \n cout << ops.size() << \"\\n\";\n for (auto& op : ops)\n cout << op[0] << \" \" << op[1] << \" \" << op[2] << \" \" << op[3] << \"\\n\";\n}","toyota2023summer-final":"#include \nusing namespace std;\nconst int D9=9;\nint D,N,M;\nbool obs[D9][D9],hasc[D9][D9];\nint cnum[D9][D9],sr[D9*D9],sc[D9*D9],prank[D9][D9];\nint er,ec;\nconst int dr[4]={-1,1,0,0},dc[4]={0,0,-1,1};\nbool in_(int r,int c){return r>=0&&r=0&&c>q;q.push({er,ec});dist[er][ec]=0;\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+dr[i],ny=y+dc[i];if(!in_(nx,ny)||dist[nx][ny]>=0||obs[nx][ny])continue;dist[nx][ny]=dist[x][y]+1;q.push({nx,ny});}}\n vector>pos;\n for(int r=0;r&a,const pair&b){if(dist[a.first][a.second]!=dist[b.first][b.second])return dist[a.first][a.second]>q;q.push({er,ec});vis[er][ec]=1;\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+dr[i],ny=y+dc[i];if(!in_(nx,ny)||vis[nx][ny]||obs[nx][ny]||hasc[nx][ny])continue;vis[nx][ny]=1;q.push({nx,ny});}}\n}\nbool safe_place(int r,int c,const vector>&reach){\n bool vis[D9][D9];memset(vis,0,sizeof vis);\n queue>q;q.push({er,ec});vis[er][ec]=1;\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+dr[i],ny=y+dc[i];if(!in_(nx,ny)||vis[nx][ny]||obs[nx][ny]||hasc[nx][ny])continue;if(nx==r&&ny==c)continue;vis[nx][ny]=1;q.push({nx,ny});}}\n for(auto[pr,pc]:reach){if(pr==r&&pc==c)continue;if(!vis[pr][pc])return false;}\n return true;\n}\npairpick_place(int t){\n bool vis[D9][D9];bfs_emp(vis);\n int ir=sr[t],ic=sc[t];\n vector>reach;\n for(int r=0;rbest{-1,-1};int bd=INT_MAX,brk=-1;bool gots=false;\n for(auto[r,c]:reach){\n if(r==ir&&c==ic)continue;\n bool s=safe_place(r,c,reach);\n int d=abs(prank[r][c]-t),rk=prank[r][c];\n bool better=(!gots&&s)||(gots==s&&(dbrk)));\n if(better){best={r,c};bd=d;brk=rk;gots=s;}\n }\n return best;\n}\nvector>transport(){\n bool h[D9][D9];memcpy(h,hasc,sizeof h);\n vector>ord;ord.reserve(M);\n for(int s=0;s>q;q.push({er,ec});vis[er][ec]=1;\n int bn=INT_MAX,br=-1,bc=-1;\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+dr[i],ny=y+dc[i];if(!in_(nx,ny)||vis[nx][ny]||obs[nx][ny])continue;vis[nx][ny]=1;if(h[nx][ny]){if(cnum[nx][ny]>D>>N;\n memset(obs,0,sizeof obs);memset(hasc,0,sizeof hasc);memset(cnum,-1,sizeof cnum);\n er=0;ec=(D-1)/2;\n for(int i=0;i>r>>c;obs[r][c]=1;}\n build_sigma();\n for(int d=0;d>t;\n auto[r,c]=pick_place(t);\n hasc[r][c]=1;cnum[r][c]=t;\n cout<\nusing namespace std;\nint n,m,g[50][50];\nbool adj[102][102];\nint acnt[102][102],ccnt[102],dep[102];\nconst int dr[]={0,0,1,-1},dc[]={1,-1,0,0};\nint gc(int r,int c){return(r<0||r>=n||c<0||c>=n)?0:g[r][c];}\nvoid compute_adj(){memset(adj,0,sizeof(adj));for(int i=0;iq;for(int c=0;c<=m;c++)if(adj[c][0]){dep[c]=0;q.push(c);}dep[0]=0;while(!q.empty()){int u=q.front();q.pop();for(int v=1;v<=m;v++)if(adj[u][v]&&dep[v]>dep[u]+1){dep[v]=dep[u]+1;q.push(v);}}}\nvoid recompute(){memset(acnt,0,sizeof(acnt));memset(ccnt,0,sizeof(ccnt));for(int i=0;i>q;q.push({sr,sc});vis[sr][sc]=1;int cnt=1;while(!q.empty()){auto[cr,cc]=q.front();q.pop();for(int d=0;d<4;d++){int nr=cr+dr[d],nc=cc+dc[d];if(nr>=0&&nr=0&&nc=0&&nr=0&&nc=n||nc<0||nc>=n)continue;int ncol=g[nr][nc];if(!ncol)continue;bool hz=0;for(int d2=0;d2<4;d2++){int nr2=nr+dr[d2],nc2=nc+dc[d2];if(nr2==r&&nc2==c)continue;if(nr2<0||nr2>=n||nc2<0||nc2>=n){hz=1;break;}if(!g[nr2][nc2]){hz=1;break;}}if(!hz)acnt[ncol][0]++;if(ncol==col)continue;bool sc2=0;for(int d2=0;d2<4;d2++){int nr2=nr+dr[d2],nc2=nc+dc[d2];if(nr2==r&&nc2==c)continue;if(nr2>=0&&nr2=0&&nc2=n||nc<0||nc>=n)continue;int c2=g[nr][nc];if(!c2||c2==col||dep[c2]>=dep[col])continue;bool ok=1;for(int d2=0;d2<4;d2++){int dc2=gc(r+dr[d2],c+dc[d2]);if(dc2&&dc2!=col&&dc2!=c2&&!adj[c2][dc2]){ok=0;break;}}if(!ok)continue;if(!conn_ok(r,c,col))continue;ok=1;for(int d2=0;d2<4;d2++){int dc2=gc(r+dr[d2],c+dc[d2]);if(dc2&&dc2!=col&&dc2!=c2&&acnt[col][dc2]<=1){ok=0;break;}}if(!ok)continue;co=c2;return 1;}return 0;}\nint main(){\n ios_base::sync_with_stdio(0);cin.tie(0);\n cin>>n>>m;\n for(int i=0;i>g[i][j];\n compute_adj();compute_depth();recompute();\n greedy_trim();\n bool global=1;\n while(global){\n global=0;bool ch=1;\n while(ch){ch=0;for(int i=0;i\nusing namespace std;\n\nint N, D, Q, q_used = 0;\n\nchar bq(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 q_used++;\n char c; cin >> c; return c;\n}\n\nint slm;\nvector ms(vector a) {\n if ((int)a.size() <= 1 || q_used >= slm) return a;\n int m = a.size() / 2;\n auto L = ms(vector(a.begin(), a.begin() + m));\n auto R = ms(vector(a.begin() + m, a.end()));\n vector r; int i = 0, j = 0;\n while (i < (int)L.size() && j < (int)R.size()) {\n if (q_used >= slm) break;\n if (bq({L[i]}, {R[j]}) != '>') r.push_back(L[i++]);\n else r.push_back(R[j++]);\n }\n while (i < (int)L.size()) r.push_back(L[i++]);\n while (j < (int)R.size()) r.push_back(R[j++]);\n return r;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> D >> Q;\n\n auto t0 = chrono::high_resolution_clock::now();\n auto el = [&]() {\n return chrono::duration(chrono::high_resolution_clock::now() - t0).count();\n };\n\n // Phase 1: Sort\n slm = Q / 2;\n vector ini(N); iota(ini.begin(), ini.end(), 0);\n vector ord = ms(ini);\n\n vector pos(N);\n for (int i = 0; i < N; i++) pos[ord[i]] = i;\n\n // Phase 2: Weight estimation via binary search on prefix sums\n int est_end = Q * 4 / 5;\n vector w(N, 1.0), ps(N + 1, 0.0);\n w[ord[0]] = 1.0; ps[1] = 1.0;\n\n for (int i = 1; i < N; i++) {\n int lo = 0, hi = i;\n while (lo < hi && q_used < est_end) {\n int mid = (lo + hi) / 2;\n if (bq({ord[i]}, vector(ord.begin(), ord.begin() + mid + 1)) == '>')\n lo = mid + 1;\n else hi = mid;\n }\n double wlo = ps[lo];\n double whi = (lo < i) ? ps[lo + 1] : ps[i] * 2.0;\n w[ord[i]] = max(w[ord[i-1]], (wlo + whi) / 2.0);\n ps[i+1] = ps[i] + w[ord[i]];\n }\n\n // Phase 3: LPT partition\n vector oi(N); iota(oi.begin(), oi.end(), 0);\n sort(oi.begin(), oi.end(), [&](int a, int b) {\n if (fabs(w[a]-w[b]) > 1e-12) return w[a] > w[b];\n return pos[a] > pos[b];\n });\n vector gw(D, 0.0);\n vector asgn(N, 0);\n for (int x : oi) {\n int g = (int)(min_element(gw.begin(), gw.end()) - gw.begin());\n asgn[x] = g; gw[g] += w[x];\n }\n\n // Phase 4: Local search with estimated weights\n double total = 0; for (double x : gw) total += x;\n double mean = total / D;\n\n for (int p = 0; p < 5000 && el() < 1.5; p++) {\n bool imp = false;\n // Single moves\n for (int x = 0; x < N; x++) {\n int g0 = asgn[x]; int bg = g0; double bd = 0;\n double d0 = gw[g0] - mean;\n for (int g = 0; g < D; g++) {\n if (g == g0) continue;\n double d1 = gw[g] - mean;\n double dc = d0*d0 + d1*d1 - (d0-w[x])*(d0-w[x]) - (d1+w[x])*(d1+w[x]);\n if (dc > bd) { bd = dc; bg = g; }\n }\n if (bg != g0) { gw[g0] -= w[x]; gw[bg] += w[x]; asgn[x] = bg; imp = true; }\n }\n // Swaps\n for (int i = 0; i < N && el() < 1.4; i++) {\n for (int j = i+1; j < N; j++) {\n if (asgn[i] == asgn[j]) continue;\n int gi = asgn[i], gj = asgn[j];\n double di = gw[gi]-mean, dj = gw[gj]-mean;\n double di2 = di-w[i]+w[j], dj2 = dj+w[i]-w[j];\n if (di*di + dj*dj > di2*di2 + dj2*dj2 + 1e-9) {\n gw[gi] += w[j]-w[i]; gw[gj] += w[i]-w[j];\n asgn[i] = gj; asgn[j] = gi; imp = true;\n }\n }\n }\n if (!imp) break;\n }\n\n // Phase 5: Actual balance improvement using remaining queries\n vector> gi(D);\n for (int x = 0; x < N; x++) gi[asgn[x]].push_back(x);\n for (int g = 0; g < D; g++)\n sort(gi[g].begin(), gi[g].end(), [&](int a, int b){ return pos[a] < pos[b]; });\n\n while (q_used + 2 <= Q && el() < 1.9) {\n int gh = (int)(max_element(gw.begin(), gw.end()) - gw.begin());\n int gl = (int)(min_element(gw.begin(), gw.end()) - gw.begin());\n if (gw[gh] <= gw[gl] + 1e-9 || gi[gh].empty() || gi[gl].empty()) break;\n\n char cmp = bq(gi[gh], gi[gl]);\n if (cmp == '=') { gw[gh] = gw[gl] = (gw[gh]+gw[gl])/2; continue; }\n if (cmp == '<') { swap(gh, gl); swap(gw[gh], gw[gl]); }\n\n auto& hv = gi[gh]; auto& lt = gi[gl];\n if ((int)hv.size() <= 1) continue;\n\n int lo = 0, hi = (int)hv.size() - 1;\n while (lo < hi && q_used + 1 <= Q && el() < 1.85) {\n int mid = (lo + hi) / 2;\n vector L2, R2 = lt;\n for (int k = 0; k < (int)hv.size(); k++) if (k != mid) L2.push_back(hv[k]);\n R2.push_back(hv[mid]);\n char r = bq(L2, R2);\n if (r == '=') { lo = hi = mid; break; }\n else if (r == '>') lo = mid + 1;\n else hi = mid;\n }\n lo = min(lo, (int)hv.size() - 1);\n if (lo > 0) {\n double da = fabs((gw[gh]-w[hv[lo]]) - (gw[gl]+w[hv[lo]]));\n double db = fabs((gw[gh]-w[hv[lo-1]]) - (gw[gl]+w[hv[lo-1]]));\n if (db < da) lo--;\n }\n\n int mv = hv[lo];\n asgn[mv] = gl;\n gw[gh] -= w[mv]; gw[gl] += w[mv];\n hv.erase(hv.begin() + lo);\n lt.insert(lower_bound(lt.begin(), lt.end(), mv,\n [&](int a, int b){ return pos[a] < pos[b]; }), mv);\n }\n\n while (q_used < Q) bq({0}, {1});\n\n for (int i = 0; i < N; i++) cout << asgn[i] << \" \\n\"[i==N-1];\n cout.flush();\n return 0;\n}","ahc026":"#include \nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n \n int n, m;\n cin >> n >> m;\n \n vector> stacks(m);\n vector stk(n + 1), pidx(n + 1);\n vector stack_min(m, n + 1);\n \n int h = n / m;\n for (int i = 0; i < m; i++) {\n stacks[i].resize(h);\n for (int j = 0; j < h; j++) {\n cin >> stacks[i][j];\n stk[stacks[i][j]] = i;\n pidx[stacks[i][j]] = j;\n }\n stack_min[i] = *min_element(stacks[i].begin(), stacks[i].end());\n }\n \n vector> ops;\n \n auto recompute_min = [&](int t) {\n stack_min[t] = stacks[t].empty() ? (n + 1) : *min_element(stacks[t].begin(), stacks[t].end());\n };\n \n for (int v = 1; v <= n; v++) {\n int s = stk[v];\n int j = pidx[v];\n \n while ((int)stacks[s].size() > j + 1) {\n int top_pos = (int)stacks[s].size() - 1;\n int run_start = top_pos;\n while (run_start > j + 1 && stacks[s][run_start - 1] > stacks[s][run_start])\n run_start--;\n \n int u1 = stacks[s][run_start];\n long long best_score = LLONG_MIN;\n int best_t = -1;\n \n for (int t = 0; t < m; t++) {\n if (t == s) continue;\n long long score;\n if (stacks[t].empty()) {\n score = 2LL * n * n;\n } else {\n int top_t = stacks[t].back();\n int min_t = stack_min[t];\n if (top_t > u1) {\n if (min_t > u1)\n score = 3LL * n * n + (n - top_t); // Perfect: patience sort tiebreak\n else\n score = 1LL * n * n + min_t; // Good valid: prefer large min_t\n } else {\n score = (long long)min_t - n * n; // Invalid: prefer large min_t\n }\n }\n if (score > best_score) { best_score = score; best_t = t; }\n }\n \n int move_box = stacks[s][run_start];\n int new_base = (int)stacks[best_t].size();\n int old_size_s = (int)stacks[s].size();\n \n ops.push_back({move_box, best_t + 1});\n \n for (int p = run_start; p < old_size_s; p++) {\n int b = stacks[s][p];\n stacks[best_t].push_back(b);\n stk[b] = best_t;\n pidx[b] = new_base + (p - run_start);\n stack_min[best_t] = min(stack_min[best_t], b);\n }\n stacks[s].resize(run_start);\n recompute_min(s);\n }\n \n ops.push_back({v, 0});\n stacks[s].pop_back();\n recompute_min(s);\n }\n \n for (auto& [v, i] : ops)\n cout << v << \" \" << i << \"\\n\";\n \n return 0;\n}","ahc027":"#include \nusing namespace std;\nconst int MAXN=41,MAXC=1601,BUD=100000;\nint N,n;bool hw[MAXN][MAXN],vw[MAXN][MAXN];int dv[MAXN][MAXN];\nconst int DI[]={0,1,0,-1},DJ[]={1,0,-1,0};const char DC[]=\"RDLU\";\nint C(int i,int j){return i*N+j;}int RI(int c){return c/N;}int RJ(int c){return c%N;}\nbool OK(int i,int j,int d){int ni=i+DI[d],nj=j+DJ[d];if(ni<0||ni>=N||nj<0||nj>=N)return false;if(d==0)return !vw[i][j];if(d==1)return !hw[i][j];if(d==2)return !vw[i][nj];return !hw[ni][j];}\nshort AP[MAXC][MAXC];int AF[MAXC][MAXC];\nvoid bfs(int s){memset(AP[s],0xFF,n*sizeof(short));int fs[MAXC];AP[s][s]=0;fs[s]=s;static int q[MAXC];int h=0,tail=0;q[tail++]=s;while(h>N;n=N*N;\n for(int i=0;i>s;for(int j=0;j>s;for(int j=0;j>dv[i][j];\n for(int s=0;s lv(n,0);int pos=0,t=0;\n {vector vis(n,false);vis[0]=true;vector> stk;stk.reserve(n);stk.push_back({0,0});\n while(!stk.empty()){int u=stk.back().first;int& nd=stk.back().second;bool found=false;\n while(nd<4){int d=nd++;if(OK(RI(u),RJ(u),d)){int v=C(RI(u)+DI[d],RJ(u)+DJ[d]);if(!vis[v]){route+=DC[d];t++;pos=v;lv[v]=t;vis[v]=true;stk.push_back({v,0});found=true;break;}}}\n if(!found){stk.pop_back();if(!stk.empty()){int par=stk.back().first;for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==par){route+=DC[d];t++;pos=par;lv[par]=t;break;}}}}}\n for(int c=0;cBUD)rrt=true;\n if(rrt){const short* Ap=AP[pos];int best=-1;float bu=0.0f;\n for(int c=0;cBUD)continue;\n float u=sqd[c]*(float)(t-lv[c]+1)/(float)(dc+1);if(u>bu){bu=u;best=c;}}\n committed=best;if(committed<0)break;}\n int nx=AF[pos][committed];bool moved=false;\n for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==nx){route+=DC[d];pos=nx;t++;lv[pos]=t;moved=true;break;}\n if(!moved)break;}\n while(pos!=0){int nx=AF[pos][0];for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==nx){route+=DC[d];pos=nx;t++;break;}}\n cout<\nusing namespace std;\nint N, M, si, sj;\nvector targets;\nvector> charPos[26];\nint ovM[200][200];\nvoid computeOvMatrix() {\n for(int i=0;i=1;k--){bool ok=true;for(int l=0;l greedyPerm(int start){\n vector used(M,false);vector perm;perm.reserve(M);perm.push_back(start);used[start]=true;\n while((int)perm.size()bov){bov=ovM[last][j];best=j;}perm.push_back(best);used[best]=true;}\n return perm;\n}\nint permOv(const vector&p){int s=0;for(int i=1;i<(int)p.size();i++)s+=ovM[p[i-1]][p[i]];return s;}\nint swapGain(const vector&perm,int i,int j){\n int m=perm.size(),a=perm[i],b=perm[j],og=0,ng=0;\n if(i>0){og+=ovM[perm[i-1]][a];ng+=ovM[perm[i-1]][b];}\n if(j0){og+=ovM[perm[j-1]][b];ng+=ovM[perm[j-1]][a];}}\n return ng-og;\n}\nbool swapOpt(vector&perm){int m=perm.size(),bg=0,bi=-1,bj=-1;for(int i=0;ibg){bg=g;bi=i;bj=j;}}if(bi==-1)return false;swap(perm[bi],perm[bj]);return true;}\nbool orOpt(vector&perm){\n int m=perm.size(),bg=0,bk=-1,bp=-1;\n for(int k=0;k rest;rest.reserve(m-1);for(int i=0;i0)?ovM[perm[k-1]][e]:0,ro=(k0&&k0)?ovM[rest[p-1]][e]:0,nr=(p<(int)rest.size())?ovM[e][rest[p]]:0,nb=(p>0&&p<(int)rest.size())?ovM[rest[p-1]][rest[p]]:0,g=nl+nr-nb-rc;if(g>bg){bg=g;bk=k;bp=p;}}}\n if(bk==-1)return false;\n int e=perm[bk];vector rest;rest.reserve(m-1);for(int i=0;i&perm){\n int m=perm.size();if(m<2)return false;\n vector diff(m-1),pref(m,0);\n for(int k=0;k0)g+=ovM[perm[i-1]][perm[j]]-ovM[perm[i-1]][perm[i]];if(jbg){bg=g;bi=i;bj=j;}}\n if(bi==-1)return false;reverse(perm.begin()+bi,perm.begin()+bj+1);return true;\n}\nvoid localSearch(vector&perm){bool imp=true;while(imp){imp=false;if(swapOpt(perm))imp=true;if(orOpt(perm))imp=true;if(reverseOpt(perm))imp=true;}}\nstring buildString(const vector&perm){string s=targets[perm[0]];for(int i=1;i<(int)perm.size();i++)s+=targets[perm[i]].substr(ovM[perm[i-1]][perm[i]]);return s;}\nvector> findPath(const string&s){\n int L=s.size(),G=N*N;const int INF=1e9;\n vector dp((L+1)*G,INF),prv((L+1)*G,-1);\n dp[si*N+sj]=0;\n for(int i=0;i> path(L);int pos=bp;\n for(int i=L;i>=1;i--){path[i-1]={pos/N,pos%N};pos=prv[i*G+pos];}\n return path;\n}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n auto t0=chrono::steady_clock::now();\n auto ms_el=[&](){return chrono::duration_cast(chrono::steady_clock::now()-t0).count();};\n cin>>N>>M>>si>>sj;\n for(int i=0;i>row;for(int j=0;j>targets[i];\n computeOvMatrix();\n vector best;int bestOv=-1;\n for(int s=0;sbestOv){bestOv=o;best=p;}}\n localSearch(best);bestOv=permOv(best);\n {\n mt19937 rng(42);uniform_real_distribution ud(0.0,1.0);\n vector cur=best;int curOv=bestOv;double T=2.0;\n for(long long it=0;;it++){\n if(it%50000==0&&ms_el()>=1700)break;\n T=max(0.05,T*0.9999998);\n int i=rng()%M,j=rng()%M;if(i==j)continue;if(i>j)swap(i,j);\n int gain=swapGain(cur,i,j);\n if(gain>0||ud(rng)bestOv){bestOv=curOv;best=cur;}}\n }\n }\n if(ms_el()<1850)localSearch(best);\n string ss=buildString(best);\n auto path=findPath(ss);\n for(auto&[r,c]:path)cout<\nusing namespace std;\nint N,M,MAX_OPS;double eps,coef;int ops=0;\nstruct Field{int d,hi,hj;vector>cells;vectorrp,cp;vector>pos;};\nvectorF;vector>drld;vector>prob,ell;\nvectorrobs,cobs;int nrr=0,nrc=0;\ndouble qdiv(const vector>&c){ops++;cout<<\"q \"<>v;return v;}\nint qdrl(int i,int j){ops++;cout<<\"q 1 \"<>v;drld[i][j]=v;return v;}\nbool qans(const vector>&o){ops++;cout<<\"a \"<>r;return r==1;}\nvoid do_row_col(int reps){for(int rep=0;rep>c;for(int j=0;j>c;for(int i=0;itmr(N,0),tmc(N,0);\n for(int k=0;kkmr(N,0),kmc(N,0);\n for(int p=0;p>drow(N,vector(F[k].hi+1)),dcol(N,vector(F[k].hj+1));\n for(int i=0;ill(np,-1e300);double mx=-1e300;\n for(int p=0;p-1e250)?exp(ll[p]-mx):0.0;s+=prob[k][p];}\n if(s>1e-15)for(int p=0;p1e-15){for(auto&pp:prob[k])pp/=s;}\n else{int cnt=0;for(int p=0;p-1e29)cnt++;\n for(int p=0;p-1e29&&cnt>0)?1.0/cnt:0;\n if(cnt==0){fill(ell[k].begin(),ell[k].end(),0);fill(prob[k].begin(),prob[k].end(),1.0/np);}}}\n }\n}\ndouble field_entropy(int k){double H=0;for(double p:prob[k])if(p>1e-12)H-=p*log(p);return H;}\nvoid do_shape_query(int k){\n if(ops>=MAX_OPS-5)return;int np=(int)F[k].pos.size();\n int p1=-1,p2=-1;for(int p=0;pprob[k][p1]){p2=p1;p1=p;}else if(p2<0||prob[k][p]>prob[k][p2])p2=p;}\n if(p1<0||prob[k][p1]>0.98)return;\n auto[di1,dj1]=F[k].pos[p1];\n vector>S;\n if(p2>=0){auto[di2,dj2]=F[k].pos[p2];set>c2;for(auto[ci,cj]:F[k].cells)c2.insert({di2+ci,dj2+cj});for(auto[ci,cj]:F[k].cells){pairc={di1+ci,dj1+cj};if(!c2.count(c))S.push_back(c);}if((int)S.size()<2){S.clear();for(auto[ci,cj]:F[k].cells)S.push_back({di1+ci,dj1+cj});}}\n else{for(auto[ci,cj]:F[k].cells)S.push_back({di1+ci,dj1+cj});}\n if((int)S.size()<2)return;\n vectorSmap(N*N,false);for(auto[i,j]:S)Smap[i*N+j]=true;\n vectorovl(np,0);for(int p=0;p-1e29)for(int p=0;p-1e29)ell[k][p]-=newmax;\n}\nvector>get_oil_prob(){\n vector>noc(N,vector(N,1.0));\n for(int k=0;k>cvk(N,vector(N,0));for(int p=0;p<(int)F[k].pos.size();p++){double pp=prob[k][p];if(pp<1e-12)continue;auto[di,dj]=F[k].pos[p];for(auto[ci,cj]:F[k].cells)cvk[di+ci][dj+cj]+=pp;}for(int i=0;i>op(N,vector(N));for(int i=0;i>make_guess(const vector>&op,double thr=0.5){\n vector>res;for(int i=0;i0)||(drld[i][j]<0&&op[i][j]>thr);if(oil)res.push_back({i,j});}return res;\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>N>>M>>eps;MAX_OPS=2*N*N;coef=1.0-2.0*eps;\n drld.assign(N,vector(N,-1));robs.assign(N,0.0);cobs.assign(N,0.0);\n F.resize(M);\n for(int k=0;k>F[k].d;F[k].cells.resize(F[k].d);F[k].hi=F[k].hj=0;\n for(int t=0;t>F[k].cells[t].first>>F[k].cells[t].second;F[k].hi=max(F[k].hi,F[k].cells[t].first);F[k].hj=max(F[k].hj,F[k].cells[t].second);}\n F[k].rp.assign(F[k].hi+1,0);F[k].cp.assign(F[k].hj+1,0);for(auto[ci,cj]:F[k].cells){F[k].rp[ci]++;F[k].cp[cj]++;}\n for(int di=0;di+F[k].hi=0.15)?3:(eps>=0.08)?2:1;\n do_row_col(n_reps);\n run_mf(200);\n {int qb=min(60,MAX_OPS-ops-20);\n for(int q=0;qbe){be=h;bk=k;}}\n if(be<0.1)break;do_shape_query(bk);run_mf(15);}}\n apply_constraints();run_mf(100);\n while(ops=0)continue;double pu=min(op[i][j],1.0-op[i][j]);if(pu>bunc){bunc=pu;bi=i;bj=j;}}\n if(bunc<0.05||bi<0){for(int i=0;i0.05&&op[i][j]<0.95)qdrl(i,j);break;}\n qdrl(bi,bj);apply_constraints();run_mf(20);}\n {auto op=get_oil_prob();auto g=make_guess(op);if(ops\nusing namespace std;\ntypedef long long ll;\ntypedef tuple T3;\nint W,D,N;vector>a;int NC;vector>C;vector>SS;vector>AR;\nvectorcompute_heights(const vector&days){vectorh(N,1);auto ben=[&](int k,int cur)->ll{ll b=0;for(int d:days){int df=a[d][k]-cur*W;if(df>0)b+=(ll)min(W,df);}return b;};priority_queuepq;for(int k=0;k0)pq.push({b,k,1});}for(int rem=W-N;rem>0&&!pq.empty();){auto[b,k,c]=pq.top();pq.pop();if(b<=0)break;h[k]++;rem--;ll nb=ben(k,h[k]);if(nb>0)pq.push({nb,k,h[k]});}sort(h.begin(),h.end());return h;}\nll area_cost(int d,const vector&h){ll c=0;for(int k=0;k0)c+=(ll)df*100;}return c;}\nsetget_bd(const vector&arr){setS;int y=0;for(int i=0;i+1<(int)arr.size();i++){y+=arr[i];S.insert(y);}return S;}\nll bdist(const set&A,const set&B){ll c=0;for(int x:A)if(!B.count(x))c++;for(int x:B)if(!A.count(x))c++;return c*(ll)W;}\nvectorarr_greedy(const vector&h,const set&t){vectortgt(t.begin(),t.end());multisetav(h.begin(),h.end());vectorarr;int S=0,j=0,nt=(int)tgt.size();while(!av.empty()){while(j=tgt[j])j++;if(j>=nt){for(int x:av)arr.push_back(x);break;}int need=tgt[j]-S;auto it=av.find(need);if(it!=av.end()){arr.push_back(need);S+=need;av.erase(it);j++;}else{auto ub=av.upper_bound(need);if(ub!=av.begin()){--ub;arr.push_back(*ub);S+=*ub;av.erase(ub);while(j=tgt[j])j++;}else{it=av.begin();arr.push_back(*it);S+=*it;av.erase(it);while(j=tgt[j])j++;}}}return arr;}\nvectorhill_climb(vectorarr,const set&t){if(t.empty()||(int)arr.size()<=1)return arr;int n=arr.size();vectorps(n+1,0);for(int i=0;i0){swap(arr[i],arr[j]);for(int k=i+1;k<=j;k++)ps[k]+=delta;impr=true;}}}}return arr;}\nvoid out_sol(const vector>&arrs){for(int d=0;dy(N+1);y[0]=0;for(int i=0;i>s(N);for(int i=0;i&s,vector>&Sv,vector&dc,int from){for(int d=from;dprev=(d>0)?Sv[d-1]:set();if(d>0&&s[d]==s[d-1]){Sv[d]=Sv[d-1];dc[d]=AR[d][s[d]];}else{auto arr=arr_greedy(C[s[d]],prev);Sv[d]=get_bd(arr);dc[d]=AR[d][s[d]]+(d>0?bdist(prev,Sv[d]):0LL);}}}\nvectorlocal_search(vectors){vector>Sv(D);vectordc(D,0);rebuild(s,Sv,dc,0);for(int iter=0;iter<20;iter++){bool any=false;for(int d=0;dprev=(d>0)?Sv[d-1]:set();auto na=arr_greedy(C[L],prev);auto nSd=get_bd(na);ll ndd=AR[d][L]+(d>0?bdist(prev,nSd):0LL);ll ndd1=0;if(d+1>>solve_final(const vector&s){vector>arrs(D);ll cost=0;arrs[0]=C[s[0]];cost+=AR[0][s[0]];setcur=get_bd(arrs[0]);for(int d=1;dns=get_bd(arrs[d]);cost+=AR[d][s[d]]+bdist(cur,ns);cur=ns;}}return{cost,arrs};}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>W>>D>>N;a.resize(D,vector(N));for(int d=0;d>a[d][k];\n vectoraidx(D);iota(aidx.begin(),aidx.end(),0);\n C.push_back(compute_heights(aidx));\n for(int d=0;d(NC));for(int d=0;d>pcg(NC,vector(NC,0));\n for(int L1=0;L1>dp(D,vector(NC,INF));vector>frm(D,vector(NC,-1));\n for(int L=0;Ldpseq(D);dpseq[D-1]=bL2;for(int d=D-2;d>=0;d--)dpseq[d]=frm[d+1][dpseq[d+1]];\n vectorgseq(D);\n {vector>Sv(D);int L0=0;for(int L=0;Lapseq(D);for(int d=0;d\nusing namespace std;\nusing namespace chrono;\nconstexpr long long MOD = 998244353;\nint N, M, K;\nlong long sv[20][3][3];\nlong long b[9][9];\nlong long cur_score;\ninline long long add_mod(long long a, long long c) { long long s=a+c; return s>=MOD?s-MOD:s; }\ninline long long sub_mod(long long a, long long c) { return a>=c?a-c:a-c+MOD; }\nvoid apply_s(int m,int p,int q){ for(int i=0;i<3;i++) for(int j=0;j<3;j++){ long long &cell=b[p+i][q+j]; long long nv=add_mod(cell,sv[m][i][j]); cur_score+=nv-cell; cell=nv; } }\nvoid undo_s(int m,int p,int q){ for(int i=0;i<3;i++) for(int j=0;j<3;j++){ long long &cell=b[p+i][q+j]; long long nv=sub_mod(cell,sv[m][i][j]); cur_score+=nv-cell; cell=nv; } }\nstruct Op{int m,p,q;};\nvoid fwd_greedy(vector&ops){ while((int)ops.size()bg){bg=g;bm=m;bp=p;bq=q;} } if(bm<0)break; apply_s(bm,bp,bq);ops.push_back({bm,bp,bq}); } }\nbool bwd_greedy(vector&ops){ bool imp=false; for(int idx=0;idx<(int)ops.size();){ long long s0=cur_score; undo_s(ops[idx].m,ops[idx].p,ops[idx].q); if(cur_score>s0){ops[idx]=ops.back();ops.pop_back();imp=true;} else{apply_s(ops[idx].m,ops[idx].p,ops[idx].q);++idx;} } return imp; }\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>N>>M>>K; cur_score=0;\n for(int i=0;i>b[i][j];b[i][j]%=MOD;cur_score+=b[i][j];}\n for(int m=0;m>sv[m][i][j];\n vectorops;ops.reserve(K);\n fwd_greedy(ops);\n for(int cyc=0;cyc<20;cyc++){if(!bwd_greedy(ops))break;fwd_greedy(ops);}\n long long best_score=cur_score; vectorbest_ops=ops;\n mt19937 rng(42); const int POS=N-2;\n auto rand_op=[&]()->Op{return{(int)(rng()%M),(int)(rng()%POS),(int)(rng()%POS)};};\n auto t0=steady_clock::now(); const long long TL_US=1850000;\n double T_start=1e8;\n if(!ops.empty()){ long long sumd=0;int cnt=0; for(int i=0;i<5000;i++){ int L=(int)ops.size();if(!L)break; int idx=rng()%L; Op old_op=ops[idx],new_op=rand_op(); long long s0=cur_score; undo_s(old_op.m,old_op.p,old_op.q); apply_s(new_op.m,new_op.p,new_op.q); long long d=cur_score-s0;sumd+=(d<0?-d:d);cnt++; undo_s(new_op.m,new_op.p,new_op.q); apply_s(old_op.m,old_op.p,old_op.q); } if(cnt>0)T_start=max(1.0,(double)sumd/cnt); }\n double T=T_start,T_end=max(T_start*1e-7,1.0);\n for(long long it=0;;it++){\n if(it%50000==0){ long long el=duration_cast(steady_clock::now()-t0).count(); if(el>=TL_US)break; T=T_start*pow(T_end/T_start,(double)el/TL_US); }\n int L=(int)ops.size(); Op n1=rand_op(),o1{},o2{},n2{}; int i1=-1,i2=-1,mt;\n if(L==0){mt=0;} else{ int r=(int)(rng()%10); if(L==K)mt=(r<2)?1:(r<7)?2:3; else mt=(r<2)?0:(r<3)?1:(r<7)?2:3; if(mt==3&&L<2)mt=2; }\n if(mt==1||mt==2){i1=(int)(rng()%L);o1=ops[i1];}\n if(mt==3){i1=(int)(rng()%L);do{i2=(int)(rng()%L);}while(i2==i1);o1=ops[i1];o2=ops[i2];n2=rand_op();}\n long long s0=cur_score;\n switch(mt){ case 0:apply_s(n1.m,n1.p,n1.q);break; case 1:undo_s(o1.m,o1.p,o1.q);break; case 2:undo_s(o1.m,o1.p,o1.q);apply_s(n1.m,n1.p,n1.q);break; case 3:undo_s(o1.m,o1.p,o1.q);undo_s(o2.m,o2.p,o2.q);apply_s(n1.m,n1.p,n1.q);apply_s(n2.m,n2.p,n2.q);break; }\n long long delta=cur_score-s0; bool acc;\n if(delta>=0)acc=true; else if(T<=0.5)acc=false; else acc=(double)(rng()%1000000)best_score){best_score=cur_score;best_ops=ops;} }\n else{ switch(mt){ case 0:undo_s(n1.m,n1.p,n1.q);break; case 1:apply_s(o1.m,o1.p,o1.q);break; case 2:undo_s(n1.m,n1.p,n1.q);apply_s(o1.m,o1.p,o1.q);break; case 3:undo_s(n2.m,n2.p,n2.q);undo_s(n1.m,n1.p,n1.q);apply_s(o2.m,o2.p,o2.q);apply_s(o1.m,o1.p,o1.q);break; } }\n }\n cout<\nusing namespace std;\nconst int N=5;\nint A[N][N],posR[N*N],posP[N*N],grid[N][N];\nint craneR,craneC,craneContainer;\nbool craneHolding;\nint recvSent[N],recvPickedUp[N],dispatchCount[N];\nmap> bufPos;\nset> usedBufs;\nbool done_[N*N];\nstring result;\nvoid sRecv(){for(int r=0;rtr)turn_('U');else if(craneC freeBuf(int tR=-1){\n if(tR>=0)for(int c=N-2;c>=1;c--){auto p=make_pair(tR,c);if(!usedBufs.count(p)&&grid[tR][c]==-1)return p;}\n for(int c=N-2;c>=1;c--)for(int r=0;r plan(){\n const int ND=N+1;int DB=1;for(int i=0;id,int r,int c)->int{int s=0;for(int i=0;i&d,int&r,int&c){c=s%N;s/=N;r=s%N;s/=N;for(int i=N-1;i>=0;i--){d[i]=s%ND;s/=ND;}};\n vectordist(NS,INT_MAX/2),pS(NS,-1),pG(NS,-1);\n priority_queue,vector>,greater<>>pq;\n arrayd0{};int s0=enc(d0,0,0);dist[s0]=0;pq.push({0,s0});\n while(!pq.empty()){auto[w,s]=pq.top();pq.pop();if(w>dist[s])continue;arrayd;int r,c;dec(s,d,r,c);\n for(int g=0;g=N)continue;int k=N*g+d[g],sR=posR[k];\n int tc=abs(r-sR)+c+abs(sR-g)+(N-1)+2+posP[k]*5;\n auto nd=d;nd[g]++;int ns=enc(nd,g,N-1);\n if(dist[s]+tcgD;gD.fill(N);int best=-1,bd=INT_MAX;\n for(int r=0;rord;if(best!=-1)for(int s=best;pS[s]!=-1;s=pS[s])ord.push_back(pG[s]);\n reverse(ord.begin(),ord.end());return ord;\n}\nvoid solve(){\n for(int r=0;r=0)deliver_(bSR,bSC,bBuf,!bBuf,bK/N);\n else{int bG=-1,bD=INT_MAX;\n for(int g=0;g=0)clearB_(posR[nNext(bG)]);}\n }\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n int n;cin>>n;for(int r=0;r>A[r][p];\n solve();cout<\nusing namespace std;\n\nint N;\nint h[20][20];\nint curR, curC, curLoad;\nvector ops;\n\nvoid doLoad(int d) {\n if (d <= 0) return;\n ops.push_back(\"+\" + to_string(d));\n h[curR][curC] -= d; curLoad += d;\n}\n\nvoid doUnload(int d) {\n d = min(d, curLoad);\n if (d <= 0) return;\n ops.push_back(\"-\" + to_string(d));\n h[curR][curC] += d; curLoad -= d;\n}\n\nvoid moveStep(char dir, int dr, int dc) {\n curR += dr; curC += dc;\n ops.push_back(string(1, dir));\n if (h[curR][curC] > 0) doLoad(h[curR][curC]);\n else if (h[curR][curC] < 0 && curLoad > 0) doUnload(min(curLoad, -h[curR][curC]));\n}\n\nvoid moveTo(int tr, int tc) {\n while (curR != tr || curC != tc) {\n bool canR = (curR != tr), canC = (curC != tc);\n if (canR && canC) {\n int dr = curR < tr ? 1 : -1, dc = curC < tc ? 1 : -1;\n int nextRh = h[curR + dr][curC], nextCh = h[curR][curC + dc];\n int valR, valC;\n if (curLoad > 0) {\n valR = abs(nextRh); valC = abs(nextCh);\n } else {\n valR = max(0, nextRh); valC = max(0, nextCh);\n if (valR == 0 && valC == 0) { valR = abs(nextRh); valC = abs(nextCh); }\n }\n if (valR >= valC) moveStep(dr > 0 ? 'D' : 'U', dr, 0);\n else moveStep(dc > 0 ? 'R' : 'L', 0, dc);\n } else if (canR) {\n int dr = curR < tr ? 1 : -1;\n moveStep(dr > 0 ? 'D' : 'U', dr, 0);\n } else {\n int dc = curC < tc ? 1 : -1;\n moveStep(dc > 0 ? 'R' : 'L', 0, dc);\n }\n }\n}\n\nbool allZero() {\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (h[i][j] != 0) return false;\n return true;\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(0);\n cin >> N;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) cin >> h[i][j];\n curR = curC = curLoad = 0;\n if (h[0][0] > 0) doLoad(h[0][0]);\n while (!allZero() && (int)ops.size() < 95000) {\n auto mhdist = [&](int i, int j) { return abs(i-curR)+abs(j-curC); };\n if (curLoad > 0) {\n int best = INT_MAX, bi = -1, bj = -1;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++)\n if (h[i][j] < 0) { int d = mhdist(i,j); if (d < best) { best=d; bi=i; bj=j; } }\n if (bi < 0) break;\n moveTo(bi, bj);\n if (h[bi][bj] < 0 && curLoad > 0) doUnload(min(curLoad, -h[bi][bj]));\n } else {\n double bestScore = -1; int bi = -1, bj = -1;\n for (int i = 0; i < N; i++) for (int j = 0; j < N; j++)\n if (h[i][j] > 0) {\n double s = (double)h[i][j] / (mhdist(i,j) + 1);\n if (s > bestScore) { bestScore = s; bi = i; bj = j; }\n }\n if (bi < 0) break;\n moveTo(bi, bj);\n if (h[bi][bj] > 0) doLoad(h[bi][bj]);\n }\n }\n for (const auto& op : ops) cout << op << \"\\n\";\n return 0;\n}","ahc035":"#include \nusing namespace std;\nint main(){\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int N,M,T; cin>>N>>M>>T;\n const int SC=2*N*(N-1),nn=N*N;\n vector> X(SC,vector(M));\n for(int i=0;i>X[i][j];\n mt19937 rng(42);\n vector> nbr(nn); vector ndeg(nn,0);\n for(int p=0;p0)nbr[p][ndeg[p]++]=p-N;if(r0)nbr[p][ndeg[p]++]=p-1;if(c vals(SC,0);\n for(int k=0;k ins(SC,false); vector sel;\n for(int l=0;lX[bk][l])bk=k;if(!ins[bk]){ins[bk]=true;sel.push_back(bk);}}\n {vector ord(SC);iota(ord.begin(),ord.end(),0);sort(ord.begin(),ord.end(),[&](int a,int b){return vals[a]>vals[b];});for(int k:ord){if((int)sel.size()>=nn)break;if(!ins[k]){ins[k]=true;sel.push_back(k);}}}\n vector pst(nn*nn);\n for(int i=0;i psum(nn,0);\n for(int i=0;i&g,int p)->int{int v=0;for(int d=0;d&g)->int{int s=0;for(int p=0;p g)->vector{bool imp=true;while(imp){imp=false;for(int a=0;abef)imp=true;else swap(g[a],g[b]);}}return g;};\n auto grinit=[&]()->vector{vector g(nn,-1);vector used(nn,false);for(int pos=0;pos0)cv+=pst[s*nn+g[pos-N]];if(c>0)cv+=pst[s*nn+g[pos-1]];int64_t ev=(int64_t)cv*1000000LL+psum[s];if(ev>bv){bv=ev;bs=s;}}g[pos]=bs;used[bs]=true;}return g;};\n int gbest=-1; vector bg;\n for(int rest=0;rest<3;rest++){\n double rt0=chrono::duration(chrono::steady_clock::now()-ts).count();\n if(rt0>=0.185) break;\n double tl=(0.185-rt0)/(3-rest),tend=rt0+tl;\n vector g(nn); double T0;\n if(rest==0){g=grinit();T0=200.0;}else{iota(g.begin(),g.end(),0);shuffle(g.begin(),g.end(),rng);T0=1000.0;}\n int cur=totsc(g),lb=cur; vector lg=g; double temp=T0;\n for(int it=0;;it++){\n if((it&0x7FF)==0){double now=chrono::duration(chrono::steady_clock::now()-ts).count();if(now>=tend)break;temp=T0*pow(0.1/T0,(now-rt0)/tl);}\n int p1=rng()%nn,p2=rng()%nn; if(p1==p2)continue;\n int bef=ctrb(g,p1)+ctrb(g,p2); swap(g[p1],g[p2]); int aft=ctrb(g,p1)+ctrb(g,p2); int d=aft-bef;\n if(d>=0||(rng()%1000000)<(int)(1e6*exp((double)d/temp))){cur+=d;if(cur>lb){lb=cur;lg=g;}}else swap(g[p1],g[p2]);\n }\n lg=locsrch(lg); int sc=totsc(lg); if(sc>gbest){gbest=sc;bg=lg;}\n }\n for(int i=0;i>X[i][j];\n }\n return 0;\n}","ahc038":"#include \nusing namespace std;\nint N,M,V;\nconst int DR[]={0,1,0,-1},DC[]={1,0,-1,0};\nint rx,ry,nfp,Vp,rfp=-1;\nint fpd[4],hld[4];\nstruct Del{int sr,sc,tr,tc;bool done;};\nvectorP;\nint np;\nvector>g;\nmap,int>sm;\nvectorops;\n\nvoid em(char mv){\n if(mv=='D')rx++;else if(mv=='U')rx--;else if(mv=='R')ry++;else if(mv=='L')ry--;\n string op(2*Vp,'.');op[0]=mv;\n for(int k=0;k=N||fc<0||fc>=N)continue;\n if(hld[k]<0){\n if(k==rfp)continue;\n auto it=sm.find({fr,fc});\n if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}\n }else{\n int di=hld[k];\n if(P[di].tr==fr&&P[di].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di].done=true;hld[k]=-1;op[Vp+1+k]='P';}\n }\n }\n ops.push_back(op);\n}\nbool navto(int tr,int tc){\n while((rx!=tr||ry!=tc)&&(int)ops.size()<99990){\n char mv='.';\n if(rxtr)mv='U';else if(ry=0)continue;\n int ar=r-DR[fpd[k]],ac=c-DC[fpd[k]];\n if(ar<0||ar>=N||ac<0||ac>=N)continue;\n int tar=P[di].tr-DR[fpd[k]],tac=P[di].tc-DC[fpd[k]];\n if(tar<0||tar>=N||tac<0||tac>=N)continue;\n int v=abs(rx-ar)+abs(ry-ac);\n if(v=0)continue;\n int ar=r-DR[fpd[k]],ac=c-DC[fpd[k]];\n if(ar<0||ar>=N||ac<0||ac>=N)continue;\n int v=abs(rx-ar)+abs(ry-ac);\n if(v=99990){sm[{r,c}]=di;return -1;}\n string op(2*Vp,'.');bool ok=false;\n for(int k=0;k=N||fc<0||fc>=N)continue;\n if(k==bk&&fr==r&&fc==c&&g[r][c]==1&&hld[k]<0){hld[k]=di;g[r][c]=0;op[Vp+1+k]='P';ok=true;}\n else if(hld[k]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}}\n else{int di2=hld[k];if(P[di2].tr==fr&&P[di2].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di2].done=true;hld[k]=-1;op[Vp+1+k]='P';}}\n }\n ops.push_back(op);\n if(!ok){sm[{r,c}]=di;return -1;}\n return bk;\n}\nbool dropfp(int k,int di){\n if(hld[k]!=di)return true;\n int r=P[di].tr,c=P[di].tc;\n int ar=r-DR[fpd[k]],ac=c-DC[fpd[k]];\n if(ar<0||ar>=N||ac<0||ac>=N)return false;\n navto(ar,ac);\n if(hld[k]!=di)return true;\n if((int)ops.size()>=99990)return false;\n string op(2*Vp,'.');bool ok=false;\n for(int k2=0;k2=N||fc<0||fc>=N)continue;\n if(k2==k&&fr==r&&fc==c&&g[r][c]==0&&hld[k2]==di){g[r][c]=1;P[di].done=true;hld[k2]=-1;op[Vp+1+k2]='P';ok=true;}\n else if(hld[k2]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k2]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k2]='P';}}\n else{int di2=hld[k2];if(P[di2].tr==fr&&P[di2].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di2].done=true;hld[k2]=-1;op[Vp+1+k2]='P';}}\n }\n ops.push_back(op);\n return ok;\n}\nbool cbh(int bk){\n if(hld[bk]<0)return false;\n int di=hld[bk];\n auto valid=[&](int r,int c)->bool{int a=r-DR[fpd[bk]],b=c-DC[fpd[bk]];return a>=0&&a=0&&btmp={-1,-1};\n {\n set>ts;\n for(auto&d:P)if(!d.done)ts.insert({d.tr,d.tc});\n for(int i=0;i>N>>M>>V;\n vectorsg(N),tg(N);\n for(auto&s:sg)cin>>s;for(auto&s:tg)cin>>s;\n vector>S,T;\n g.assign(N,vector(N,0));\n for(int i=0;imt(m,-1);\n {\n vectorsu(m,false),tu(m,false);\n for(int i=0;i=N||fc<0||fc>=N)continue;\n if(hld[k]<0){\n auto it=sm.find({fr,fc});\n if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}\n }else{\n int di=hld[k];\n if(P[di].tr==fr&&P[di].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di].done=true;hld[k]=-1;op[Vp+1+k]='P';}\n }\n }\n };\n if(nfp>=2){\n string op(2*Vp,'.');\n if(nfp>=2){op[2]='R';fpd[1]=1;}\n if(nfp>=3){op[3]='R';fpd[2]=1;}\n if(nfp>=4){op[4]='L';fpd[3]=3;}\n orient_check(op);ops.push_back(op);\n }\n if(nfp>=3){\n string op(2*Vp,'.');op[3]='R';fpd[2]=2;\n orient_check(op);ops.push_back(op);\n }\n int stall=0;\n while((int)ops.size()<97000){\n int tdone=0;for(auto&d:P)if(d.done)tdone++;\n if(tdone==np)break;\n bool prog=false;\n // Step 1: deliver nearest held with unblocked target\n {\n int bk=-1,bd=INT_MAX;\n for(int k=0;k=N||ac<0||ac>=N)continue;\n int d=abs(rx-ar)+abs(ry-ac);\n if(d=0){if(!dropfp(bk,hld[bk]))cbh(bk);prog=true;}\n }\n // Step 2: pick and deliver from sm\n if(!prog){\n int fi=-1,bd=INT_MAX;\n for(auto&[src,di]:sm){\n if(g[P[di].tr][P[di].tc]!=0)continue;\n for(int k=0;k=0)continue;\n int ar=src.first-DR[fpd[k]],ac=src.second-DC[fpd[k]];\n if(ar<0||ar>=N||ac<0||ac>=N)continue;\n int d=abs(rx-ar)+abs(ry-ac);\n if(d=0){\n int k=pickfp(fi,P[fi].sr,P[fi].sc);\n if(k>=0){if(!dropfp(k,fi))cbh(k);prog=true;}\n }\n }\n // Step 3: cycle break\n if(!prog){\n for(int k=0;k=0){if(cbh(k))prog=true;break;}\n }\n if(!prog){\n int ci=-1,bd=INT_MAX;\n for(auto&[src,di]:sm){\n int d=abs(rx-src.first)+abs(ry-src.second);\n if(d=0){int k=pickfp(ci,P[ci].sr,P[ci].sc);if(k>=0&&cbh(k))prog=true;}\n }\n }\n if(prog)stall=0;\n else{stall++;if(stall>300)break;em('.');}\n }\n for(auto&op:ops)cout<\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n using Clock = chrono::steady_clock;\n auto t0 = Clock::now();\n auto elapsedMs = [&]() {\n return (long long)chrono::duration_cast(Clock::now()-t0).count();\n };\n int N; cin >> N;\n int M = 2*N;\n vector X(M), Y(M), W(M);\n for (int i=0; i>X[i]>>Y[i]; W[i]=(ix2)swap(x1,x2);if(y1>y2)swap(y1,y2);\n cout<<4<<\"\\n\"< bx(M),by(M);\n {\n vector idx(M); iota(idx.begin(),idx.end(),0);\n sort(idx.begin(),idx.end(),[&](int a,int b){return X[a]&fish,int lo,int hi)->pair{\n int cur=0,cs=-1,mx=0,blo=-1,bhi=-1;bool ir=false;\n for(int i=0,n=(int)fish.size();i=lo&&fish[i].other<=hi)gs+=fish[i].w;i++;}\n if(!ir){if(gs>0){cs=xv;cur=gs;ir=true;if(cur>mx){mx=cur;blo=cs;bhi=xv;}}}\n else{cur+=gs;if(cur>mx){mx=cur;blo=cs;bhi=xv;}if(cur<0){cur=0;ir=false;}}\n }\n return{blo,bhi};\n };\n auto evalRect=[&](int x1,int x2,int y1,int y2){\n int s=0;\n for(int i=0;i=x1&&X[i]<=x2&&Y[i]>=y1&&Y[i]<=y2)s+=W[i];\n return s;\n };\n auto coordDescent=[&](int x1,int x2,int y1,int y2)->tuple{\n x1=max(0,min(CMAX,x1));x2=max(0,min(CMAX,x2));\n y1=max(0,min(CMAX,y1));y2=max(0,min(CMAX,y2));\n if(x1>x2)swap(x1,x2);if(y1>y2)swap(y1,y2);\n int px1=-1,px2=-1,py1=-1,py2=-1;\n for(int it=0;it<20;it++){\n if(x1==px1&&x2==px2&&y1==py1&&y2==py2)break;\n px1=x1;px2=x2;py1=y1;py2=y2;\n auto[nx1,nx2]=kadane(bx,y1,y2);if(nx1>=0){x1=nx1;x2=nx2;}\n auto[ny1,ny2]=kadane(by,x1,x2);if(ny1>=0){y1=ny1;y2=ny2;}\n }\n return make_tuple(evalRect(x1,x2,y1,y2),x1,x2,y1,y2);\n };\n // Grid Kadane's\n const int G=200,step=CMAX/G;\n vector> grid(G,vector(G,0));\n for(int i=0;i cs(G,0);\n for(int gx2=gx1;gx2mx){mx=cur;ms=cst;me=gy;}if(cur<0){cur=0;cst=gy+1;}}\n if(me>=0&&mx>bgs){bgs=mx;bgx1=gx1;bgx2=gx2;bgy1=ms;bgy2=me;}\n }\n }\n int ix1=bgx1*step,ix2=min((bgx2+1)*step,CMAX);\n int iy1=bgy1*step,iy2=min((bgy2+1)*step,CMAX);\n int gscore=-1,rx1=0,rx2=1,ry1=0,ry2=1;\n auto tryRun=[&](int x1,int x2,int y1,int y2){\n auto[s,a,b,c,d]=coordDescent(x1,x2,y1,y2);\n if(s>gscore){gscore=s;rx1=a;rx2=b;ry1=c;ry2=d;}\n };\n tryRun(ix1,ix2,iy1,iy2);\n tryRun(0,CMAX,0,CMAX);\n {\n long long cx=0,cy=0;\n for(int i=0;i1500)break;\n int seed=rng()%N;\n int hx=200+(int)(rng()%50000),hy=200+(int)(rng()%50000);\n tryRun(X[seed]-hx,X[seed]+hx,Y[seed]-hy,Y[seed]+hy);\n }\n // ARM SEARCH\n // findArm: sweep along one direction, Kadane's on cross-section\n // fish_sorted: (sweep_coord, cross_coord, weight), cross in [clo,chi]\n // Returns (score, cross1, cross2, sweep_end)\n auto findArm=[&](const vector>&fish_sorted,int clo,int chi)\n ->tuple{\n vector xs;\n for(auto&[sw,cr,w]:fish_sorted)if(cr>=clo&&cr<=chi)xs.push_back(cr);\n sort(xs.begin(),xs.end());xs.erase(unique(xs.begin(),xs.end()),xs.end());\n if(xs.empty())return{0,-1,-1,0};\n int kx=(int)xs.size();\n vector cum(kx,0);\n int bsc=0,bc1=-1,bc2=-1,bsw=0;\n int i=0,n=(int)fish_sorted.size();\n while(i(fish_sorted[i]);\n while(i(fish_sorted[i])==csw){\n auto&[sw,cr,w]=fish_sorted[i];\n if(cr>=clo&&cr<=chi){\n int idx=(int)(lower_bound(xs.begin(),xs.end(),cr)-xs.begin());\n cum[idx]+=w;\n }\n i++;\n }\n int cur=0,cs=-1,mx=0,blo=-1,bhi=-1;bool ir=false;\n for(int j=0;j0){cs=xs[j];cur=gs;ir=true;if(cur>mx){mx=cur;blo=cs;bhi=xs[j];}}}\n else{cur+=gs;if(cur>mx){mx=cur;blo=cs;bhi=xs[j];}if(cur<0){cur=0;ir=false;}}\n }\n if(mx>bsc){bsc=mx;bc1=blo;bc2=bhi;bsw=csw;}\n }\n return{bsc,bc1,bc2,bsw};\n };\n // Build sorted fish for 4 arm directions (restricted to base cross-section)\n vector> ft,fb,fright,fl;\n for(int i=0;iry2&&X[i]>=rx1&&X[i]<=rx2)ft.emplace_back(Y[i],X[i],W[i]);\n if(Y[i]=rx1&&X[i]<=rx2)fb.emplace_back(-Y[i],X[i],W[i]);\n if(X[i]>rx2&&Y[i]>=ry1&&Y[i]<=ry2)fright.emplace_back(X[i],Y[i],W[i]);\n if(X[i]=ry1&&Y[i]<=ry2)fl.emplace_back(-X[i],Y[i],W[i]);\n }\n sort(ft.begin(),ft.end());sort(fb.begin(),fb.end());\n sort(fright.begin(),fright.end());sort(fl.begin(),fl.end());\n auto[ts,tax1,tax2,tay2]=findArm(ft,rx1,rx2);\n auto[bms,bax1,bax2,neg_bay]=findArm(fb,rx1,rx2); int bay1=-neg_bay;\n auto[rms,ray1,ray2,rax2]=findArm(fright,ry1,ry2);\n auto[ls,lay1,lay2,neg_lax]=findArm(fl,ry1,ry2); int lax1=-neg_lax;\n // Perimeter budget\n int P_base=2*(rx2-rx1)+2*(ry2-ry1);\n int budget=400000-P_base;\n // Arm validity (strict interior to avoid duplicate vertices)\n bool ht=ts>0&&tax1>rx1&&tax2ry2;\n bool hb=bms>0&&bax1>rx1&&bax20&&ray1>ry1&&ray2rx2;\n bool hl=ls>0&&lay1>ry1&&lay2budget){\n vector> eff;\n if(ht&&ct>0)eff.push_back({(double)ts/ct,0});\n if(hb&&cb>0)eff.push_back({(double)bms/cb,1});\n if(hr&&cr2>0)eff.push_back({(double)rms/cr2,2});\n if(hl&&cl>0)eff.push_back({(double)ls/cl,3});\n sort(eff.begin(),eff.end());\n for(auto&[e,idx]:eff){\n if(total_cost<=budget)break;\n if(idx==0){ht=false;total_cost-=ct;}\n else if(idx==1){hb=false;total_cost-=cb;}\n else if(idx==2){hr=false;total_cost-=cr2;}\n else{hl=false;total_cost-=cl;}\n }\n }\n int combined=gscore+(ht?ts:0)+(hb?bms:0)+(hr?rms:0)+(hl?ls:0);\n if(combined>=1){\n vector> v;\n // Bottom edge\n v.push_back({rx1,ry1});\n if(hb){if(bax1>rx1)v.push_back({bax1,ry1});v.push_back({bax1,bay1});v.push_back({bax2,bay1});if(bax2ry1)v.push_back({rx2,ray1});v.push_back({rax2,ray1});v.push_back({rax2,ray2});if(ray2rx1)v.push_back({tax1,ry2});}\n v.push_back({rx1,ry2});\n // Left edge (going down)\n if(hl){if(lay2ry1)v.push_back({rx1,lay1});}\n // Remove consecutive duplicates\n vector> res;\n for(auto&p:v){if(res.empty()||res.back()!=p)res.push_back(p);}\n while(res.size()>1&&res.front()==res.back())res.pop_back();\n // Check all distinct\n set> vs(res.begin(),res.end());\n bool ok=(int)vs.size()==(int)res.size()&&(int)res.size()>=4;\n if(ok){\n cout<<(int)res.size()<<\"\\n\";\n for(auto&[x,y]:res)cout<=1){\n if(rx1>=rx2){if(rx2=ry2){if(ry2\nusing namespace std;\ntypedef long long ll;\n\nint N, T;\nvector W, H;\ndouble sW, sH, mxW, mxH, totA;\n\nstruct Op { int p, r; char d; int b; };\n\npair simulate(const vector& ops) {\n vector x0(N,0),y0(N,0),x1(N,0),y1(N,0);\n vector pl(N,false);\n for (const auto& o : ops) {\n int p = o.p;\n ll w = max(1LL, llround(o.r ? H[p] : W[p]));\n ll h = max(1LL, llround(o.r ? W[p] : H[p]));\n if (o.d == 'U') {\n ll xl = o.b >= 0 ? x1[o.b] : 0LL;\n ll yt = 0;\n for (int i = 0; i < N; i++)\n if (pl[i] && x0[i] < xl+w && x1[i] > xl)\n yt = max(yt, y1[i]);\n x0[p]=xl; y0[p]=yt; x1[p]=xl+w; y1[p]=yt+h;\n } else {\n ll yt = o.b >= 0 ? y1[o.b] : 0LL;\n ll xl = 0;\n for (int i = 0; i < N; i++)\n if (pl[i] && y0[i] < yt+h && y1[i] > yt)\n xl = max(xl, x1[i]);\n x0[p]=xl; y0[p]=yt; x1[p]=xl+w; y1[p]=yt+h;\n }\n pl[p] = true;\n }\n ll rW=0, rH=0;\n for (int i = 0; i < N; i++)\n if (pl[i]) { rW=max(rW,x1[i]); rH=max(rH,y1[i]); }\n return {rW, rH};\n}\n\n// col=false: shelf packing (rows); col=true: column packing\n// For col=false, line0 uses U, rest use L\n// For col=true, line0 uses L, rest use U\nvector make_pack(const vector& rot, double tgt, bool col) {\n vector ops; ops.reserve(N);\n int cl = -1; double cm = 0;\n vector lr; vector lc;\n int p0 = -1;\n for (int i = 0; i < N; i++) {\n double m = col ? (rot[i] ? W[i] : H[i]) : (rot[i] ? H[i] : W[i]);\n double c = col ? (rot[i] ? H[i] : W[i]) : (rot[i] ? W[i] : H[i]);\n if (cl < 0 || cm + m > tgt) {\n cl++; cm = m;\n lr.push_back(i); lc.push_back(c);\n if (cl == 0) {\n ops.push_back({i, rot[i], col?'L':'U', -1});\n p0 = i;\n } else {\n ops.push_back({i, rot[i], col?'U':'L', lr[cl-1]});\n }\n } else {\n cm += m;\n if (c > lc[cl]) { lc[cl]=c; lr[cl]=i; }\n if (cl == 0) {\n ops.push_back({i, rot[i], col?'L':'U', p0});\n p0 = i;\n } else {\n ops.push_back({i, rot[i], col?'U':'L', lr[cl-1]});\n }\n }\n }\n return ops;\n}\n\ndouble calc_score(const vector& rot, double tgt, bool col) {\n auto [a,b] = simulate(make_pack(rot, tgt, col));\n return (double)(a+b);\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n\n double sigma;\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 sW=sH=mxW=mxH=totA=0;\n for (int i = 0; i < N; i++) {\n sW+=W[i]; sH+=H[i];\n mxW=max(mxW,W[i]); mxH=max(mxH,H[i]);\n totA+=W[i]*H[i];\n }\n\n const double BUDGET = 2600.0;\n auto t0 = chrono::steady_clock::now();\n auto now = [&]() {\n return chrono::duration(chrono::steady_clock::now()-t0).count();\n };\n\n vector g_rot;\n double g_tgt=0, g_score=1e18;\n bool g_col=false;\n\n for (int t = 0; t < T; t++) {\n double ts = now();\n double per = max(1.0, (BUDGET - ts) / (T - t));\n double dl = ts + per * 0.95;\n\n mt19937 rng(t * 1234567891u ^ 987654321u);\n uniform_real_distribution uni(0,1);\n\n bool col;\n double lo, hi, tgt;\n vector rot(N);\n\n if (t < (T+1)/2) {\n col = (t & 1);\n lo = col ? mxH : mxW;\n hi = col ? sH : sW;\n tgt = max(lo, min(hi, sqrt(totA)));\n // Init rotation: minimize cross-dim\n for (int i = 0; i < N; i++)\n rot[i] = col ? (H[i] br=rot;\n double bt=tgt;\n bool bc=col;\n double bs=cur;\n\n double Th = cur*0.05+1.0;\n double Tl = max(1.0, cur*1e-5);\n\n // Simulated Annealing\n for (int it=0; ; it++) {\n if ((it&63)==0 && now()>=dl) break;\n double frac = max(0.0, min(1.0, (now()-ts)/per));\n double Tc = max(Tl, Th * pow(Tl/Th, frac));\n\n int mv = rng()%10, fi=-1;\n double ot=tgt;\n bool oc=col;\n double olo=lo, ohi=hi;\n\n if (mv < 7) {\n fi = rng()%N;\n rot[fi] ^= 1;\n } else if (mv < 9) {\n tgt = max(lo, min(hi, tgt * exp((uni(rng)*2-1)*0.35)));\n } else {\n col ^= 1;\n lo = col ? mxH : mxW;\n hi = col ? sH : sW;\n tgt = max(lo, min(hi, ot));\n }\n\n double ns = calc_score(rot, tgt, col);\n double d = ns - cur;\n if (d <= 0 || uni(rng) < exp(-d/Tc)) {\n cur = ns;\n if (ns < bs) { bs=ns; br=rot; bt=tgt; bc=col; }\n } else {\n if (fi >= 0) rot[fi] ^= 1;\n else if (mv < 9) tgt = ot;\n else { col=oc; lo=olo; hi=ohi; tgt=ot; }\n }\n }\n\n // Final greedy passes\n for (int pass=0; pass<3; pass++) {\n bool imp=false;\n for (int i=0; i> Wf >> Hf;\n }\n\n return 0;\n}","ahc041":"#include \nusing namespace std;\ntypedef long long ll;\nint N,M,H,A[1000];\nvectorG[1000];\nint par[1000],dep[1000],ssm[1000],mdn[1000];\nvectorch[1000];\nvoid dfs_init(int v){ssm[v]=A[v];mdn[v]=0;for(int c:ch[v]){dfs_init(c);ssm[v]+=ssm[c];mdn[v]=max(mdn[v],mdn[c]+1);}}\nvoid push_dep(int v,int d){dep[v]=d;for(int c:ch[v])push_dep(c,d+1);}\nbool in_sub(int w,int v){for(;w!=-1;w=par[w])if(w==v)return true;return false;}\nvoid pull_ssm(int v){for(;v!=-1;v=par[v]){int s=A[v];for(int c:ch[v])s+=ssm[c];ssm[v]=s;}}\nvoid pull_mdn(int v){for(;v!=-1;v=par[v]){int m=0;for(int c:ch[v])m=max(m,mdn[c]+1);mdn[v]=m;}}\nvoid do_move(int v,int np){int op=par[v];if(op!=-1){auto&c=ch[op];c.erase(find(c.begin(),c.end(),v));}par[v]=np;if(np!=-1){ch[np].push_back(v);push_dep(v,dep[np]+1);}else push_dep(v,0);if(op!=-1){pull_ssm(op);pull_mdn(op);}if(np!=-1){pull_ssm(np);pull_mdn(np);}}\nvoid rebuild(){for(int i=0;iq;q.push(v);while(!q.empty()){int u=q.front();q.pop();for(int c:ch[u]){dep[c]=dep[u]+1;q.push(c);}}}for(int v=0;vp(N);iota(p.begin(),p.end(),0);shuffle(p.begin(),p.end(),rng);for(int v:p){int lim=H-1-mdn[v];if(lim<0)continue;int bp=par[v];ll bg=0;for(int w:G[v]){if(dep[w]>lim||in_sub(w,v))continue;ll g=(ll)(dep[w]+1-dep[v])*ssm[v];if(g>bg){bg=g;bp=w;}}if(bg>0){do_move(v,bp);ok=true;}}if(!ok)break;}}\nvoid build_bfs(vector&ord){fill(par,par+N,-1);fill(dep,dep+N,0);for(int i=0;ivis(N,false);for(int s:ord){if(vis[s])continue;queueq;q.push(s);vis[s]=true;while(!q.empty()){int v=q.front();q.pop();if(dep[v]>=H)continue;for(int u:G[v])if(!vis[u]){vis[u]=true;par[u]=v;dep[u]=dep[v]+1;ch[v].push_back(u);q.push(u);}}}for(int v=0;v>N>>M>>H;for(int i=0;i>A[i];\n for(int i=0;i>u>>v;G[u].push_back(v);G[v].push_back(u);}\n for(int i=0;i>x>>y;}\n auto t0=chrono::steady_clock::now();\n mt19937 rng(42);\n ll best_sc=-1;vectorbest_par(N);\n for(int trial=0;;trial++){\n if(chrono::duration(chrono::steady_clock::now()-t0).count()>0.3)break;\n vectorord(N);iota(ord.begin(),ord.end(),0);\n if(trial==0)sort(ord.begin(),ord.end(),[](int a,int b){return A[a]best_sc){best_sc=sc;copy(par,par+N,best_par.begin());}\n }\n copy(best_par.begin(),best_par.end(),par);rebuild();\n ll cur=best_sc;\n uniform_real_distributionuni(0,1);\n auto ts=chrono::steady_clock::now();\n double sa_t=1.80-chrono::duration(ts-t0).count();\n if(sa_t<0.05)sa_t=0.05;\n double T=1000;\n for(long long step=0;;step++){\n if(step%10000==0){double t=chrono::duration(chrono::steady_clock::now()-ts).count();if(t>=sa_t)break;T=1000*pow(0.001,t/sa_t);}\n int v=rng()%N;int lim=H-1-mdn[v];if(lim<0)continue;\n if(G[v].empty())continue;int w=G[v][rng()%G[v].size()];\n if(w==par[v]||dep[w]>lim||in_sub(w,v))continue;\n ll gain=(ll)(dep[w]+1-dep[v])*ssm[v];\n if(gain>0||(T>0.01&&uni(rng)best_sc){best_sc=cur;copy(par,par+N,best_par.begin());}\n }\n }\n for(int v=0;v\nusing namespace std;\nint N,M,OR_[42],OC_[42],ctop_[21],cbot_[21],rleft_[21],rright_[21];\nlong long gmask(int dir,int idx,int depth){long long m=0;for(int k=0;k=depth)m|=1LL<=depth)m|=1LL<=0)t+=gcost(d,sel[d][i]);return t;}};\nvoid dr_impl(Sol&s,int sd,int si){for(;;){bool ch=false;for(int d=0;d<4&&!ch;d++)for(int i=0;i=0)ot|=s.sm[d2][i2];long long un=s.sm[d][i]&~ot;if(!un){s.sel[d][i]=-1;s.sm[d][i]=0;ch=true;break;}int nd;if(d==0){nd=0;for(int k=0;k>k)&1)nd=max(nd,OR_[k]);}else if(d==1){nd=N-1;for(int k=0;k>k)&1)nd=min(nd,OR_[k]);}else if(d==2){nd=0;for(int k=0;k>k)&1)nd=max(nd,OC_[k]);}else{nd=N-1;for(int k=0;k>k)&1)nd=min(nd,OC_[k]);}if(nd!=s.sel[d][i]){s.sel[d][i]=nd;s.sm[d][i]=gmask(d,i,nd);ch=true;}}if(!ch)break;}}\nvoid depth_red(Sol&s){dr_impl(s,-1,-1);}\nvoid local_search(Sol&s,const vector&cands){for(int it=0;it<10;it++){long long cov1=0;{int cnt[64]={};for(int d=0;d<4;d++)for(int i=0;i=0)for(int k=0;k>k)&1)cnt[k]++;for(int k=0;k=0){int cu=s.sel[d][idx];if((d==0||d==2)?dep<=cu:dep>=cu)continue;}Sol ts=s;ts.sel[d][idx]=dep;ts.sm[d][idx]=c.mask;dr_impl(ts,d,idx);dr_impl(ts,-1,-1);int nc=ts.cost();if(nc>N;vectorboard(N);for(int i=0;i>board[i];M=0;for(int i=0;icands;for(int k=0;kcbot_[c])cands.push_back({1,c,r,gcost(1,r),gmask(1,c,r)});if(crright_[r])cands.push_back({3,r,c,gcost(3,c),gmask(3,r,c)});}\nmt19937 rng(42);Sol best;best.init();int best_cost=INT_MAX;\nfor(int trial=0;trial<10;trial++){if(trial>0)shuffle(cands.begin(),cands.end(),rng);Sol cur;cur.init();long long rem=(1LL<=0){int cu=cur.sel[d][idx];if((d==0||d==2)?dep<=cu:dep>=cu)continue;ac-=gcost(d,cu);}if(ac<=0)continue;double rv=(double)ac/__builtin_popcountll(nm);if(rv\nusing namespace std;\nconst int MAXN = 100;\nint N, L, T[MAXN], a[MAXN], b[MAXN], cv[MAXN], fv[MAXN], flow[MAXN];\nvoid computeFlow(){fill(flow,flow+N,0);for(int i=0;iq;vis[0]=true;q.push(0);while(!q.empty()){int x=q.front();q.pop();if(!vis[a[x]]){vis[a[x]]=true;q.push(a[x]);}if(!vis[b[x]]){vis[b[x]]=true;q.push(b[x]);}}for(int j=0;j0&&!vis[j])return false;return true;}\nvoid fixConn(){for(int pass=0;passq;vis[0]=true;q.push(0);while(!q.empty()){int x=q.front();q.pop();if(!vis[a[x]]){vis[a[x]]=true;q.push(a[x]);}if(!vis[b[x]]){vis[b[x]]=true;q.push(b[x]);}}int u=-1;for(int j=0;j0&&!vis[j]){u=j;break;}if(u<0)break;long long bestD=(long long)4e18;int besti=-1;bool bestA=false;for(int i=0;i0)?((long long)(abs(flow[old]-w-T[old])-abs(flow[old]-T[old]))+(long long)(abs(flow[u]+w-T[u])-abs(flow[u]-T[u]))):0LL;if(d0)?((long long)(abs(flow[old]-w-T[old])-abs(flow[old]-T[old]))+(long long)(abs(flow[u]+w-T[u])-abs(flow[u]-T[u]))):0LL;if(d0){flow[a[besti]]-=cv[besti];flow[u]+=cv[besti];}a[besti]=u;}else{if(fv[besti]>0){flow[b[besti]]-=fv[besti];flow[u]+=fv[besti];}b[besti]=u;}}}\nvoid flowSearch(){long long curErr=flowErr();bool improved=true;while(improved){improved=false;for(int i=0;i0)?((long long)(abs(flow[old]-w-T[old])-abs(flow[old]-T[old]))+(long long)(abs(flow[j]+w-T[j])-abs(flow[j]-T[j]))):0LL;if(d=0){if(w>0){flow[old]-=w;flow[bestJ]+=w;}curErr+=bestD;if(t2)b[i]=bestJ;else a[i]=bestJ;improved=true;}}}}}\nlong long simulate(){int cnt[MAXN]={},vc[MAXN]={};int cur=0;cnt[0]++;vc[0]++;for(int w=2;w<=L;w++){int nxt=(vc[cur]&1)?a[cur]:b[cur];cur=nxt;cnt[cur]++;vc[cur]++;}long long e=0;for(int j=0;j>N>>L;for(int i=0;i>T[i];\n for(int i=0;i>items;\n for(int i=0;i0)rem[0]--;\n priority_queue>pq;for(int j=0;j(chrono::steady_clock::now()-t0).count();\n if(el>1800000LL)break;\n int i=rng()%N,type=rng()%2,jNew=(int)(rng()%N);\n int&ptr=type?b[i]:a[i];int old=ptr;\n if(jNew==old)continue;\n ptr=jNew;\n if(!checkConn()){ptr=old;continue;}\n long long err=simulate();\n if(err<=curErr){curErr=err;if(err\nusing namespace std;\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int N,M,Q,L,W; cin>>N>>M>>Q>>L>>W;\n vector G(M); for(int& g:G) cin>>g;\n vector cx(N),cy(N);\n for(int i=0;i>lx>>rx>>ly>>ry;cx[i]=(lx+rx)/2.0;cy[i]=(ly+ry)/2.0;}\n auto ed2=[&](int a,int b)->double{double dx=cx[a]-cx[b],dy=cy[a]-cy[b];return dx*dx+dy*dy;};\n vector mst_par(N,-1);\n {vector vis(N,false);vector key(N,1e18);key[0]=0;\n for(int iter=0;iter> mch(N);for(int v=1;v post;{stack> stk;stk.push({0,0});while(!stk.empty()){auto&[v,ci]=stk.top();if(ci<(int)mch[v].size())stk.push({mch[v][ci++],0});else{post.push_back(v);stk.pop();}}}\n vector esz(N);vector sc(N,false);multiset remG(G.begin(),G.end());\n for(int v:post){esz[v]=1;for(int c:mch[v])if(!sc[c])esz[v]+=esz[c];if(v!=0&&remG.count(esz[v])){sc[v]=true;remG.erase(remG.find(esz[v]));}}\n bool ok=(remG.size()==1&&*remG.begin()==esz[0]);\n vector> grp(M);\n {map> sg;for(int i=0;i asn(N,false);\n for(int v:post){if(v==0||!sc[v])continue;int gid=sg[esz[v]].front();sg[esz[v]].pop();queueq;q.push(v);while(!q.empty()){int u=q.front();q.pop();if(asn[u])continue;grp[gid].push_back(u);asn[u]=true;for(int c:mch[u])if(!asn[c])q.push(c);}}\n int gid=sg[esz[0]].front();sg[esz[0]].pop();for(int v=0;vuint64_t{uint64_t r=0;for(int i=0;i<16;i++)r|=((uint64_t)((x>>i)&1))<<(2*i);return r;};\n vector ord(N);iota(ord.begin(),ord.end(),0);sort(ord.begin(),ord.end(),[&](int a,int b){uint64_t ma=eb((uint32_t)cx[a])|(eb((uint32_t)cy[a])<<1);uint64_t mb=eb((uint32_t)cx[b])|(eb((uint32_t)cy[b])<<1);return ma>>> ae(M);\n auto dq=[&](const vector&qc,int gi){if((int)qc.size()<2||qrem<=0)return;qrem--;cout<<\"? \"<>a>>b;ae[gi].push_back({ed2(a,b),{a,b}});}};\n auto nq=[&](int g)->int{if(g<=1)return 0;if(g<=L)return 1;return(g-2)/(L-1)+1;};\n int tmand=0;for(int i=0;i it(g,false);it[0]=true;vector dt(g,1e18);vector nt(g,0);for(int j=1;j0){int bj=-1;double bd=1e18;for(int j=0;j>cands;for(int j=0;jqc={v[rep]};for(auto&[d,j]:cands)qc.push_back(v[j]);dq(qc,i);\n for(auto&[d,j]:cands)if(!it[j]){it[j]=true;tsz++;for(int k=0;klg;for(int i=0;iL)lg.push_back(i);if(!lg.empty()&&xtra>0)for(int qi=0;qi0;qi++){int gi=lg[qi%(int)lg.size()];int g=G[gi];auto&v=grp[gi];int st=max(1,g/L),off=(qi/(int)lg.size())%st;vectorwin;for(int k=off;k=2)dq(win,gi);}}\n vectorpar(N);auto fu=[&](int x)->int{while(par[x]!=x){par[x]=par[par[x]];x=par[x];}return x;};\n vector>>ans(M);\n for(int i=0;i0)cout<<\" \";cout<\nusing namespace std;\nconst int N=20;\nbool grid[N][N];\nconst int DR[]={-1,1,0,0},DC[]={0,0,-1,1};\ninline bool inB(int r,int c){return(unsigned)r<(unsigned)N&&(unsigned)c<(unsigned)N;}\n\nconst int NS1=N*N*21*21;\nstatic int d1[NS1],p1[NS1],q1[NS1];\nstatic uint8_t a1[NS1];\n\nvector> fp1(int r0,int c0,int tr,int tc){\n memset(d1,-1,sizeof(d1));\n int S=(r0*N+c0)*441,G=(tr*N+tc)*441;\n if(S==G)return{};\n d1[S]=0;int qh=0,qt=0;q1[qt++]=S;\n while(qh> res;int r=r0,c=c0;\n while(r!=tr){res.push_back({'M',r> path;\n for(int cur=G;cur!=S;cur=p1[cur])path.push_back({\"MSA\"[a1[cur]>>2],\"UDLR\"[a1[cur]&3]});\n reverse(path.begin(),path.end());return path;\n}\n\nconst int NS2=N*N*2*21*21;\nstatic int d2[NS2],p2[NS2],q2[NS2];\nstatic uint8_t a2[NS2];\n\nvector> fp2(int r0,int c0,int tr1,int tc1,int tr2,int tc2){\n memset(d2,-1,sizeof(d2));\n auto E=[](int r,int c,int v,int ebr,int ebc){\n return (r*N+c)*2*441+v*441+(ebr+1)*21+(ebc+1);};\n int S=E(r0,c0,0,-1,-1),G=E(tr2,tc2,1,-1,-1);\n d2[S]=0;int qh=0,qt=0;q2[qt++]=S;\n while(qh> path;\n for(int cur=G;cur!=S;cur=p2[cur])path.push_back({\"MSA\"[a2[cur]>>2],\"UDLR\"[a2[cur]&3]});\n reverse(path.begin(),path.end());return path;\n}\n\nint cr,cc,eebr=-1,eebc=-1;\n\nvoid execPath(const vector>&path){\n for(auto[a,d]:path){\n cout<>Nin>>M;\n vector> pts(M);\n for(int i=0;i>pts[i].first>>pts[i].second;\n memset(grid,0,sizeof(grid));\n cr=pts[0].first;cc=pts[0].second;\n eebr=eebc=-1;\n int k=1;\n while(k\nusing namespace std;\nconst int MAXN=205;\nint n,px[MAXN],py[MAXN];long long pr[MAXN];\ndouble score_pi(double si,long long ri){if(si<=0)return 0;double r=(si<=(double)ri)?si/ri:(double)ri/si;return 1-(1-r)*(1-r);}\nstruct Split{int x1,y1,x2,y2,dir,sp,lo,hi;vectorL,R;};\nvectorsplits;int rx1[MAXN],ry1[MAXN],rx2[MAXN],ry2[MAXN];\nvoid recompute(){for(int i=0;icomp,int x1,int y1,int x2,int y2){\n int nc=(int)comp.size();if(nc==1)return;\n long long tr=0;for(int i:comp)tr+=pr[i];long long H=y2-y1,W=x2-x1;\n vectorbx(comp),by(comp);\n sort(bx.begin(),bx.end(),[](int a,int b){return px[a]cands;\n auto ss=[](long long AL,long long RL,int nL,long long AR,long long RR,int nR){double a=(RL<=0||AL>=RL)?(double)nL:nL*(1-pow(1-(double)AL/RL,2));double b=(RR<=0||AR>=RR)?(double)nR:nR*(1-pow(1-(double)AR/RR,2));return a+b;};\n {long long pf=0;for(int k=1;k=px[bx[k]])continue;int lo=max(px[bx[k-1]]+1,x1+1),hi=min(px[bx[k]],x2-1);if(lo>hi)continue;int sp=(int)round(x1+(double)W*pf/tr);sp=max(lo,min(hi,sp));cands.push_back({ss((long long)(sp-x1)*H,pf,k,(long long)(x2-sp)*H,tr-pf,nc-k),0,k,sp,lo,hi});}}\n {long long pf=0;for(int k=1;k=py[by[k]])continue;int lo=max(py[by[k-1]]+1,y1+1),hi=min(py[by[k]],y2-1);if(lo>hi)continue;int sp=(int)round(y1+(double)H*pf/tr);sp=max(lo,min(hi,sp));cands.push_back({ss((long long)(sp-y1)*W,pf,k,(long long)(y2-sp)*W,tr-pf,nc-k),1,k,sp,lo,hi});}}\n if(cands.empty())return;\n sort(cands.begin(),cands.end(),[](const Cand&a,const Cand&b){return a.sc>b.sc;});\n int ch=0;if(p_rand>0&&(int)cands.size()>1){int K=min((int)cands.size(),5);if(uniform_real_distribution(0,1)(rng)=s.hi)continue;int bsp=s.sp;double bs=evalAt(s,s.sp);int lo=s.lo,hi=s.hi;while(hi-lo>=3){int m1=lo+(hi-lo)/3,m2=hi-(hi-lo)/3;double s1=evalAt(s,m1),s2=evalAt(s,m2);if(s1bs){bs=sc;bsp=sp;}}if(bsp!=s.sp){s.sp=bsp;recompute();imp=true;}}return imp;}\ndouble computeScore(){double t=0;for(int i=0;i>n;for(int i=0;i>px[i]>>py[i]>>pr[i];\n vectorall(n);iota(all.begin(),all.end(),0);\n auto t0=chrono::steady_clock::now();\n auto msf=[&](){return(int)chrono::duration_cast(chrono::steady_clock::now()-t0).count();};\n const double prs[]={0.0,0.1,0.2,0.3,0.4,0.5};\n double best=-1;int bx1[MAXN],by1[MAXN],bx2[MAXN],by2[MAXN];\n auto save=[&](){for(int i=0;i>tinfo;\n vector>ph1;\n // Phase 1: Quick 2-pass evaluation\n for(int trial=0;msf()<2200;trial++){\n uint32_t seed=(uint32_t)(trial*7919+12345);\n double pr=prs[trial==0?0:1+(trial-1)%5];\n splits.clear();rng.seed(seed);p_rand=pr;\n doBuild(all,0,0,10000,10000);recompute();\n for(int p=0;p<2&&msf()<2200;p++)if(!lsPass())break;\n double q=computeScore();\n tinfo.emplace_back(seed,pr);\n ph1.emplace_back(q,(int)tinfo.size()-1);\n if(q>best){best=q;save();}\n }\n // Phase 2: Full LS on top trials\n sort(ph1.rbegin(),ph1.rend());\n for(auto&[q,tid]:ph1){\n if(msf()>4500)break;\n splits.clear();rng.seed(tinfo[tid].first);p_rand=tinfo[tid].second;\n doBuild(all,0,0,10000,10000);recompute();\n while(msf()<4500)if(!lsPass())break;\n double sc=computeScore();\n if(sc>best){best=sc;save();}\n }\n for(int i=0;i(long long)H)continue;long long area=(long long)w*hh;double ratio=area<=(long long)ri?(double)area/ri:(double)ri/area;if(ratio>br){br=ratio;bw=w;bh=(int)hh;if(br>=1-1e-9){done=true;break;}}}}\n int a=max(x1,xi+1-bw),b=max(y1,yi+1-bh);\n cout<\nusing namespace std;\ntypedef chrono::steady_clock Clock;\nconst int N=50,MAXM=N*N+1;\nint si,sj,M,tid[N][N],pval[N][N];\nconst int dx[]={-1,1,0,0},dy[]={0,0,-1,1};\nconst char dc[]={'U','D','L','R'};\nmt19937 rng;\nbool tu[MAXM],btu[MAXM];\nint pi_[MAXM],pj_[MAXM],pt_[MAXM],bpi[MAXM],bpj[MAXM],bpt[MAXM];\nchar pmv[MAXM],bpmv[MAXM];\nint plen,blen;long long cscore,bscore;int ci,cj;\nvoid save_best(){if(cscore<=bscore)return;bscore=cscore;blen=plen;memcpy(btu,tu,M);memcpy(bpi,pi_,plen*4);memcpy(bpj,pj_,plen*4);memcpy(bpt,pt_,plen*4);if(plen>1)memcpy(bpmv,pmv,plen-1);}\nvoid restore_best(){cscore=bscore;plen=blen;memcpy(tu,btu,M);memcpy(pi_,bpi,plen*4);memcpy(pj_,bpj,plen*4);memcpy(pt_,bpt,plen*4);if(plen>1)memcpy(pmv,bpmv,plen-1);ci=pi_[plen-1];cj=pj_[plen-1];}\nvoid walk_init(){fill(tu,tu+M,false);plen=1;ci=si;cj=sj;pi_[0]=si;pj_[0]=sj;pt_[0]=tid[si][sj];tu[tid[si][sj]]=true;cscore=pval[si][sj];}\nbool walk_step(double a,double b,double g,double g2){\n int bd=-1;double bh=-1e18;\n for(int d=0;d<4;d++){\n int ni=ci+dx[d],nj=cj+dy[d];\n if((unsigned)ni>=(unsigned)N||(unsigned)nj>=(unsigned)N)continue;\n int t=tid[ni][nj];if(tu[t])continue;\n tu[t]=true;\n int cnt=0;double nv=0,nv2=0;\n for(int d2=0;d2<4;d2++){\n int nni=ni+dx[d2],nnj=nj+dy[d2];\n if((unsigned)nni>=(unsigned)N||(unsigned)nnj>=(unsigned)N)continue;\n int t2=tid[nni][nnj];if(tu[t2])continue;\n cnt++;nv+=pval[nni][nnj];\n for(int d3=0;d3<4;d3++){\n int n3i=nni+dx[d3],n3j=nnj+dy[d3];\n if((unsigned)n3i>=(unsigned)N||(unsigned)n3j>=(unsigned)N)continue;\n int t3=tid[n3i][n3j];\n if(!tu[t3]&&t3!=t2)nv2+=pval[n3i][n3j];\n }\n }\n tu[t]=false;\n double h=a*pval[ni][nj]+g*nv+g2*nv2-b*cnt+(cnt==0?-1e6:0.0)\n +uniform_real_distribution(-0.5,0.5)(rng);\n if(h>bh){bh=h;bd=d;}\n }\n if(bd==-1)return false;\n int ni=ci+dx[bd],nj=cj+dy[bd];\n tu[tid[ni][nj]]=true;cscore+=pval[ni][nj];pmv[plen-1]=dc[bd];\n pi_[plen]=ni;pj_[plen]=nj;pt_[plen]=tid[ni][nj];plen++;ci=ni;cj=nj;return true;\n}\nvoid walk_extend(double a,double b,double g,double g2){while(walk_step(a,b,g,g2));}\nvoid walk_undo(int s){s=min(s,plen-1);while(s-->0){plen--;tu[pt_[plen]]=false;cscore-=pval[pi_[plen]][pj_[plen]];}ci=pi_[plen-1];cj=pj_[plen-1];}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n rng.seed(chrono::steady_clock::now().time_since_epoch().count());\n cin>>si>>sj;\n for(int i=0;i>tid[i][j];\n for(int i=0;i>pval[i][j];\n M=0;for(int i=0;i(0.5,2.0)(rng);\n double b=uniform_real_distribution(0,25)(rng);\n double g=uniform_real_distribution(0,1.0)(rng);\n double g2=uniform_real_distribution(0,0.1)(rng);\n if(iter%4==0||blen<=1){walk_init();}\n else{\n restore_best();\n int mb=blen-1,back,r=rng()%10;\n if(r<5)back=uniform_int_distribution(1,max(1,mb/10))(rng);\n else if(r<8)back=uniform_int_distribution(max(1,mb/10),max(1,mb/3))(rng);\n else back=uniform_int_distribution(max(1,mb/3),mb)(rng);\n walk_undo(back);\n }\n walk_extend(a,b,g,g2);\n save_best();\n }\n cout<\nusing namespace std;\nconst int N=30;\nconst double DELTA_VAR=1e6,INIT_SIG2_R=1e8,INIT_SIG2_E=1e7,MIN_SIG2=1e4;\ndouble mu_row[N],sig2_row[N],mu_col[N],sig2_col[N];\ndouble mu_h[N][N-1],sig2_h[N][N-1],mu_v[N-1][N],sig2_v[N-1][N];\nbool obs_h[N][N-1],obs_v[N-1][N];\ndouble wh(int i,int j){return obs_h[i][j]?mu_h[i][j]:mu_row[i];}\ndouble wv(int i,int j){return obs_v[i][j]?mu_v[i][j]:mu_col[j];}\nstring dijkstra(int sr,int sc,int tr,int tc){\n static double dist[N*N];static int par[N*N];static char pdir[N*N];\n fill(dist,dist+N*N,1e18);\n priority_queue,vector>,greater<>> pq;\n int src=sr*N+sc,dst=tr*N+tc;dist[src]=0;pq.push({0.0,src});\n while(!pq.empty()){\n auto[d,u]=pq.top();pq.pop();\n if(d>dist[u]+1e-9)continue;if(u==dst)break;\n int r=u/N,c=u%N;\n if(r>0){int nv=(r-1)*N+c;double nd=d+wv(r-1,c);if(nd0){int nv=r*N+(c-1);double nd=d+wh(r,c-1);if(nd>sr>>sc>>tr>>tc;\n string path=dijkstra(sr,sc,tr,tc);cout<>obs;\n double noise_var=(double)obs*obs/300.0;\n int kh[N]={},lv[N]={};\n struct E{bool is_h;int i,j;};vector edges;\n int r=sr,c=sc;\n for(char ch:path){\n if(ch=='U'){edges.push_back({false,r-1,c});lv[c]++;r--;}\n else if(ch=='D'){edges.push_back({false,r,c});lv[c]++;r++;}\n else if(ch=='L'){edges.push_back({true,r,c-1});kh[r]++;c--;}\n else{edges.push_back({true,r,c});kh[r]++;c++;}\n }\n double pred_r=0,pvar_r=0;\n for(int i=0;i0){pred_r+=kh[i]*mu_row[i];pvar_r+=(double)kh[i]*kh[i]*sig2_row[i]+kh[i]*DELTA_VAR;}\n for(int j=0;j0){pred_r+=lv[j]*mu_col[j];pvar_r+=(double)lv[j]*lv[j]*sig2_col[j]+lv[j]*DELTA_VAR;}\n double tvr=pvar_r+noise_var,resr=(double)obs-pred_r;\n for(int i=0;i0){double K=sig2_row[i]*kh[i]/tvr;mu_row[i]=clamp(mu_row[i]+K*resr,1000.0,9000.0);sig2_row[i]=max(sig2_row[i]*(1.0-K*kh[i]),MIN_SIG2);}\n for(int j=0;j0){double K=sig2_col[j]*lv[j]/tvr;mu_col[j]=clamp(mu_col[j]+K*resr,1000.0,9000.0);sig2_col[j]=max(sig2_col[j]*(1.0-K*lv[j]),MIN_SIG2);}\n for(auto& e:edges){\n if(e.is_h&&!obs_h[e.i][e.j]){obs_h[e.i][e.j]=true;mu_h[e.i][e.j]=mu_row[e.i];sig2_h[e.i][e.j]=INIT_SIG2_E;}\n else if(!e.is_h&&!obs_v[e.i][e.j]){obs_v[e.i][e.j]=true;mu_v[e.i][e.j]=mu_col[e.j];sig2_v[e.i][e.j]=INIT_SIG2_E;}\n }\n double pred_e=0,pvar_e=0;\n for(auto& e:edges){pred_e+=(e.is_h?mu_h[e.i][e.j]:mu_v[e.i][e.j]);pvar_e+=(e.is_h?sig2_h[e.i][e.j]:sig2_v[e.i][e.j]);}\n double tve=pvar_e+noise_var,rese=(double)obs-pred_e;\n for(auto& e:edges){\n double& mu=e.is_h?mu_h[e.i][e.j]:mu_v[e.i][e.j];\n double& s2=e.is_h?sig2_h[e.i][e.j]:sig2_v[e.i][e.j];\n double K=s2/tve;mu=clamp(mu+K*rese,1000.0,9000.0);s2=max(s2*(1.0-K),MIN_SIG2);\n }\n }\n return 0;\n}","ahc004":"#include \nusing namespace std;\nconst int N=20,MAXM=800,MAXL=12;\nint M,bs,score;\nint8_t grid[N][N],bg[N][N],h_mm[N][MAXM][N],v_mm[N][MAXM][N];\nint match_count[MAXM],slen[MAXM];\nint8_t S[MAXM][MAXL],char_pos[MAXM][8][MAXL],char_pos_cnt[MAXM][8];\nuint8_t char_appears[MAXM];\nint unsat_arr[MAXM],unsat_cnt,unsat_pos[MAXM];\nvoid unsat_remove(int k){int pos=unsat_pos[k];if(pos<0)return;int last=unsat_arr[--unsat_cnt];unsat_arr[pos]=last;unsat_pos[last]=pos;unsat_pos[k]=-1;}\nvoid unsat_add(int k){if(unsat_pos[k]>=0)return;unsat_pos[k]=unsat_cnt;unsat_arr[unsat_cnt++]=k;}\nvoid apply_cell(int r,int c,int oc,int nc){\n uint8_t mask=(1u<0&&nm==0){unsat_add(k);score--;}else if(om==0&&nm>0){unsat_remove(k);score++;}}grid[r][c]=nc;}\nint compute_delta(int r,int c,int oc,int nc){\n uint8_t mask=(1u<0)-(match_count[k]>0);}return d;}\nvoid recompute(){score=0;unsat_cnt=0;fill(unsat_pos,unsat_pos+M,-1);\n for(int r=0;r0)score++;else unsat_add(k);}}\nvoid safe_refresh(){\n int votes[N][N][8];memset(votes,0,sizeof(votes));\n for(int k=0;k=7?slen[k]-4:slen[k]-5));\n if(bm>rthr)continue;\n for(int p=0;pbv){bv=votes[r][c][ch];bc=ch;}\n if(bv>0&&grid[r][c]!=bc){int d=compute_delta(r,c,grid[r][c],bc);\n if(d>0){apply_cell(r,c,grid[r][c],bc);if(score>bs){bs=score;memcpy(bg,grid,sizeof(grid));}}}}}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n int n;cin>>n>>M;\n for(int k=0;k>s;slen[k]=s.size();char_appears[k]=0;memset(char_pos_cnt[k],0,8);\n for(int p=0;p0){double el=chrono::duration(chrono::steady_clock::now()-t0).count();\n if(el>=0.15||score>=M*2/5)break;\n int k=unsat_arr[rng()%(uint32_t)unsat_cnt];int bm=INT_MAX,br=0,bj=0,bd=0;\n for(int r=0;rbs){bs=score;memcpy(bg,grid,sizeof(grid));}}\n if(score!=bs){memcpy(grid,bg,sizeof(grid));recompute();}}\n double sa0=chrono::duration(chrono::steady_clock::now()-t0).count();\n double sad=max(0.1,TL-sa0);\n double phase1_end=sa0+sad*0.50;\n bool restart_triggered=false,restart_done=false;\n double T=5.0;\n for(int iter=0;;iter++){\n if((iter&0xFFF)==0){\n double el=chrono::duration(chrono::steady_clock::now()-t0).count();\n if(el>=TL)break;\n if(!restart_triggered&&el>=phase1_end){\n restart_triggered=true;\n if(bs0&&(iter%100000)==0&&bs0&&rng()%(uint32_t)M<(uint32_t)unsat_cnt){\n int k=unsat_arr[rng()%(uint32_t)unsat_cnt];int bm=INT_MAX,br=0,bj=0,bd=0;\n for(int rr=0;rr=7?slen[k]-4:slen[k]-5));\n if(bm>=1&&bm<=thr)for(int p=0;p=0||(double)rng()bs){bs=score;memcpy(bg,grid,sizeof(grid));}}\n }\n for(int i=0;i\nusing namespace std;\nint N, si, sj;\nvector grid;\nbool isRoad(int r, int c) { return r>=0&&r=0&&c,vector> dijkstra(int src) {\n vector dist(N*N,INF),par(N*N,-1);\n priority_queue,vector>,greater<>> pq;\n dist[src]=0; pq.push({0,src});\n const int DR[]={-1,1,0,0},DC[]={0,0,-1,1};\n while(!pq.empty()){auto[dd,u]=pq.top();pq.pop();if(dd>dist[u])continue;int r=u/N,c=u%N;for(int i=0;i<4;i++){int nr=r+DR[i],nc=c+DC[i];if(!isRoad(nr,nc))continue;int v=nr*N+nc,nd=dd+(grid[nr][nc]-'0');if(nd>N>>si>>sj;grid.resize(N);for(int i=0;i>grid[i];\n vector roads;vector rIdx(N*N,-1);\n for(int r=0;r> vis(R);\n for(int i=0;i=0&&isRoad(r,c-dd);dd++)vis[i].push_back(rIdx[r*N+(c-dd)]);for(int dd=1;r+dd=0&&isRoad(r-dd,c);dd++)vis[i].push_back(rIdx[(r-dd)*N+c]);}\n vector covered(R,false);int uncov=R;vector cnt(R);for(int i=0;i> pqsc;for(int i=0;i sents;\n while(uncov>0){int best=-1;while(!pqsc.empty()){auto[cv,id]=pqsc.top();pqsc.pop();if(cv==cnt[id]){best=id;break;}}if(best<0)break;sents.push_back(roads[best]);for(int j:vis[best])if(!covered[j]){covered[j]=true;uncov--;for(int k:vis[j]){cnt[k]--;pqsc.push({cnt[k],k});}}}\n int stSq=si*N+sj;{auto it=find(sents.begin(),sents.end(),stSq);if(it==sents.end())sents.insert(sents.begin(),stSq);else swap(*it,sents[0]);}\n int S=sents.size();\n {vector covCnt(R,0);for(int sq:sents)for(int j:vis[rIdx[sq]])covCnt[j]++;bool changed=true;while(changed){changed=false;for(int i=S-1;i>=1;i--){if(sents[i]<0)continue;int ridx=rIdx[sents[i]];bool red=true;for(int j:vis[ridx])if(covCnt[j]<=1){red=false;break;}if(red){for(int j:vis[ridx])covCnt[j]--;sents[i]=-1;changed=true;}}}sents.erase(remove(sents.begin(),sents.end(),-1),sents.end());S=sents.size();}\n vector> allDist(S),allPar(S);\n for(int i=0;i> dm(S,vector(S,INF));for(int i=0;i tvis(S,false);vector tour={0};tvis[0]=true;\n for(int s=1;s path;for(int cur=toSq;cur!=srcSq;cur=allPar[fi][cur])path.push_back(cur);reverse(path.begin(),path.end());int pp=srcSq;for(int nx:path){int pr=pp/N,pc=pp%N,nr=nx/N,nc=nx%N;if(nrpr)res+='D';else if(nc\nusing namespace std;\nint N,M,K,R;\nvector> d,succs;\nvector task_st,task_pre,task_w,worker_t,task_sd;\nvector> sk,et;\nvector> lb;\nvector>> obs;\nvector cp;\nint cur_day; double prior_sk;\nvoid upd_et(int w){for(int i=0;i0)ww+=df;}et[i][w]=ww<0.5?1.0:ww;}}\nvoid calc_cp(){cp.assign(N,0.0);for(int i=N-1;i>=0;i--){if(task_st[i]==2)continue;double mn;if(task_st[i]==1){double rem=task_sd[i]+et[i][task_w[i]]-cur_day;mn=max(1.0,rem);}else{mn=et[i][0];for(int j=1;j0)wh+=df;}double tgt=to==1?0.0:(double)to,err=wh-tgt;loss+=err*err;for(int k=0;ksk[w][k])delta[k]+=err;else if(err<-0.5&&d[ti][k]>0)delta[k]+=0.3*err;}}bool ch=false;for(int k=0;k>N>>M>>K>>R;d.assign(N,vector(K));for(int i=0;i>d[i][k];\nsuccs.assign(N,{});task_pre.assign(N,0);for(int r=0;r>u>>v;u--;v--;succs[u].push_back(v);task_pre[v]++;}\ntask_st.assign(N,0);task_w.assign(N,-1);worker_t.assign(M,-1);task_sd.assign(N,0);\nprior_sk=40.0/sqrt((double)K);sk.assign(M,vector(K,prior_sk));lb.assign(M,vector(K,0));obs.resize(M);\net.assign(N,vector(M));for(int j=0;javail,idle;for(int i=0;iav(avail.begin(),avail.end());sort(av.begin(),av.end(),[](int a,int b){return cp[a]>cp[b];});\nvector>asgn;setid=idle;\nfor(int t:av){if(id.empty())break;int bw=-1;double bt=1e18;for(int j:id)if(et[t][j]=2){vectorrcp_a(na,0.0);for(int i=0;i>nc;if(nc==-1)break;\nfor(int i=0;i>w;w--;int t=worker_t[w];int tk=cur_day-task_sd[t]+1;\nobs[w].push_back({t,tk});if(tk==1)for(int k=0;k\nusing namespace std;\nconst int OX=400,OY=400,TOT=1000,K=50,NN=2*K+1;\nint A[TOT],B[TOT],C[TOT],D[TOT],sel[K],NX[NN],NY[NN];\nint md(int x1,int y1,int x2,int y2){return abs(x1-x2)+abs(y1-y2);}\nint ec(int u,int v){return md(NX[u],NY[u],NX[v],NY[v]);}\nvoid refresh(){NX[0]=OX;NY[0]=OY;for(int i=0;i&r){int s=0;for(int i=0;i+1<(int)r.size();i++)s+=ec(r[i],r[i+1]);return s;}\nbool feasible(const vector&r){bool p[K+1]={};for(int v:r){if(v>=1&&v<=K)p[v]=true;else if(v>K&&!p[v-K])return false;}return true;}\nvector build_nn(){bool vis[NN]={},has[K+1]={};vector r={0};vis[0]=true;for(int s=0;s<2*K;s++){int cur=r.back(),bv=-1,bd=INT_MAX;for(int v=1;vK&&!has[v-K]))continue;int dd=ec(cur,v);if(dd&r){int n=r.size();bool any=false;for(int i=1;i&r){int n=r.size();bool any=false;for(int i=1;ibd){bd=rem-ins;bj=j;}}if(bj<0)continue;vector nr;nr.reserve(n);for(int k=0;k&r){int n=r.size();bool any=false;for(int i=1;ibd){bd=rem-ins;bj=j;}}if(bj<0)continue;vector nr;nr.reserve(n);for(int k=0;k&r){for(;;){bool a=two_opt_pass(r),b=or1_pass(r),c=or2_pass(r);if(!a&&!b&&!c)break;}}\nvoid quick_search(vector&r,int it=5){for(int i=0;i build_perturbed(const vector&base,int si){int pi=si+1,di=K+si+1;vector r;r.reserve(base.size()-2);for(int v:base)if(v!=pi&&v!=di)r.push_back(v);int n=r.size();int bc=INT_MAX,bp=0,bd2=1;for(int p=0;p res=r;res.insert(res.begin()+bp+1,pi);res.insert(res.begin()+bd2+1,di);return res;}\nvector double_bridge(const vector&r,mt19937&rng){int n=r.size();if(n<8)return r;int pos[4];do{for(int i=0;i<4;i++)pos[i]=1+rng()%(n-2);}while(pos[0]==pos[1]||pos[0]==pos[2]||pos[0]==pos[3]||pos[1]==pos[2]||pos[1]==pos[3]||pos[2]==pos[3]);sort(pos,pos+4);int a=pos[0],b=pos[1],c=pos[2],d=pos[3];vector nr;nr.reserve(n);for(int i=0;i&r){cout<(Clk::now()-T0).count();}\nint bcost=INT_MAX;vector broute;int bsel[K];bool inS[TOT]={};\nvoid trysel(){refresh();auto r=build_nn();full_search(r);int c=tcost(r);if(c pos(NN,-1);for(int i=0;i rem(K);for(int i=0;i> cands;for(int j=0;j0)cands.emplace_back(g,si,j);}}\nif(cands.empty())return false;int tk=min(10,(int)cands.size());partial_sort(cands.begin(),cands.begin()+tk,cands.end(),greater>());for(int ci=0;ci>A[i]>>B[i]>>C[i]>>D[i];\n {vector> sc(TOT);for(int i=0;i> sc(TOT);for(int i=0;i> sc(TOT);for(int i=0;i1.95)break;bool a=two_opt_pass(broute),b=or1_pass(broute),c=or2_pass(broute);if(!a&&!b&&!c)break;}\n emit(broute);\n return 0;\n}","ahc007":"#include \nusing namespace std;\nconst int N=400,M=1995;\nint px[N],py[N],eu[M],ev[M];\nlong long ed[M];\nstruct UF{\n int p[N],r[N];\n void init(){for(int i=0;i>>cadj(nc);\n for(int j=ie+1;jdist(nc,1e18);vectorhops(nc,0);\n priority_queue,vector>,greater<>>pq;\n dist[src]=0;pq.push({0.0,src});\n while(!pq.empty()){\n auto[dv,u]=pq.top();pq.pop();\n if(dv>dist[u]+1e-9)continue;\n if(u==dst)break;\n for(auto[v,w]:cadj[u]){double nd=dist[u]+w;if(nd1e17)return 2.0*ed[ie];\n int n=hops[dst];if(n<=0)return 2.0*ed[ie];\n return dist[dst]*(3.0*n+1.0)/(2.0*n*(n+1.0));\n}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n for(int i=0;i>px[i]>>py[i];\n for(int i=0;i>eu[i]>>ev[i];\n double dx=px[eu[i]]-px[ev[i]],dy=py[eu[i]]-py[ev[i]];\n ed[i]=llround(sqrt(dx*dx+dy*dy));\n }\n uf.init();\n for(int i=0;i>l;\n if(uf.same(eu[i],ev[i])){cout<<0<1){cout<<1<0)thr=(double)mn*(1.0+2.0/(k+1.0));\n else thr=corrected_dijkstra(i,cu,cv);\n if((double)l<=thr){cout<<1<\nusing namespace std;\nconst int G=30;\nint N,M,px[20],py[20],hx[10],hy[10];\nbool wall[G+2][G+2];\nint spx[20],spy[20],shx[10],shy[10];\nconst int ddx[]={-1,1,0,0},ddy[]={0,0,-1,1};\nconst char DIRS[]=\"UDLR\",WDIRS[]=\"udlr\";\nbool inb(int x,int y){return x>=1&&x<=G&&y>=1&&y<=G;}\nint dbuf[G+2][G+2];\nvoid bfs(int tx,int ty){\n for(int i=0;i<=G+1;i++)fill(dbuf[i],dbuf[i]+G+2,-1);\n dbuf[tx][ty]=0;queue>q;q.push({tx,ty});\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int d=0;d<4;d++){int nx=x+ddx[d],ny=y+ddy[d];if(!inb(nx,ny)||wall[nx][ny]||dbuf[nx][ny]!=-1)continue;dbuf[nx][ny]=dbuf[x][y]+1;q.push({nx,ny});}}\n}\nchar gmv(int sx,int sy,int tx,int ty){\n if(sx==tx&&sy==ty)return '.';bfs(tx,ty);if(dbuf[sx][sy]==-1)return '.';\n for(int d=0;d<4;d++){int nx=sx+ddx[d],ny=sy+ddy[d];if(!inb(nx,ny)||wall[nx][ny])continue;if(dbuf[nx][ny]==dbuf[sx][sy]-1)return DIRS[d];}return '.';\n}\nbool cpl(int wx,int wy){\n if(!inb(wx,wy)||wall[wx][wy])return false;\n for(int i=0;i>N;for(int i=0;i>px[i]>>py[i]>>t;}cin>>M;for(int i=0;i>hx[i]>>hy[i];\n double bv=-1e18;int wt=0,wp=16;bool hp=true;\n auto ch_cnt=[&](int wtype,int wpos,bool hpos)->int{int c=0;for(int i=0;i=wpos):(hpos?hx[i]=wpos);if(ok)c++;}return c;};\n auto ev=[&](int area,int pets,int wtype,int wpos,bool hpos)->double{return (double)area/900.0*pow(2.0,-(double)pets)*(0.7+0.3*ch_cnt(wtype,wpos,hpos)/M);};\n for(int c=2;c<=G;c++){int lp=0,rp=0;for(int i=0;ibv){bv=vl;wt=0;wp=c;hp=true;}if(vr>bv){bv=vr;wt=0;wp=c;hp=false;}}\n for(int r=2;r<=G;r++){int tp=0,bp=0;for(int i=0;ibv){bv=vt;wt=1;wp=r;hp=true;}if(vb>bv){bv=vb;wt=1;wp=r;hp=false;}}\n struct Task{int wx,wy,sx,sy,wd;};vector tasks(G);\n if(wt==0){if(hp)for(int r=1;r<=G;r++)tasks[r-1]={r,wp,r,wp-1,3};else for(int r=1;r<=G;r++)tasks[r-1]={r,wp-1,r,wp,2};}\n else{if(hp)for(int c=1;c<=G;c++)tasks[c-1]={wp,c,wp-1,c,1};else for(int c=1;c<=G;c++)tasks[c-1]={wp-1,c,wp,c,0};}\n vector hord(M);iota(hord.begin(),hord.end(),0);\n if(wt==0)sort(hord.begin(),hord.end(),[&](int a,int b){return hx[a] te(M),ct(M);for(int i=0;ibool{return wt==0?(hp?hy[h]=wp):(hp?hx[h]=wp);};\n for(int turn=0;turn<300;turn++){\n for(int i=0;i> pw;vector isp(M,false);\n // PASS 1: Wall placements first\n for(int h=0;h=te[h])continue;\n Task&t=tasks[ct[h]];bool ig=(ct[h]==G-1)&&!all_safe;\n if(hx[h]==t.sx&&hy[h]==t.sy&&!ig&&cpl(t.wx,t.wy)&&!pw.count({t.wx,t.wy})){\n acts[h]=WDIRS[t.wd];pw.insert({t.wx,t.wy});wall[t.wx][t.wy]=true;ct[h]++;isp[h]=true;\n }\n }\n // PASS 2: Movements using updated wall state\n for(int h=0;h=te[h]){acts[h]='.';continue;}\n Task&t=tasks[ct[h]];\n if(hx[h]==t.sx&&hy[h]==t.sy){acts[h]='.';continue;}\n char mv=gmv(hx[h],hy[h],t.sx,t.sy);\n acts[h]=mv;if(mv!='.')for(int d=0;d<4;d++)if(DIRS[d]==mv){hx[h]+=ddx[d];hy[h]+=ddy[d];break;}\n }\n cout<>s;for(char c:s){if(c=='U')px[i]--;else if(c=='D')px[i]++;else if(c=='L')py[i]--;else if(c=='R')py[i]++;}}\n }\n}","ahc009":"#include \nusing namespace std;\nint si,sj,ti,tj; double pf;\nbool H[20][19],V[19][20];\nint nb[400][4],G;\nvoid initNb(){for(int i=0;i<20;i++)for(int j=0;j<20;j++){int c=i*20+j;nb[c][0]=(i>0&&!V[i-1][j])?(i-1)*20+j:c;nb[c][1]=(i<19&&!V[i][j])?(i+1)*20+j:c;nb[c][2]=(j>0&&!H[i][j-1])?i*20+(j-1):c;nb[c][3]=(j<19&&!H[i][j])?i*20+(j+1):c;}}\nint dc(char c){return c=='U'?0:c=='D'?1:c=='L'?2:3;}\ndouble PP[201][400],PE[201];\nvoid buildP(const string&s,int fr){for(int t=fr;t<200;t++){int d=dc(s[t]);double*a=PP[t],*b=PP[t+1];memset(b,0,3200);for(int k=0;k<400;k++){double v=a[k];if(v<1e-15)continue;b[k]+=v*pf;b[nb[k][d]]+=v*(1-pf);}double e=b[G]*(401.-(t+1));b[G]=0;PE[t+1]=PE[t]+e;}}\ndouble evalF(const string&s,int fr){double p[400],q[400];memcpy(p,PP[fr],3200);double E=PE[fr];for(int t=fr;t<200;t++){int d=dc(s[t]);memset(q,0,3200);for(int k=0;k<400;k++){double v=p[k];if(v<1e-15)continue;q[k]+=v*pf;q[nb[k][d]]+=v*(1-pf);}E+=q[G]*(401.-(t+1));q[G]=0;memcpy(p,q,3200);}return E;}\nvoid setP(const string&s){memset(PP[0],0,3200);PP[0][si*20+sj]=1;PE[0]=0;buildP(s,0);}\nchrono::time_pointT0;\ndouble el(){return chrono::duration(chrono::steady_clock::now()-T0).count();}\ndouble hc(string&s,double E0,double tl){double be=E0;for(;;){if(el()>tl)break;bool imp=false;for(int t=0;t<200;t++){int od=dc(s[t]);for(int d=0;d<4;d++){if(d==od)continue;s[t]=\"UDLR\"[d];double e=evalF(s,t);if(e>be+1e-12){be=e;od=d;buildP(s,t);imp=true;}else s[t]=\"UDLR\"[od];}}if(!imp)break;}return be;}\nstring bfsPath(){int ds[400];fill(ds,ds+400,-1);int pr[400],pd[400];int src=si*20+sj;queueq;q.push(src);ds[src]=0;while(!q.empty()){int k=q.front();q.pop();for(int d=0;d<4;d++){int nk=nb[k][d];if(nk==k||ds[nk]!=-1)continue;ds[nk]=ds[k]+1;pr[nk]=k;pd[nk]=d;q.push(nk);}}string r;for(int c=G;c!=src;c=pr[c])r+=\"UDLR\"[pd[c]];reverse(r.begin(),r.end());return r;}\nstring greedyPath(){int bd[400];fill(bd,bd+400,-1);queueq;q.push(G);bd[G]=0;while(!q.empty()){int k=q.front();q.pop();for(int d=0;d<4;d++){int nk=nb[k][d];if(nk==k||bd[nk]!=-1)continue;bd[nk]=bd[k]+1;q.push(nk);}}double p[400]={},np[400];p[si*20+sj]=1;string s(200,'D');for(int t=0;t<200;t++){double bst=-1e18;int bd2=0;for(int d=0;d<4;d++){double g=0;for(int k=0;k<400;k++){if(p[k]<1e-15)continue;g+=p[k]*(1-pf)*(bd[k]-bd[nb[k][d]]);}if(g>bst){bst=g;bd2=d;}}s[t]=\"UDLR\"[bd2];memset(np,0,3200);for(int k=0;k<400;k++){if(p[k]<1e-15)continue;np[k]+=p[k]*pf;np[nb[k][bd2]]+=p[k]*(1-pf);}np[G]=0;memcpy(p,np,3200);}return s;}\nint main(){\n ios::sync_with_stdio(0);cin.tie(0);\n cin>>si>>sj>>ti>>tj>>pf;\n for(int i=0;i<20;i++){string r;cin>>r;for(int j=0;j<19;j++)H[i][j]=(r[j]=='1');}\n for(int i=0;i<19;i++){string r;cin>>r;for(int j=0;j<20;j++)V[i][j]=(r[j]=='1');}\n initNb();G=ti*20+tj;T0=chrono::steady_clock::now();\n string path=bfsPath();int K=(int)path.size();\n string s1(200,'D');for(int i=0;i<200;i++)s1[i]=path[i%K];\n string s2=greedyPath();\n setP(s1);double e1=hc(s1,PE[200],0.2);\n setP(s2);double e2=hc(s2,PE[200],0.4);\n string gb=(e1>=e2)?s1:s2;double gbE=max(e1,e2);\n setP(gb);\n mt19937 rng(42);uniform_real_distributionud(0,1);\n {\n string sc=gb;double scE=gbE;double T=2.0;int stp=0;double sa0=el();\n while(el()<1.2){\n int t=rng()%200,od=dc(sc[t]),nd=(od+1+(int)(rng()%3))%4;\n sc[t]=\"UDLR\"[nd];double e=evalF(sc,t),dlt=e-scE;\n if(dlt>0||ud(rng)gbE){gbE=e;gb=sc;}}\n else sc[t]=\"UDLR\"[od];\n if(++stp%500==0){double f=min(1.,max(0.,(el()-sa0)/(1.2-sa0)));T=2.*exp(-7.*f);if(scEgbE+1e-12){gbE=e;gb=p2;}\n }\n cout<\nusing namespace std;\nconst int N=30,TOTAL=N*N*4;\nconst int to_t[8][4]={{1,0,-1,-1},{3,-1,-1,0},{-1,-1,3,2},{-1,2,1,-1},{1,0,3,2},{3,2,1,0},{2,-1,0,-1},{-1,3,-1,1}};\nconst int di[4]={0,-1,0,1},dj[4]={-1,0,1,0};\nint tiles[N][N],init_t[N][N],rots[N][N],best_rots[N][N];\nlong long global_best=0;\ninline int apply_rot(int t,int r){if(t<=3)return(t+r)&3;if(t<=5)return 4+((t-4+r)&1);return 6+((t-6+r)&1);}\nint nxt[TOTAL];uint8_t col[TOTAL];\ninline void update_nxt(int i,int j){int base=(i*N+j)*4,t=tiles[i][j];for(int d=0;d<4;d++){int d2=to_t[t][d];if(d2<0){nxt[base+d]=-1;continue;}int ni=i+di[d2],nj=j+dj[d2];if((unsigned)ni>=(unsigned)N||(unsigned)nj>=(unsigned)N){nxt[base+d]=-1;continue;}nxt[base+d]=(ni*N+nj)*4+((d2+2)&3);}}\nlong long evaluate(){memset(col,0,TOTAL);int t1=0,t2=0;for(int s=0;s=0&&!col[c]){col[c]=1;c=nxt[c];}if(c>=0&&col[c]==1){int len=0,cc=c;do{cc=nxt[cc];len++;}while(cc!=c);if(len>t1){t2=t1;t1=len;}else if(len>t2)t2=len;}c=s;while(c>=0&&col[c]==1){col[c]=2;c=nxt[c];}}return(long long)t1*t2;}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n for(int i=0;i>s;for(int j=0;j(chrono::steady_clock::now()-ts).count();};\n const double TL=1.85;\n const double lnr=log(0.005/0.1);\n memset(best_rots,0,sizeof(best_rots));\n const int NUM_RESTART=6;\n double tpr=(TL-0.01)/NUM_RESTART;\n for(int restart=0;restart=2)r=(rng()%2)?1:0;}\n rots[i][j]=r;tiles[i][j]=apply_rot(t,r);\n }\n for(int i=0;i=(unsigned)N||(unsigned)nj>=(unsigned)N)continue;if(to_t[tiles[ni][nj]][(d+2)%4]>=0)cnt++;}if(cnt>bc){bc=cnt;br=r;}}\n if(br!=rots[i][j]){rots[i][j]=br;tiles[i][j]=apply_rot(t,br);update_nxt(i,j);chg=true;}\n }\n if(!chg)break;\n }\n long long cur=evaluate();\n double rs=gt(),re=rs+tpr;\n // Score greedy\n for(bool imp=true;imp&>()bl){bl=ns;bd=dr;}tiles[i][j]=st;update_nxt(i,j);}\n if(bd){rots[i][j]=(rots[i][j]+bd)&3;tiles[i][j]=apply_rot(ti,rots[i][j]);update_nxt(i,j);cur=bl;if(bl>global_best){global_best=bl;memcpy(best_rots,rots,sizeof(rots));}imp=true;}\n }\n }\n // SA with adaptive temperature\n double sa_init=max(100.0,(double)cur);\n double e=gt(),sa0=e;int cnt=0;\n while(e=0||rng()/4294967296.0global_best){global_best=ns;memcpy(best_rots,rots,sizeof(rots));}\n }else{tiles[i][j]=ot;update_nxt(i,j);}\n }\n }\n string out(N*N,'0');\n for(int i=0;i\nusing namespace std;\nint N,T,board[10][10],board_label[10][10],er,ec,tgt[10][10],avail[16];\nbool fixed_cells[10][10];\nstring out;\nvoid read_input(){cin>>N>>T;for(int i=0;i>s;for(int j=0;j='0'&&c<='9')?c-'0':c-'a'+10;if(!board[i][j]){er=i;ec=j;}}}}\nbool valid_pos(int v,int i,int j){return!((v&1)&&!j)&&!((v&2)&&!i)&&!((v&4)&&j==N-1)&&!((v&8)&&i==N-1);}\nbool is_tree(){bool vis[10][10]={};int sr=-1,sc=0;for(int i=0;i0){sr=i;sc=j;break;}if(sr<0)return false;queue>q;q.push({sr,sc});vis[sr][sc]=true;int cnt=1,ed=0;int dr[]={0,1,0,-1},dc[]={1,0,-1,0},cb[]={4,8,1,2},nb[]={1,2,4,8};while(!q.empty()){auto[r,c]=q.front();q.pop();for(int d=0;d<4;d++){int nr=r+dr[d],nc=c+dc[d];if(nr<0||nr>=N||nc<0||nc>=N||tgt[nr][nc]<=0)continue;if((tgt[r][c]&cb[d])&&(tgt[nr][nc]&nb[d])){ed++;if(!vis[nr][nc]){vis[nr][nc]=true;cnt++;q.push({nr,nc});}}}}return cnt==N*N-1&&ed==2*(N*N-2);}\nbool find_target(int pos){if(pos==N*N)return is_tree();int i=pos/N,j=pos%N;if(i==N-1&&j==N-1){tgt[i][j]=0;return find_target(pos+1);}bool fl=(j>0),nl=fl&&(tgt[i][j-1]&4);bool fu=(i>0),nu=fu&&(tgt[i-1][j]&8);for(int v=1;v<=15;v++){if(!avail[v]||!valid_pos(v,i,j))continue;if(fl&&!!(v&1)!=nl)continue;if(fu&&!!(v&2)!=nu)continue;avail[v]--;tgt[i][j]=v;if(find_target(pos+1))return true;avail[v]++;}tgt[i][j]=-1;return false;}\nvoid init_labels(){vector>cp[16],tp[16];for(int i=0;i0)cp[board[i][j]].push_back({i,j});if(tgt[i][j]>0)tp[tgt[i][j]].push_back({i,j});}for(int v=1;v<=15;v++){sort(cp[v].begin(),cp[v].end());sort(tp[v].begin(),tp[v].end());for(int k=0;k<(int)cp[v].size();k++){auto[cr,cc]=cp[v][k];auto[tr,tc]=tp[v][k];board_label[cr][cc]=tr*N+tc;}}}\nbool check_solvable(){vectors;for(int i=0;i=0)s.push_back(board_label[i][j]);int inv=0;for(int a=0;a<(int)s.size();a++)for(int b=a+1;b<(int)s.size();b++)if(s[a]>s[b])inv++;if(N%2)return!(inv%2);return(inv+er)%2==1;}\nvoid fix_parity(){if(check_solvable())return;for(int v=1;v<=15;v++){vector>cp;for(int i=0;i=2){swap(board_label[cp[0].first][cp[0].second],board_label[cp[1].first][cp[1].second]);if(check_solvable())return;swap(board_label[cp[0].first][cp[0].second],board_label[cp[1].first][cp[1].second]);}}}\nvoid do_move(char m){int tr=er,tc=ec;if(m=='U')tr--;else if(m=='D')tr++;else if(m=='L')tc--;else tc++;board[er][ec]=board[tr][tc];board_label[er][ec]=board_label[tr][tc];board[tr][tc]=0;board_label[tr][tc]=-1;er=tr;ec=tc;out+=m;}\nbool move_empty(int gr,int gc){if(er==gr&&ec==gc)return true;if((int)out.size()>=T||fixed_cells[gr][gc])return false;int NN=N*N;vectorprv(NN,-2);int s=er*N+ec,g=gr*N+gc;prv[s]=-1;queueq;q.push(s);int dr[]={-1,1,0,0},dcc[]={0,0,-1,1};while(!q.empty()){int cur=q.front();q.pop();if(cur==g)break;int r=cur/N,c=cur%N;for(int d=0;d<4;d++){int nr=r+dr[d],nc=c+dcc[d];if(nr<0||nr>=N||nc<0||nc>=N||fixed_cells[nr][nc])continue;int nxt=nr*N+nc;if(prv[nxt]!=-2)continue;prv[nxt]=cur;q.push(nxt);}}if(prv[g]==-2)return false;vectorpath;int cur=g;while(cur!=s){path.push_back(cur);cur=prv[cur];}reverse(path.begin(),path.end());for(int nxt:path){if((int)out.size()>=T)return false;int nr=nxt/N,nc=nxt%N;char m;if(nr==er-1)m='U';else if(nr==er+1)m='D';else if(nc==ec-1)m='L';else m='R';do_move(m);}return true;}\nbool bfs_tile(int&tr,int&tc,int dr,int dc){if(tr==dr&&tc==dc)return true;if((int)out.size()>=T)return false;int NN=N*N,t0=tr*N+tc,e0=er*N+ec,tg=dr*N+dc,tot=NN*NN;vectorprv(tot,-2);vectormv(tot,0);prv[t0*NN+e0]=-1;queueq;q.push(t0*NN+e0);int ddr[]={-1,1,0,0},ddc[]={0,0,-1,1};const char dch[]={'U','D','L','R'};int goal=-1;while(!q.empty()){int cur=q.front();q.pop();int ct=cur/NN,ce=cur%NN;if(ct==tg){goal=cur;break;}int er_=ce/N,ec_=ce%N;for(int d=0;d<4;d++){int nr=er_+ddr[d],nc=ec_+ddc[d];if(nr<0||nr>=N||nc<0||nc>=N||fixed_cells[nr][nc])continue;int np=nr*N+nc,nt=(np==ct)?ce:ct,ne=np;if(nt==ne)continue;int nst=nt*NN+ne;if(nst<0||nst>=tot||prv[nst]!=-2)continue;prv[nst]=cur;mv[nst]=dch[d];q.push(nst);}}if(goal<0){for(int e=0;epath;int cur=goal;while(cur!=t0*NN+e0){path.push_back(mv[cur]);cur=prv[cur];}reverse(path.begin(),path.end());for(char m:path){if((int)out.size()>=T)return false;do_move(m);}tr=dr;tc=dc;return true;}\npairfind_lbl(int lbl){for(int i=0;i=T)return;for(int col=0;col<=N-3&&(int)out.size()=T)return;auto[ar,ac]=find_lbl(row*N+(N-2));auto[br,bc]=find_lbl(row*N+(N-1));if(ar<0||br<0)return;if(ar==row&&ac==N-2&&br==row&&bc==N-1){fixed_cells[row][N-2]=fixed_cells[row][N-1]=true;return;}bfs_tile(ar,ac,row,N-1);if((int)out.size()>=T)return;auto[br2,bc2]=find_lbl(row*N+(N-1));if(br2<0)return;fixed_cells[row][N-1]=true;bfs_tile(br2,bc2,row+1,N-1);fixed_cells[row][N-1]=false;if((int)out.size()>=T)return;fixed_cells[row][N-1]=fixed_cells[row+1][N-1]=true;move_empty(row,N-2);fixed_cells[row][N-1]=fixed_cells[row+1][N-1]=false;if((int)out.size()=T)return;auto[ar,ac]=find_lbl((N-2)*N+col);auto[br,bc]=find_lbl((N-1)*N+col);if(ar<0||br<0)return;if(ar==N-2&&ac==col&&br==N-1&&bc==col){fixed_cells[N-2][col]=fixed_cells[N-1][col]=true;return;}bfs_tile(ar,ac,N-1,col);if((int)out.size()>=T)return;auto[br2,bc2]=find_lbl((N-1)*N+col);if(br2<0)return;fixed_cells[N-1][col]=true;bfs_tile(br2,bc2,N-1,col+1);fixed_cells[N-1][col]=false;if((int)out.size()>=T)return;fixed_cells[N-1][col]=fixed_cells[N-1][col+1]=true;move_empty(N-2,col);fixed_cells[N-1][col]=fixed_cells[N-1][col+1]=false;if((int)out.size()=T)return;int p0=(N-2)*N+(N-2),p1=(N-2)*N+(N-1),p2=(N-1)*N+(N-2);int a=board_label[N-2][N-2],b=board_label[N-2][N-1],c=board_label[N-1][N-2],d=board_label[N-1][N-1];if(a==p0&&b==p1&&c==p2&&d==-1)return;auto el=[&](int l)->int{if(l==p0)return 0;if(l==p1)return 1;if(l==p2)return 2;return 3;};auto enc=[](int v0,int v1,int v2,int v3){return v0*64+v1*16+v2*4+v3;};int gs=enc(0,1,2,3),ss=enc(el(a),el(b),el(c),el(d));if(ss==gs)return;arraypar;par.fill(-2);arraymfr;mfr.fill(0);queueq;q.push(ss);par[ss]=-1;static const int adj[4][2]={{1,2},{0,3},{0,3},{1,2}};static const char amv[4][2]={{'R','D'},{'L','D'},{'U','R'},{'U','L'}};while(!q.empty()){int cur=q.front();q.pop();if(cur==gs)break;int v[4]={(cur>>6)&3,(cur>>4)&3,(cur>>2)&3,cur&3};int ep=-1;for(int p=0;p<4;p++)if(v[p]==3){ep=p;break;}if(ep<0)continue;for(int k=0;k<2;k++){int np=adj[ep][k];char m=amv[ep][k];int nv[4]={v[0],v[1],v[2],v[3]};nv[ep]=nv[np];nv[np]=3;int nst=enc(nv[0],nv[1],nv[2],nv[3]);if(par[nst]==-2){par[nst]=cur;mfr[nst]=m;q.push(nst);}}}if(par[gs]==-2)return;vectorpath;int cur=gs;while(cur!=ss){path.push_back(mfr[cur]);cur=par[cur];}reverse(path.begin(),path.end());for(char m:path){if((int)out.size()>=T)break;do_move(m);}}\nvoid solve(){for(int row=0;row<=N-3&&(int)out.size()0)avail[board[i][j]]++;memset(tgt,-1,sizeof(tgt));memset(fixed_cells,0,sizeof(fixed_cells));memset(board_label,-1,sizeof(board_label));if(!find_target(0)){cout<<\"\\n\";return 0;}init_labels();fix_parity();solve();cout<\nusing namespace std;\ntypedef long long ll;\ntypedef unsigned long long ull;\ntypedef pair puu;\nstruct PH{size_t operator()(const puu&p)const{size_t h=hash()(p.first);h^=hash()(p.second)+0x9e3779b9ULL+(h<<6)+(h>>2);return h;}};\nmt19937 rng(42);\nint N,K,a[11],stx[5501],sty[5501];\nstruct Line{ll px,py,qx,qy;};\nconst int MK=100;\nLine cur_lines[MK],best_lines[MK];\nint8_t sgn_data[5501][MK];\null slo[5501],shi[5501];\nunordered_mapgrps;\nint b_arr[12],cscore,best_score;\nstruct Change{int idx;puu old_sig,new_sig;int8_t new_sgn;};\nvectorpending;\nvector>dvec;\nll ecross(const Line&l,ll x,ll y){return(l.qx-l.px)*(y-l.py)-(l.qy-l.py)*(x-l.px);}\nvoid upd(int oc,int nc){if(oc>=1&&oc<=10){cscore-=min(a[oc],b_arr[oc]);b_arr[oc]--;cscore+=min(a[oc],b_arr[oc]);}if(nc>=1&&nc<=10){cscore-=min(a[nc],b_arr[nc]);b_arr[nc]++;cscore+=min(a[nc],b_arr[nc]);}}\nvoid build(){grps.clear();grps.reserve(32768);grps.max_load_factor(0.3f);memset(b_arr,0,sizeof(b_arr));cscore=0;for(int i=0;i=0)?1:-1;sgn_data[i][j]=s;if(s==1){if(j<64)slo[i]|=(1ULL<second,it->second+1);it->second++;}}\nint try_ch(int j,const Line&nl){pending.clear();dvec.clear();for(int i=0;i=0)?1:-1;if(ns==sgn_data[i][j])continue;puu os{slo[i],shi[i]};ull nl2=slo[i],nh2=shi[i];if(j<64){if(ns==1)nl2|=(1ULL<second:0,nc=c+d;if(c>=1&&c<=10){nsc-=min(a[c],nb[c]);nb[c]--;nsc+=min(a[c],nb[c]);}if(nc>=1&&nc<=10){nsc-=min(a[nc],nb[nc]);nb[nc]++;nsc+=min(a[nc],nb[nc]);}}i=j2;}return nsc;}\nvoid do_ch(int j,const Line&nl){for(auto&ch:pending){{auto it=grps.find(ch.old_sig);upd(it->second,it->second-1);if(!--it->second)grps.erase(it);}slo[ch.idx]=ch.new_sig.first;shi[ch.idx]=ch.new_sig.second;sgn_data[ch.idx][j]=ch.new_sgn;{auto[it2,ins]=grps.emplace(ch.new_sig,0);upd(it2->second,it2->second+1);it2->second++;}}cur_lines[j]=nl;}\nLine rline(){double th=(rng()%314159)*(M_PI/314159.0);double r=(int)(rng()%18001)-9000;double cx=r*cos(th),cy=r*sin(th),sdx=-sin(th)*9000,sdy=cos(th)*9000;return{llround(cx+sdx),llround(cy+sdy),llround(cx-sdx),llround(cy-sdy)};}\nLine pline(const Line&l,int s){ll dx=(ll)(rng()%(2*s+1))-s,dy=(ll)(rng()%(2*s+1))-s;int t=rng()%3;if(t==0)return{l.px+dx,l.py+dy,l.qx,l.qy};if(t==1)return{l.px,l.py,l.qx+dx,l.qy+dy};return{l.px+dx,l.py+dy,l.qx-dx,l.qy-dy};}\nLine pline_perp(const Line&l,int s){ll ddx=l.qx-l.px,ddy=l.qy-l.py;double len=hypot((double)ddx,(double)ddy);if(len<1.0)return l;ll delta=(ll)(rng()%(2*s+1))-s;ll dx2=llround(delta*(-ddy)/len),dy2=llround(delta*ddx/len);return{l.px+dx2,l.py+dy2,l.qx+dx2,l.qy+dy2};}\nLine pline_rot(const Line&l,int max_mrad){\n double mx=(l.px+l.qx)*0.5,my=(l.py+l.qy)*0.5;\n double hdx=(l.qx-l.px)*0.5,hdy=(l.qy-l.py)*0.5;\n double angle=((int)(rng()%(2*max_mrad+1))-max_mrad)*0.001;\n double ca=cos(angle),sa=sin(angle);\n ll ndx=llround(hdx*ca-hdy*sa),ndy=llround(hdx*sa+hdy*ca);\n return{llround(mx)-ndx,llround(my)-ndy,llround(mx)+ndx,llround(my)+ndy};\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>N>>K;for(int d=1;d<=10;d++)cin>>a[d];for(int i=0;i>stx[i]>>sty[i];\n for(int i=0;i<50;i++){ll y=llround(-9000.0+18000.0*i/49.0);cur_lines[i]={-10000,y,10000,y};}\n for(int i=0;i<50;i++){ll x=llround(-9000.0+18000.0*i/49.0);cur_lines[50+i]={x,-10000,x,10000};}\n build();best_score=cscore;memcpy(best_lines,cur_lines,sizeof(cur_lines));\n pending.reserve(N+10);dvec.reserve(2*N+10);\n auto t0=chrono::steady_clock::now();\n double T=15.0;int iter=0;\n while(true){\n if(!(++iter&511)){\n double e=chrono::duration(chrono::steady_clock::now()-t0).count();\n if(e>2.90)break;\n T=max(0.05,15.0*pow(0.05/15.0,e/2.90));\n }\n int j=rng()%MK;Line nl;\n int sel=rng()%100;\n if(sel<22)nl=pline(cur_lines[j],30);\n else if(sel<38)nl=pline_perp(cur_lines[j],50);\n else if(sel<50)nl=pline_rot(cur_lines[j],10);\n else if(sel<68)nl=pline(cur_lines[j],300);\n else if(sel<82)nl=pline(cur_lines[j],2000);\n else nl=rline();\n if(nl.px==nl.qx&&nl.py==nl.qy)continue;\n int ns=try_ch(j,nl);int ds=ns-cscore;bool acc=(ds>=0);\n if(!acc&&T>0.01)acc=((double)(rng()>>8)/(double)(1u<<24))best_score){best_score=cscore;memcpy(best_lines,cur_lines,sizeof(cur_lines));}}\n }\n cout<\nusing namespace std;\nconst int MAXN=65;\nint N,M,cc;\nbool dots[MAXN][MAXN],h_seg[MAXN][MAXN],v_seg[MAXN][MAXN],d1_seg[MAXN][MAXN],d2_seg[MAXN][MAXN],inPQ[MAXN][MAXN];\nvector row_dots[MAXN],col_dots[MAXN],diag_dots[130],ad_dots[130];\nstruct Op{int x1,y1,x2,y2,x3,y3,x4,y4;};\nvector ops,best_ops;\npriority_queue>> work_pq;\nlong long best_score=0;\nint init_M; pair init_list[400];\nmt19937 rng(0); int run_mode=0;\nvoid ins(vector&v,int x){v.insert(lower_bound(v.begin(),v.end(),x),x);}\nvoid addDot(int x,int y){dots[x][y]=true;ins(row_dots[y],x);ins(col_dots[x],y);ins(diag_dots[x-y+64],x);ins(ad_dots[x+y],x);}\nbool ec(int x1,int y1,int x2,int y2){\n if(x1==x2){for(int y=min(y1,y2);yx1)==(y2>y1)){int xm=min(x1,x2),ym=min(y1,y2);for(int t=0;tx1)?1:-1,dy=(y2>y1)?1:-1;for(int t=1;tx1)==(y2>y1)){int xm=min(x1,x2),ym=min(y1,y2);for(int t=0;t=N||y2<0||y2>=N||x3<0||x3>=N||y3<0||y3>=N||x4<0||x4>=N||y4<0||y4>=N)return false;\n if(!dots[x2][y2]||!dots[x3][y3]||!dots[x4][y4])return false;\n if(!en(nx,ny,x2,y2)||!en(x2,y2,x3,y3)||!en(x3,y3,x4,y4)||!en(x4,y4,nx,ny))return false;\n if(!ec(nx,ny,x2,y2)||!ec(x2,y2,x3,y3)||!ec(x3,y3,x4,y4)||!ec(x4,y4,nx,ny))return false;\n ops.push_back({nx,ny,x2,y2,x3,y3,x4,y4});addDot(nx,ny);de(nx,ny,x2,y2);de(x2,y2,x3,y3);de(x3,y3,x4,y4);de(x4,y4,nx,ny);return true;}\nbool fap(int nx,int ny){\n if(dots[nx][ny])return false;\n vector> cands;\n for(int x2:row_dots[ny]){if(x2==nx)continue;for(int y2:col_dots[nx]){if(y2==ny||!dots[x2][y2])continue;int k=(abs(x2-nx)+abs(y2-ny))*2;if(run_mode>=2)k+=rng()%8;cands.emplace_back(k,x2,ny,x2,y2,nx,y2);}}\n for(int xa:diag_dots[nx-ny+64]){if(xa==nx)continue;int a=xa-nx;for(int xb:ad_dots[nx+ny]){if(xb==nx)continue;int b=xb-nx;int x3=nx+a+b,y3=ny+a-b;if(x3>=0&&x3=0&&y3=2)k+=rng()%8;cands.emplace_back(k,xa,ny+a,x3,y3,xb,ny-b);}}}\n sort(cands.begin(),cands.end());\n for(auto&[p,x2,y2,x3,y3,x4,y4]:cands)if(cando(nx,ny,x2,y2,x3,y3,x4,y4))return true;\n return false;}\nvoid addWork(int x,int y){if(x<0||x>=N||y<0||y>=N||dots[x][y]||inPQ[x][y])return;inPQ[x][y]=true;work_pq.push({(x-cc)*(x-cc)+(y-cc)*(y-cc)+1,{x,y}});}\nvoid afterPlace(int x,int y){\n for(int i=0;i>>();\n for(int i=0;i(chrono::steady_clock::now()-t0).count()>=lim)return;\n auto[w,pos]=work_pq.top();work_pq.pop();auto[x,y]=pos;inPQ[x][y]=false;\n if(dots[x][y])continue;if(fap(x,y))afterPlace(x,y);}}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>N>>M;cc=(N-1)/2;init_M=M;\n for(int i=0;i>init_list[i].first>>init_list[i].second;}\n vector>> pts;\n for(int x=0;x(chrono::steady_clock::now()-t0).count();};\n long long time_limit=4400;\n // Run 0 gets most time, subsequent runs get less\n long long run0_time=3200;\n long long other_time=300;\n int run=0;\n while(el()=2)rng.seed((long long)run*31337+12345);\n resetRun();\n long long run_start=el();\n long long run_end=(run==0)?min(time_limit-50,run_start+run0_time):min(time_limit-50,run_start+other_time);\n drainQ(run_end,t0);\n bool changed=true;\n while(changed&&el()=run_end)break;\n auto[x,y]=pos;if(dots[x][y])continue;\n if(fap(x,y)){changed=true;afterPlace(x,y);drainQ(run_end,t0);}\n }\n }\n long long sc=0;\n for(int x=0;xbest_score){best_score=sc;best_ops=ops;}\n run++;\n if(run==1&&el()>=run0_time)continue;\n }\n cout<\nusing namespace std;\ntypedef array,10> Grid;\n\nGrid applyTilt(Grid g, char dir) {\n if(dir=='L'){for(int i=0;i<10;i++){int p=0;for(int j=0;j<10;j++)if(g[i][j])g[i][p++]=g[i][j];for(;p<10;p++)g[i][p]=0;}}\n else if(dir=='R'){for(int i=0;i<10;i++){int p=9;for(int j=9;j>=0;j--)if(g[i][j])g[i][p--]=g[i][j];for(;p>=0;p--)g[i][p]=0;}}\n else if(dir=='F'){for(int j=0;j<10;j++){int p=0;for(int i=0;i<10;i++)if(g[i][j])g[p++][j]=g[i][j];for(;p<10;p++)g[p][j]=0;}}\n else{for(int j=0;j<10;j++){int p=9;for(int i=9;i>=0;i--)if(g[i][j])g[p--][j]=g[i][j];for(;p>=0;p--)g[p][j]=0;}}\n return g;\n}\nlong long computeScore(const Grid& g){\n bool vis[10][10]={};long long sum=0;int stk[100][2];\n const int dx[]={-1,1,0,0},dy[]={0,0,-1,1};\n for(int si=0;si<10;si++)for(int sj=0;sj<10;sj++){\n if(!g[si][sj]||vis[si][sj])continue;\n int f=g[si][sj],sz=0,top=0;stk[top][0]=si;stk[top][1]=sj;top++;vis[si][sj]=true;\n while(top>0){--top;int x=stk[top][0],y=stk[top][1];sz++;\n for(int d=0;d<4;d++){int nx=x+dx[d],ny=y+dy[d];\n if(nx>=0&&nx<10&&ny>=0&&ny<10&&!vis[nx][ny]&&g[nx][ny]==f){vis[nx][ny]=true;stk[top][0]=nx;stk[top][1]=ny;top++;}}}\n sum+=(long long)sz*sz;}\n return sum;\n}\nGrid placeCandy(Grid g,int p,int flav){\n int cnt=0;for(int i=0;i<10;i++)for(int j=0;j<10;j++)if(!g[i][j]&&++cnt==p){g[i][j]=flav;return g;}return g;\n}\nconst char DIRS[]={'F','B','L','R'};\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n int fl[100];for(int t=0;t<100;t++)cin>>fl[t];\n Grid grid={};\n mt19937 rng(20230101);\n const int S=5;\n for(int t=0;t<100;t++){\n int p;cin>>p;grid=placeCandy(grid,p,fl[t]);\n char bestDir='F';\n if(t<99){\n int nc1=99-t, nc2=98-t;\n // Pre-sample step t+2 positions (CRN across d1)\n int s3[S],s_cnt=0;\n if(t+2<100){\n s_cnt=min(S,nc2);\n if(nc2<=S){ for(int s=0;sbest){best=total;bestDir=d1;}\n }\n }\n cout<\n#include \nusing namespace std;\nusing namespace Eigen;\nint M, N; double eps;\ndouble normalCDF(double x){return 0.5*erfc(-x*M_SQRT1_2);}\nvector getDeg(const string& s,int n){vector d(n,0);int idx=0;for(int i=0;i getEig(const string& s,int n){MatrixXd A(n,n);A.setZero();int idx=0;for(int i=0;i sol(A,EigenvaluesOnly);vector ev(n);for(int i=0;iint{if(a>b)swap(a,b);return a*(2*n-a-1)/2+(b-a-1);};int cnt=0;for(int d=1;d> centers(M);\n for(int k=0;kbestScore){bestScore=score;optN=n;}\n }\n return optN;\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>M>>eps;N=computeOptimalN(M,eps);\n int ME=N*(N-1)/2;vector G(M);\n for(int k=0;k=20);\n int NS,FD;\n if(useEig){NS=min(500,NS_eig);FD=2*N;}\n else{long long opPS_deg=(long long)N*N;NS=max(30,min(1000,(int)(budget/max(1LL,(long long)M*opPS_deg))));FD=N;}\n vector> C(M,vector(FD,0.0));\n if(eps<1e-9){\n for(int k=0;k u(0.0,1.0);\n for(int k=0;k>h;\n vector hf(FD);auto dh=getDeg(h,N);for(int i=0;i\nusing namespace std;\ntypedef long long ll;\ntypedef pair pli;\nconst ll INF=1e18;\nconst int MXN=1005,MXM=3005,MXD=35,MAXCP=10;\nint N,M,D,K,EU[MXM],EV[MXM];ll EW[MXM];\nvector> G[MXN];\nll gd[MXN][MXN];double imp[MXM];int aday[MXM];\ndouble ADJ[MXM][MXD];int cutD[MXM][MXD];\nvector ladj[MXM],cpairs[MXM],dayE[MXD];int dpos[MXM];\nuint64_t rs=0xdeadbeef123ULL;\nuint64_t rng(){rs^=rs<<13;rs^=rs>>7;rs^=rs<<17;return rs;}\nint ri(int n){return(int)(rng()%(unsigned)n);}\ndouble rd(){return(rng()>>11)*(1.0/(1ull<<53));}\nvoid dijk(int s){fill(gd[s]+1,gd[s]+N+1,INF);gd[s][s]=0;priority_queue,greater>pq;pq.push({0,s});while(!pq.empty()){auto[d,u]=pq.top();pq.pop();if(d>gd[s][u])continue;for(auto&[v,e]:G[u]){ll nd=d+EW[e];if(nd,greater>pq;pq.push({0,s});while(!pq.empty()){auto[dd,u]=pq.top();pq.pop();if(dd>d[u])continue;if(u==t)return d[t];for(auto&[v,e]:G[u]){if(e==sk)continue;ll nd=dd+EW[e];if(nd bstk;\nvoid findBr(int sk,vector&br){fill(bdt+1,bdt+N+1,-1);int tm=0;bstk.clear();if((int)bstk.capacity()bdt[p.u])br.push_back({pe,sz});}}}}\nbool cvis[MXN];int cq[MXN];\nint main(){\n ios_base::sync_with_stdio(0);cin.tie(0);auto tst=chrono::steady_clock::now();\n cin>>N>>M>>D>>K;for(int i=0;i>EU[i]>>EV[i]>>EW[i];G[EU[i]].push_back({EV[i],i});G[EV[i]].push_back({EU[i],i});}\n for(int i=1;i<=N;i++){int x,y;cin>>x>>y;}\n for(int s=1;s<=N;s++)dijk(s);\n {vectorpar(N+1,-1),sv(N);vectorsz(N+1,1);iota(sv.begin(),sv.end(),1);for(int s=1;s<=N;s++){fill(par.begin(),par.end(),-1);fill(sz.begin(),sz.end(),1LL);sort(sv.begin(),sv.end(),[s](int a,int b){return gd[s][a]=0;i--){int v=sv[i];if(par[v]<0)continue;int p=(EU[par[v]]==v)?EV[par[v]]:EU[par[v]];sz[p]+=sz[v];}for(int v:sv){if(par[v]<0)continue;imp[par[v]]+=(double)sz[v];}}}\n for(int e=0;ebr;for(int e=0;emin(b.sz,N-b.sz);});for(auto&bi:br){if((int)cpairs[e].size()>=MAXCP)break;auto it=lower_bound(cpairs[e].begin(),cpairs[e].end(),bi.e);if(it==cpairs[e].end()||*it!=bi.e)cpairs[e].insert(it,bi.e);}}}\n for(int u=1;u<=N;u++){int dg=G[u].size();for(int i=0;ieo(M);iota(eo.begin(),eo.end(),0);sort(eo.begin(),eo.end(),[](int a,int b){return imp[a]>imp[b];});for(int e:eo){int best=-1;double bs=1e18;int bc=INT_MAX;for(int d=0;d=K)continue;int cuts=0;for(int f:cpairs[e])if(aday[f]==d)cuts++;double cf=0;for(int e2:ladj[e])if(aday[e2]==d)cf+=imp[e2];double sc=cf+1e-12*dc[d];if(cuts0)continue;double dl=imp[e1]*(ADJ[e1][d2]-ADJ[e1][d1])+imp[e2]*(ADJ[e2][d1]-ADJ[e2][d2])-2.*isAdj(e1,e2)*imp[e1]*imp[e2];sm+=fabs(dl);c++;}if(c>0)T=sm/c;if(T<1e-9)T=1.0;}\n double T0=T;\n for(long long step=0;;step++){\n if(step%200000==0){double el=chrono::duration(chrono::steady_clock::now()-tst).count();if(el>5.3)break;T=T0*exp(-10.*el/5.3);}\n int d1=ri(D),d2=ri(D);if(d1==d2||dayE[d1].empty()||dayE[d2].empty())continue;\n int e1=dayE[d1][ri(dayE[d1].size())],e2=dayE[d2][ri(dayE[d2].size())];\n int ic=isCut(e1,e2)?1:0;\n double dl=imp[e1]*(ADJ[e1][d2]-ADJ[e1][d1])+imp[e2]*(ADJ[e2][d1]-ADJ[e2][d2])-2.*isAdj(e1,e2)*imp[e1]*imp[e2];\n int dlc=(cutD[e1][d2]-ic)+(cutD[e2][d1]-ic)-cutD[e1][d1]-cutD[e2][d2];\n double dtot=dl+BIG*dlc;\n if(dtot<=0||(T>1e-9&&rd()0){fill(cvis+1,cvis+N+1,false);int h=0,t=0;cvis[1]=true;cq[t++]=1;while(h=K)continue;for(int ef:ladj[e]){ADJ[ef][d]-=imp[e];ADJ[ef][dd]+=imp[e];}for(int f:cpairs[e]){cutD[f][d]--;cutD[f][dd]++;}int p=dpos[e],L=dayE[d].back();dayE[d][p]=L;dpos[L]=p;dayE[d].pop_back();dpos[e]=dayE[dd].size();dayE[dd].push_back(e);aday[e]=dd;fx=true;}}if(!fx)break;}}\n for(int i=0;i\nusing namespace std;\nint D;string Fs[2][14],Rs[2][14];int bid,B[2][2744];bool occ[2][2744];\nstruct Box{int x,y,z,a,b,c;};\nbool bf(int r,int x0,int y0,int z0,int a,int b,int c){for(int i=0;i eB(int arr){vectorv;uint16_t fz[14]={},rz[14]={};for(int z=0;z gRL(int arr,int ax){vectorL;if(ax==0){for(int y=0;y=0){L.push_back({s,y,z,x-s,0});s=-1;}}}}else if(ax==1){for(int x=0;x=0){L.push_back({x,s,z,y-s,1});s=-1;}}}}else{for(int x=0;x=0){L.push_back({x,y,s,z-s,2});s=-1;}}}}return L;}\ndouble mS(const vector&L0,const vector&L1){mapc0,c1;for(auto&l:L0)c0[l.len]++;for(auto&l:L1)c1[l.len]++;double sc=0;int v0=0,v1=0;for(auto&[l,c]:c0){int cl=c1.count(l)?c1[l]:0;sc+=min(c,cl)*1.0/l;v0+=(c-min(c,cl))*l;}for(auto&[l,c]:c1){int cl=c0.count(l)?c0[l]:0;if(c>cl)v1+=(c-cl)*l;}return sc+max(v0,v1);}\nvoid doBox(){auto bx0=eB(0),bx1=eB(1);typedef arrayKey;auto gk=[](const Box&b)->Key{Key k={b.a,b.b,b.c};sort(k.begin(),k.end());return k;};map>g0,g1;for(int i=0;i<(int)bx0.size();i++)g0[gk(bx0[i])].push_back(i);for(int i=0;i<(int)bx1.size();i++)g1[gk(bx1[i])].push_back(i);vector>grps;for(auto&[k,v]:g0)if(g1.count(k))grps.push_back({k[0]*k[1]*k[2],k});sort(grps.rbegin(),grps.rend());for(auto&[vol,key]:grps){auto&v0=g0[key];auto&v1=g1[key];int p1=0;for(int i0:v0){auto&B0=bx0[i0];if(!bf(0,B0.x,B0.y,B0.z,B0.a,B0.b,B0.c))continue;while(p1<(int)v1.size()&&!bf(1,bx1[v1[p1]].x,bx1[v1[p1]].y,bx1[v1[p1]].z,bx1[v1[p1]].a,bx1[v1[p1]].b,bx1[v1[p1]].c))p1++;if(p1>=(int)v1.size())break;auto&B1=bx1[v1[p1++]];bid++;fB(0,B0.x,B0.y,B0.z,B0.a,B0.b,B0.c,bid);fB(1,B1.x,B1.y,B1.z,B1.a,B1.b,B1.c,bid);}}int bax0=1,bax1=1;double bsc=1e18;for(int a0=0;a0<3;a0++){auto Lt0=gRL(0,a0);for(int a1=0;a1<3;a1++){auto Lt1=gRL(1,a1);double sc=mS(Lt0,Lt1);if(sc>gl0,gl1;for(int i=0;i<(int)L0.size();i++)gl0[L0[i].len].push_back(i);for(int i=0;i<(int)L1.size();i++)gl1[L1[i].len].push_back(i);vectorlu0(L0.size(),false),lu1(L1.size(),false);for(auto&[l,v0]:gl0){auto it=gl1.find(l);if(it==gl1.end())continue;auto&v1=it->second;int mc=min((int)v0.size(),(int)v1.size());for(int j=0;j>rv0,rv1;for(int i=0;i<(int)L0.size();i++)if(!lu0[i])rv0.push_back({L0[i].len,i});for(int i=0;i<(int)L1.size();i++)if(!lu1[i])rv1.push_back({L1[i].len,i});sort(rv0.rbegin(),rv0.rend());sort(rv1.begin(),rv1.end());struct SO{int idx,off;};dequer0,r1;for(auto&[l,i]:rv0)r0.push_back({i,0});for(auto&[l,i]:rv1)r1.push_back({i,0});auto gp=[&](const Ln&s,int off)->tuple{return{s.x+(s.ax==0?off:0),s.y+(s.ax==1?off:0),s.z+(s.ax==2?off:0)};};while(!r0.empty()&&!r1.empty()){auto&[i0,o0]=r0.front();auto&[i1,o1]=r1.front();int ml=min(L0[i0].len-o0,L1[i1].len-o1);bid++;auto[x0,y0,z0]=gp(L0[i0],o0);auto[x1,y1,z1]=gp(L1[i1],o1);fL(0,x0,y0,z0,ml,L0[i0].ax,bid);fL(1,x1,y1,z1,ml,L1[i1].ax,bid);o0+=ml;o1+=ml;if(o0==L0[i0].len)r0.pop_front();if(o1==L1[i1].len)r1.pop_front();}while(!r0.empty()){auto[i0,o0]=r0.front();r0.pop_front();bid++;auto[x,y,z]=gp(L0[i0],o0);fL(0,x,y,z,L0[i0].len-o0,L0[i0].ax,bid);}while(!r1.empty()){auto[i1,o1]=r1.front();r1.pop_front();bid++;auto[x,y,z]=gp(L1[i1],o1);fL(1,x,y,z,L1[i1].len-o1,L1[i1].ax,bid);}}\nstruct Seg{int x,y,z,len,ax;};\nvector mF(int arr,int ax){vectorc;if(ax==2)for(int x=0;x=0){c.push_back({x,y,zs,z-zs,2});zs=-1;}}}else if(ax==1)for(int x=0;x=0){c.push_back({x,ys,z,y-ys,1});ys=-1;}}}else for(int y=0;y=0){c.push_back({xs,y,z,x-xs,0});xs=-1;}}}sort(c.begin(),c.end(),[](auto&a,auto&b){return a.len>b.len;});bool cx[14][14]={},cy[14][14]={};vectorsel;for(auto&s:c){bool u=false;for(int k=0;k&S0,const vector&S1){mapc0,c1;for(auto&s:S0)c0[s.len]++;for(auto&s:S1)c1[s.len]++;double sc=0;int v0=0,v1=0;for(auto&[l,n]:c0){int m=c1.count(l)?c1[l]:0;sc+=min(n,m)*1.0/l;v0+=(n-min(n,m))*l;}for(auto&[l,n]:c1){int m=c0.count(l)?c0[l]:0;if(n>m)v1+=(n-m)*l;}return sc+max(v0,v1);}\nvoid fS(int arr,const Seg&s,int id,int off,int len){for(int k=0;k&F0,const vector&F1){map>g0,g1;for(int i=0;i<(int)F0.size();i++)g0[F0[i].len].push_back(i);for(int i=0;i<(int)F1.size();i++)g1[F1[i].len].push_back(i);vectoru0(F0.size(),false),u1(F1.size(),false);for(auto&[l,v0]:g0){auto it=g1.find(l);if(it==g1.end())continue;auto&v1=it->second;int mc=min((int)v0.size(),(int)v1.size());for(int j=0;j>rv0,rv1;for(int i=0;i<(int)F0.size();i++)if(!u0[i])rv0.push_back({F0[i].len,i});for(int i=0;i<(int)F1.size();i++)if(!u1[i])rv1.push_back({F1[i].len,i});sort(rv0.rbegin(),rv0.rend());sort(rv1.begin(),rv1.end());deque>r0,r1;for(auto&[l,i]:rv0)r0.push_back({i,0});for(auto&[l,i]:rv1)r1.push_back({i,0});while(!r0.empty()&&!r1.empty()){auto&[i0,o0]=r0.front();auto&[i1,o1]=r1.front();int ml=min(F0[i0].len-o0,F1[i1].len-o1);bid++;fS(0,F0[i0],bid,o0,ml);fS(1,F1[i1],bid,o1,ml);o0+=ml;o1+=ml;if(o0==F0[i0].len)r0.pop_front();if(o1==F1[i1].len)r1.pop_front();}while(!r0.empty()){auto[i0,o0]=r0.front();r0.pop_front();bid++;fS(0,F0[i0],bid,o0,F0[i0].len-o0);}while(!r1.empty()){auto[i1,o1]=r1.front();r1.pop_front();bid++;fS(1,F1[i1],bid,o1,F1[i1].len-o1);}}\ndouble cScore(int mb){vectorv0(mb+1,0),v1(mb+1,0);for(int i=0;i0&&v1[k]>0)sc+=1.0/v0[k];else if(v0[k]>0)sc+=v0[k];else sc+=v1[k];}return sc;}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>D;for(int i=0;i<2;i++){for(int z=0;z>Fs[i][z];for(int z=0;z>Rs[i][z];}\n int bax0=2,bax1=2;double bscMF=1e18;vectorbF0,bF1;\n for(int a0=0;a0<3;a0++){auto F0=mF(0,a0);for(int a1=0;a1<3;a1++){auto F1=mF(1,a1);double sc=eS(F0,F1);if(sc\nusing namespace std;\ntypedef long long ll;\n\nint main() {\n auto tStart = chrono::steady_clock::now();\n auto msElapsed = [&]() {\n return (int)chrono::duration_cast(chrono::steady_clock::now()-tStart).count();\n };\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int N,M,K; cin>>N>>M>>K;\n vector X(N),Y(N);\n for(int i=0;i>X[i]>>Y[i];\n vector EU(M),EV(M); vector EW(M);\n for(int j=0;j>EU[j]>>EV[j]>>EW[j];EU[j]--;EV[j]--;}\n vector A(K),B(K);\n for(int k=0;k>A[k]>>B[k];\n const ll MAXP=5000,MAXP2=MAXP*MAXP,INF=(ll)4e18;\n // D2[i][k] and D2T[k][i] (transposed, cache-efficient for fixed k, varying i)\n vector> D2(N,vector(K)),D2T(K,vector(N));\n for(int i=0;i>> adj(N);\n for(int j=0;jll{if(!d2)return 0;ll p=(ll)sqrt((double)d2);while(p*p> spD(N,vector(N,INF));\n vector> spE(N,vector(N,-1)),spPr(N,vector(N,-1));\n for(int s=0;s,vector>,greater<>> pq;pq.push({0,s});\n while(!pq.empty()){auto[d,v]=pq.top();pq.pop();if(d>spD[s][v])continue;\n for(auto&[u,j]:adj[v]){ll nd=d+EW[j];if(nd term)->vector{\n term[0]=true;vectorT;for(int i=0;iin(TN,false);vectorkey(TN,INF);vectorpar(TN,-1);key[0]=0;\n for(int it=0;it=INF)break;in[u]=true;\n for(int w=0;weo(M,false);\n for(int i=0;i&reach)->pair,ll>{\n vector>vR(N);vectorvMx(N,0);\n for(int k=0;kMAXP2)return{{},INF};\n vR[bv].push_back(k);vMx[bv]=max(vMx[bv],best);\n }\n vectorPv(N,0);for(int i=0;itp(N);\n for(int u=0;utp[u].d[0]){tp[u].d[3]=tp[u].d[2];tp[u].k[3]=tp[u].k[2];tp[u].d[2]=tp[u].d[1];tp[u].k[2]=tp[u].k[1];tp[u].d[1]=tp[u].d[0];tp[u].k[1]=tp[u].k[0];tp[u].d[0]=d;tp[u].k[0]=k;}\n else if(d>tp[u].d[1]){tp[u].d[3]=tp[u].d[2];tp[u].k[3]=tp[u].k[2];tp[u].d[2]=tp[u].d[1];tp[u].k[2]=tp[u].k[1];tp[u].d[1]=d;tp[u].k[1]=k;}\n else if(d>tp[u].d[2]){tp[u].d[3]=tp[u].d[2];tp[u].k[3]=tp[u].k[2];tp[u].d[2]=d;tp[u].k[2]=k;}\n else if(d>tp[u].d[3]){tp[u].d[3]=d;tp[u].k[3]=k;}\n }}\n ll bD=0;int bU=-1,bV=-1,bT=-1;\n for(int u=0;u=0){ll d1v=D2T[tp[u].k[1]][v];if(d1v<=MAXP2){ll nPu=pVal(tp[u].d[2]),nPv=pVal(max({vMx[v],d0v,d1v}));ll d=nPu*nPu+nPv*nPv-Pu2-Pv2;if(d=0){ll d1v=D2T[tp[u].k[1]][v],d2v=D2T[tp[u].k[2]][v];if(d1v<=MAXP2&&d2v<=MAXP2){ll nPu=pVal(tp[u].d[3]),nPv=pVal(max({vMx[v],d0v,d1v,d2v}));ll d=nPu*nPu+nPv*nPv-Pu2-Pv2;if(du&&f0&&tp[v].k[0]>=0){ll d0u=D2T[tp[v].k[0]][u];if(d0u<=MAXP2){ll nMxU=max(tp[u].d[1],d0u),nMxV=max(tp[v].d[1],d0v);ll nPu=pVal(nMxU),nPv=pVal(nMxV);ll d=nPu*nPu+nPv*nPv-Pu2-Pv2;if(dP(N,0);ll pc=0;for(int i=0;i&eo)->tuple,ll,bool>{\n vectorreach(N,false);queueq;q.push(0);reach[0]=true;\n while(!q.empty()){int v=q.front();q.pop();for(auto&[u,j]:adj[v])if(eo[j]&&!reach[u]){reach[u]=true;q.push(u);}}\n ll ec=0;for(int j=0;jmstPar(N,-1),mstPE(N,-1);vector>mstCh(N);\n {vectorvis(N,false);vectorkey(N,INF);key[0]=0;\n priority_queue,vector>,greater<>>pq;pq.push({0,0});\n while(!pq.empty()){auto[d,v]=pq.top();pq.pop();if(vis[v])continue;vis[v]=true;for(auto&[u,j]:adj[v])if(!vis[u]&&EW[j]act(N,true);vector>vRes(N);vectorvmx(N,0),Pv(N,0);\n for(int k=0;k>bAs;vector>bAf;\n for(int v=1;vtmp;vector>ta;bool ok=true;\n for(int k:vRes[v]){ll best=INF;int bu=-1;for(int u=0;uMAXP2){ok=false;break;}ta.push_back({k,bu});if(!tmp.count(bu))tmp[bu]=vmx[bu];tmp[bu]=max(tmp[bu],best);}\n if(!ok)continue;\n for(auto&[u,nd]:tmp){ll np=pVal(nd);delta+=np*np-Pv[u]*Pv[u];}\n if(delta=0){act[bV]=false;ec0-=EW[mstPE[bV]];pc0-=Pv[bV]*Pv[bV];Pv[bV]=0;vmx[bV]=0;vRes[bV].clear();\n for(auto&[k,u]:bAs)vRes[u].push_back(k);\n for(auto&[u,nd]:bAf){pc0-=Pv[u]*Pv[u];vmx[u]=nd;Pv[u]=pVal(nd);pc0+=Pv[u]*Pv[u];}imp2=true;}\n }\n ll bestCost=INF;vectorbestEO(M,false);vectorbestP(N,0);\n auto updateBest=[&](const vector&eo,const vector&P,ll cost){if(costeo(M,false);for(int v=1;vterm,int maxIter=20){\n term[0]=true;\n for(int sit=0;sitnt(N,false);nt[0]=true;for(int i=0;i0)nt[i]=true;\n if(nt==term)break;term=nt;\n }\n };\n {vectort(N,false);for(int i=0;i0)t[i]=true;runSteiner(t);}\n {vectort(N,true);runSteiner(t);}\n // Time-based systematic terminal set search\n auto getTerms=[&]()->vector{\n vectort(N,false);t[0]=true;for(int i=0;i0)t[i]=true;return t;\n };\n bool sysImp=true;\n while(sysImp&&msElapsed()<1850){\n sysImp=false;\n vectorcurT=getTerms();\n // Try adding each non-terminal\n for(int v=1;vt=curT;t[v]=true;\n auto eo=buildSteiner(t);auto[sp,sc,sf]=evalEO(eo);\n if(sf&&sct=curT;t[v]=false;\n auto eo=buildSteiner(t);auto[sp,sc,sf]=evalEO(eo);\n if(sf&&sc\nusing namespace std;\n\nconst int N = 30;\nint init_board[N][N];\n\nint main() {\n ios::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 >> init_board[x][y];\n \n mt19937 rng(42);\n vector> best;\n \n auto do_heapify = [&](bool shuffle_within) -> vector> {\n int board[N][N];\n memcpy(board, init_board, sizeof(board));\n vector> ops;\n ops.reserve(5000);\n \n int ys[N];\n for (int x = N-2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) ys[y] = y;\n if (shuffle_within) {\n for (int i = x; i > 0; i--) {\n int j = rng() % (i + 1);\n swap(ys[i], ys[j]);\n }\n }\n for (int i = 0; i <= x; i++) {\n int y = ys[i];\n int cx = x, cy = y;\n while (cx < N-1) {\n int ny = (board[cx+1][cy] <= board[cx+1][cy+1]) ? cy : cy+1;\n if (board[cx][cy] <= board[cx+1][ny]) break;\n swap(board[cx][cy], board[cx+1][ny]);\n ops.push_back({cx, cy, cx+1, ny});\n cy = ny;\n cx++;\n }\n }\n }\n return ops;\n };\n \n // Standard left-to-right\n best = do_heapify(false);\n \n // Right-to-left\n {\n int board[N][N];\n memcpy(board, init_board, sizeof(board));\n vector> ops;\n ops.reserve(5000);\n for (int x = N-2; x >= 0; x--) {\n for (int y = x; y >= 0; y--) {\n int cx = x, cy = y;\n while (cx < N-1) {\n int ny = (board[cx+1][cy] <= board[cx+1][cy+1]) ? cy : cy+1;\n if (board[cx][cy] <= board[cx+1][ny]) break;\n swap(board[cx][cy], board[cx+1][ny]);\n ops.push_back({cx, cy, cx+1, ny});\n cy = ny;\n cx++;\n }\n }\n }\n if (ops.size() < best.size()) best = move(ops);\n }\n \n // Many random orderings - explore different valid heap targets\n for (int t = 0; t < 2000; t++) {\n auto ops = do_heapify(true);\n if (ops.size() < best.size())\n best = move(ops);\n }\n \n cout << best.size() << \"\\n\";\n for (auto& op : best)\n cout << op[0] << \" \" << op[1] << \" \" << op[2] << \" \" << op[3] << \"\\n\";\n}","toyota2023summer-final":"#include \nusing namespace std;\nconst int D9=9;\nint D,N,M;\nbool obs[D9][D9],hasc[D9][D9];\nint cnum[D9][D9],sr[D9*D9],sc[D9*D9],prank[D9][D9];\nint er,ec;\nconst int dr[4]={-1,1,0,0},dc[4]={0,0,-1,1};\nbool in_(int r,int c){return r>=0&&r=0&&c>q;q.push({er,ec});dist[er][ec]=0;\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+dr[i],ny=y+dc[i];if(!in_(nx,ny)||dist[nx][ny]>=0||obs[nx][ny])continue;dist[nx][ny]=dist[x][y]+1;q.push({nx,ny});}}\n vector>pos;\n for(int r=0;r&a,const pair&b){if(dist[a.first][a.second]!=dist[b.first][b.second])return dist[a.first][a.second]>q;q.push({er,ec});vis[er][ec]=1;\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+dr[i],ny=y+dc[i];if(!in_(nx,ny)||vis[nx][ny]||obs[nx][ny]||hasc[nx][ny])continue;vis[nx][ny]=1;q.push({nx,ny});}}\n}\nbool safe_place(int r,int c,const vector>&reach){\n bool vis[D9][D9];memset(vis,0,sizeof vis);\n queue>q;q.push({er,ec});vis[er][ec]=1;\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+dr[i],ny=y+dc[i];if(!in_(nx,ny)||vis[nx][ny]||obs[nx][ny]||hasc[nx][ny])continue;if(nx==r&&ny==c)continue;vis[nx][ny]=1;q.push({nx,ny});}}\n for(auto[pr,pc]:reach){if(pr==r&&pc==c)continue;if(!vis[pr][pc])return false;}\n return true;\n}\npairpick_place(int t){\n bool vis[D9][D9];bfs_emp(vis);\n int ir=sr[t],ic=sc[t];\n vector>reach;\n for(int r=0;rbest{-1,-1};int bd=INT_MAX,brk=-1;bool gots=false;\n for(auto[r,c]:reach){\n if(r==ir&&c==ic)continue;\n bool s=safe_place(r,c,reach);\n int d=abs(prank[r][c]-t),rk=prank[r][c];\n bool better=(!gots&&s)||(gots==s&&(dbrk)));\n if(better){best={r,c};bd=d;brk=rk;gots=s;}\n }\n return best;\n}\nvector>transport(){\n bool h[D9][D9];memcpy(h,hasc,sizeof h);\n vector>ord;ord.reserve(M);\n for(int s=0;s>q;q.push({er,ec});vis[er][ec]=1;\n int bn=INT_MAX,br=-1,bc=-1;\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+dr[i],ny=y+dc[i];if(!in_(nx,ny)||vis[nx][ny]||obs[nx][ny])continue;vis[nx][ny]=1;if(h[nx][ny]){if(cnum[nx][ny]>D>>N;\n memset(obs,0,sizeof obs);memset(hasc,0,sizeof hasc);memset(cnum,-1,sizeof cnum);\n er=0;ec=(D-1)/2;\n for(int i=0;i>r>>c;obs[r][c]=1;}\n build_sigma();\n for(int d=0;d>t;\n auto[r,c]=pick_place(t);\n hasc[r][c]=1;cnum[r][c]=t;\n cout<\nusing namespace std;\nusing namespace chrono;\nint n,m,g[50][50],og[50][50];\nbool adj[102][102];\nint ac[102][102],cc[102],dp[102];\nconst int dr[]={0,0,1,-1},dc[]={1,-1,0,0};\nauto t0=steady_clock::now();\nbool tok(){return duration_cast(steady_clock::now()-t0).count()<1700;}\nint gc(int r,int c){return(r<0||r>=n||c<0||c>=n)?0:g[r][c];}\nvoid cajad(){memset(adj,0,sizeof(adj));for(int i=0;iq;for(int c=0;c<=m;c++)if(adj[c][0]){dp[c]=0;q.push(c);}dp[0]=0;while(!q.empty()){int u=q.front();q.pop();for(int v=1;v<=m;v++)if(adj[u][v]&&dp[v]>dp[u]+1){dp[v]=dp[u]+1;q.push(v);}}}\nvoid rcp(){memset(ac,0,sizeof(ac));memset(cc,0,sizeof(cc));for(int i=0;i>q;q.push({sr,sc});v[sr][sc]=1;int cnt=1;while(!q.empty()){auto[cr,cc2]=q.front();q.pop();for(int d=0;d<4;d++){int nr=cr+dr[d],nc=cc2+dc[d];if(nr>=0&&nr=0&&nc=0&&nr=0&&nc=n||nc<0||nc>=n)continue;int ncol=g[nr][nc];if(!ncol)continue;bool hz=0;for(int d2=0;d2<4;d2++){int nr2=nr+dr[d2],nc2=nc+dc[d2];if(nr2==r&&nc2==c)continue;if(nr2<0||nr2>=n||nc2<0||nc2>=n){hz=1;break;}if(!g[nr2][nc2]){hz=1;break;}}if(!hz)ac[ncol][0]++;if(ncol==col)continue;bool s2=0;for(int d2=0;d2<4;d2++){int nr2=nr+dr[d2],nc2=nc+dc[d2];if(nr2==r&&nc2==c)continue;if(nr2>=0&&nr2=0&&nc2=n||nc<0||nc>=n)continue;int ncol=g[nr][nc];if(!ncol)continue;if(ncol!=col){bool st=0;for(int d2=0;d2<4;d2++){int nr2=nr+dr[d2],nc2=nc+dc[d2];if(nr2==r&&nc2==c)continue;if(nr2>=0&&nr2=0&&nc2=0&&nr2=0&&nc2=n||nc<0||nc>=n)continue;int c2=g[nr][nc];if(!c2||c2==col||dp[c2]>dp[col])continue;bool ok=1;for(int d2=0;d2<4;d2++){int dc2=gc(r+dr[d2],c+dc[d2]);if(dc2&&dc2!=col&&dc2!=c2&&!adj[c2][dc2]){ok=0;break;}}if(!ok)continue;ok=1;for(int d2=0;d2<4;d2++){int dc2=gc(r+dr[d2],c+dc[d2]);if(dc2&&dc2!=col&&dc2!=c2&&ac[col][dc2]<=1){ok=0;break;}}if(!ok)continue;if(dp[c2]=0){co=best;return 1;}return 0;}\nint czero(){int c=0;for(int i=0;i&ord){rcp();gtrim();int pz=czero();while(tok()){rcp();for(int p=0;p<10;p++){bool a=0;for(int idx:ord){int i=idx/n,j=idx%n,col=g[i][j],co;if(cra(i,j,co)){dra(i,j,col,co);a=1;}}if(!a)break;}gtrim();int z=czero();if(z<=pz)break;pz=z;}}\nstatic int bg[50][50];int bz=-1;\nvoid sv(){int z=czero();if(z>bz){bz=z;memcpy(bg,g,sizeof(g));}}\nint main(){\n t0=steady_clock::now();ios_base::sync_with_stdio(0);cin.tie(0);\n cin>>n>>m;for(int i=0;i>g[i][j];og[i][j]=g[i][j];}\n cajad();cdep();\n vectorord(n*n);iota(ord.begin(),ord.end(),0);\n mt19937 rng(42);\n for(int t=0;t==0||tok();t++){memcpy(g,og,sizeof(g));if(t>0)shuffle(ord.begin(),ord.end(),rng);run(ord);sv();}\n for(int i=0;i\nusing namespace std;\n\nint N, D, Q, q_used = 0;\n\nchar bq(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 q_used++;\n char c; cin >> c; return c;\n}\n\nint slm;\nvector ms(vector a) {\n if ((int)a.size() <= 1 || q_used >= slm) return a;\n int m = a.size() / 2;\n auto L = ms(vector(a.begin(), a.begin() + m));\n auto R = ms(vector(a.begin() + m, a.end()));\n vector r; int i = 0, j = 0;\n while (i < (int)L.size() && j < (int)R.size()) {\n if (q_used >= slm) break;\n if (bq({L[i]}, {R[j]}) != '>') r.push_back(L[i++]);\n else r.push_back(R[j++]);\n }\n while (i < (int)L.size()) r.push_back(L[i++]);\n while (j < (int)R.size()) r.push_back(R[j++]);\n return r;\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n cin >> N >> D >> Q;\n\n auto t0 = chrono::high_resolution_clock::now();\n auto el = [&]() {\n return chrono::duration(chrono::high_resolution_clock::now() - t0).count();\n };\n\n // Phase 1: Sort\n slm = Q / 2;\n vector ini(N); iota(ini.begin(), ini.end(), 0);\n vector ord = ms(ini);\n\n vector pos(N);\n for (int i = 0; i < N; i++) pos[ord[i]] = i;\n\n // Phase 2: Weight estimation via binary search on prefix sums\n int est_end = Q * 4 / 5;\n vector w(N, 1.0), ps(N + 1, 0.0);\n w[ord[0]] = 1.0; ps[1] = 1.0;\n\n for (int i = 1; i < N; i++) {\n int lo = 0, hi = i;\n while (lo < hi && q_used < est_end) {\n int mid = (lo + hi) / 2;\n if (bq({ord[i]}, vector(ord.begin(), ord.begin() + mid + 1)) == '>')\n lo = mid + 1;\n else hi = mid;\n }\n double wlo = ps[lo];\n double whi = (lo < i) ? ps[lo + 1] : ps[i] * 2.0;\n w[ord[i]] = max(w[ord[i-1]], (wlo + whi) / 2.0);\n ps[i+1] = ps[i] + w[ord[i]];\n }\n\n // Phase 3: LPT partition\n vector oi(N); iota(oi.begin(), oi.end(), 0);\n sort(oi.begin(), oi.end(), [&](int a, int b) {\n if (fabs(w[a]-w[b]) > 1e-12) return w[a] > w[b];\n return pos[a] > pos[b];\n });\n vector gw(D, 0.0);\n vector asgn(N, 0);\n for (int x : oi) {\n int g = (int)(min_element(gw.begin(), gw.end()) - gw.begin());\n asgn[x] = g; gw[g] += w[x];\n }\n\n // Phase 4: Local search with estimated weights\n double total = 0; for (double x : gw) total += x;\n double mean = total / D;\n\n for (int p = 0; p < 5000 && el() < 1.5; p++) {\n bool imp = false;\n // Single moves\n for (int x = 0; x < N; x++) {\n int g0 = asgn[x]; int bg = g0; double bd = 0;\n double d0 = gw[g0] - mean;\n for (int g = 0; g < D; g++) {\n if (g == g0) continue;\n double d1 = gw[g] - mean;\n double dc = d0*d0 + d1*d1 - (d0-w[x])*(d0-w[x]) - (d1+w[x])*(d1+w[x]);\n if (dc > bd) { bd = dc; bg = g; }\n }\n if (bg != g0) { gw[g0] -= w[x]; gw[bg] += w[x]; asgn[x] = bg; imp = true; }\n }\n // Swaps\n for (int i = 0; i < N && el() < 1.4; i++) {\n for (int j = i+1; j < N; j++) {\n if (asgn[i] == asgn[j]) continue;\n int gi = asgn[i], gj = asgn[j];\n double di = gw[gi]-mean, dj = gw[gj]-mean;\n double di2 = di-w[i]+w[j], dj2 = dj+w[i]-w[j];\n if (di*di + dj*dj > di2*di2 + dj2*dj2 + 1e-9) {\n gw[gi] += w[j]-w[i]; gw[gj] += w[i]-w[j];\n asgn[i] = gj; asgn[j] = gi; imp = true;\n }\n }\n }\n if (!imp) break;\n }\n\n // Phase 5: Actual balance improvement using remaining queries\n vector> gi(D);\n for (int x = 0; x < N; x++) gi[asgn[x]].push_back(x);\n for (int g = 0; g < D; g++)\n sort(gi[g].begin(), gi[g].end(), [&](int a, int b){ return pos[a] < pos[b]; });\n\n while (q_used + 2 <= Q && el() < 1.9) {\n int gh = (int)(max_element(gw.begin(), gw.end()) - gw.begin());\n int gl = (int)(min_element(gw.begin(), gw.end()) - gw.begin());\n if (gw[gh] <= gw[gl] + 1e-9 || gi[gh].empty() || gi[gl].empty()) break;\n\n char cmp = bq(gi[gh], gi[gl]);\n if (cmp == '=') { gw[gh] = gw[gl] = (gw[gh]+gw[gl])/2; continue; }\n if (cmp == '<') { swap(gh, gl); swap(gw[gh], gw[gl]); }\n\n auto& hv = gi[gh]; auto& lt = gi[gl];\n if ((int)hv.size() <= 1) continue;\n\n int lo = 0, hi = (int)hv.size() - 1;\n while (lo < hi && q_used + 1 <= Q && el() < 1.85) {\n int mid = (lo + hi) / 2;\n vector L2, R2 = lt;\n for (int k = 0; k < (int)hv.size(); k++) if (k != mid) L2.push_back(hv[k]);\n R2.push_back(hv[mid]);\n char r = bq(L2, R2);\n if (r == '=') { lo = hi = mid; break; }\n else if (r == '>') lo = mid + 1;\n else hi = mid;\n }\n lo = min(lo, (int)hv.size() - 1);\n if (lo > 0) {\n double da = fabs((gw[gh]-w[hv[lo]]) - (gw[gl]+w[hv[lo]]));\n double db = fabs((gw[gh]-w[hv[lo-1]]) - (gw[gl]+w[hv[lo-1]]));\n if (db < da) lo--;\n }\n\n int mv = hv[lo];\n asgn[mv] = gl;\n gw[gh] -= w[mv]; gw[gl] += w[mv];\n hv.erase(hv.begin() + lo);\n lt.insert(lower_bound(lt.begin(), lt.end(), mv,\n [&](int a, int b){ return pos[a] < pos[b]; }), mv);\n }\n\n while (q_used < Q) bq({0}, {1});\n\n for (int i = 0; i < N; i++) cout << asgn[i] << \" \\n\"[i==N-1];\n cout.flush();\n return 0;\n}","ahc026":"#include \nusing namespace std;\nint n, m;\nlong long run_algo(int mode, long long noise, vector> stacks, vector stk, vector pidx, vector sm, vector>& ops, mt19937_64& rng) {\n bool psfx = (mode <= 1), pat = (mode==1||mode==3);\n ops.clear(); long long energy = 0;\n auto recomp = [&](int t){ sm[t]=stacks[t].empty()?n+1:*min_element(stacks[t].begin(),stacks[t].end()); };\n for (int v = 1; v <= n; v++) {\n int s = stk[v], j = pidx[v];\n while ((int)stacks[s].size() > j+1) {\n int re=(int)stacks[s].size()-1, rs=re;\n while (rs>j+1&&stacks[s][rs-1]>stacks[s][rs]) rs--;\n int fu1=stacks[s][rs], ars=rs, bt=-1;\n if (psfx) {\n for (int sp=rs; sp<=re&&bt==-1; sp++) {\n int u1c=stacks[s][sp]; long long bs=LLONG_MIN; int bk=-1;\n for (int t=0;tu1c&&mt>u1c){ long long sc=(long long)n-tt; if(noise>0)sc+=(long long)(rng()%(2*noise+1))-noise; if(sc>bs){bs=sc;bk=t;} } }\n if(bk!=-1){ars=sp;bt=bk;}\n }\n }\n if (bt==-1) {\n long long best=LLONG_MIN;\n for (int t=0;tfu1)sc=(mt>fu1)?3LL*n*n+(n-tt):n*n+mt; else sc=mt-(long long)n*n; }\n else{ if(emp)sc=(long long)n; else if(tt>fu1)sc=2LL*n*n+(n-tt); else sc=tt-(long long)n*n; }\n if(noise>0)sc+=(long long)(rng()%(2*noise+1))-noise;\n if(sc>best){best=sc;bt=t;} }\n }\n energy+=(re-ars+1)+1; ops.push_back({stacks[s][ars],bt+1});\n int nb=(int)stacks[bt].size(), oz=(int)stacks[s].size();\n for(int p=ars;p>n>>m; int h=n/m;\n vector> is(m,vector(h)); vector ist(n+1),ip(n+1),ism(m,n+1);\n for(int i=0;i>is[i][j];ist[is[i][j]]=i;ip[is[i][j]]=j;} ism[i]=*min_element(is[i].begin(),is[i].end()); }\n long long be=LLONG_MAX; vector> bops; mt19937_64 rng(0);\n for(int mode=0;mode<4;mode++){ mt19937_64 d(0); vector> ops; long long e=run_algo(mode,0,is,ist,ip,ism,ops,d); if(e> ops; long long e=run_algo(mode,2000,is,ist,ip,ism,ops,rng);\n if(e\nusing namespace std;\nconst int MAXN=41,MAXC=1601,BUD=100000;\nint N,n;bool hw[MAXN][MAXN],vw[MAXN][MAXN];int dv[MAXN][MAXN];\nconst int DI[]={0,1,0,-1},DJ[]={1,0,-1,0};const char DC[]=\"RDLU\";\nint C(int i,int j){return i*N+j;}int RI(int c){return c/N;}int RJ(int c){return c%N;}\nbool OK(int i,int j,int d){int ni=i+DI[d],nj=j+DJ[d];if(ni<0||ni>=N||nj<0||nj>=N)return false;if(d==0)return !vw[i][j];if(d==1)return !hw[i][j];if(d==2)return !vw[i][nj];return !hw[ni][j];}\nshort AP[MAXC][MAXC];int AF[MAXC][MAXC];\nvoid bfs(int s){memset(AP[s],0xFF,n*sizeof(short));int fs[MAXC];AP[s][s]=0;fs[s]=s;static int q[MAXC];int h=0,tail=0;q[tail++]=s;while(h>N;n=N*N;\n for(int i=0;i>s;for(int j=0;j>s;for(int j=0;j>dv[i][j];\n for(int s=0;s lv(n,0);int pos=0,t=0;\n {vector vis(n,false);vis[0]=true;vector> stk;stk.reserve(n);stk.push_back({0,0});\n while(!stk.empty()){int u=stk.back().first;int& nd=stk.back().second;bool found=false;\n while(nd<4){int d=nd++;if(OK(RI(u),RJ(u),d)){int v=C(RI(u)+DI[d],RJ(u)+DJ[d]);if(!vis[v]){route+=DC[d];t++;pos=v;lv[v]=t;vis[v]=true;stk.push_back({v,0});found=true;break;}}}\n if(!found){stk.pop_back();if(!stk.empty()){int par=stk.back().first;for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==par){route+=DC[d];t++;pos=par;lv[par]=t;break;}}}}}\n for(int c=0;cBUD)rrt=true;\n if(rrt){const short* Ap=AP[pos];int best=-1;float bu=0.0f;\n for(int c=0;cBUD)continue;\n float u=sqd[c]*(float)(t-lv[c]+1)/(float)(dc+1);if(u>bu){bu=u;best=c;}}\n committed=best;if(committed<0)break;}\n int nx=AF[pos][committed];bool moved=false;\n for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==nx){route+=DC[d];pos=nx;t++;lv[pos]=t;moved=true;break;}\n if(!moved)break;}\n while(pos!=0){int nx=AF[pos][0];for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==nx){route+=DC[d];pos=nx;t++;break;}}\n cout<\nusing namespace std;\nint N,M,si,sj;\nvector targets;\nvector> charPos[26];\nint ovM[200][200];\nfloat amd[26][26],tC[200][200];\nvoid computeOvMatrix(){for(int i=0;i=1;k--){bool ok=true;for(int l=0;l greedyPerm(int start){vector used(M,false);vector perm;perm.reserve(M);perm.push_back(start);used[start]=true;while((int)perm.size()bov||(ov==bov&&tc greedyPermTC(int start){vector used(M,false);vector perm;perm.reserve(M);perm.push_back(start);used[start]=true;while((int)perm.size()&p){int s=0;for(int i=1;i<(int)p.size();i++)s+=ovM[p[i-1]][p[i]];return s;}\nfloat totalTCf(const vector&p){float s=0;for(int i=1;i<(int)p.size();i++)s+=tC[p[i-1]][p[i]];return s;}\nfloat combineScore(const vector&p){return permOv(p)*2.0f-totalTCf(p);}\nint swapGain(const vector&perm,int i,int j){int m=perm.size(),a=perm[i],b=perm[j],og=0,ng=0;if(i>0){og+=ovM[perm[i-1]][a];ng+=ovM[perm[i-1]][b];}if(j0){og+=ovM[perm[j-1]][b];ng+=ovM[perm[j-1]][a];}}return ng-og;}\nfloat swapDeltaTC(const vector&perm,int i,int j){int m=perm.size();int a=perm[i],b=perm[j];float oc=0,nc=0;if(i>0){oc+=tC[perm[i-1]][a];nc+=tC[perm[i-1]][b];}if(j0){oc+=tC[perm[j-1]][b];nc+=tC[perm[j-1]][a];}}return nc-oc;}\nfloat combinedGain(const vector&perm,int i,int j){return swapGain(perm,i,j)*2.0f-swapDeltaTC(perm,i,j);}\nbool swapOpt(vector&perm){int m=perm.size(),bg=0,bi=-1,bj=-1;for(int i=0;ibg){bg=g;bi=i;bj=j;}}if(bi==-1)return false;swap(perm[bi],perm[bj]);return true;}\nbool orOpt(vector&perm){int m=perm.size(),bg=0,bk=-1,bp=-1;for(int k=0;k rest;rest.reserve(m-1);for(int i=0;i0)?ovM[perm[k-1]][e]:0,ro=(k0&&k0)?ovM[rest[p-1]][e]:0,nr=(p<(int)rest.size())?ovM[e][rest[p]]:0,nb=(p>0&&p<(int)rest.size())?ovM[rest[p-1]][rest[p]]:0,g=nl+nr-nb-rc;if(g>bg){bg=g;bk=k;bp=p;}}}if(bk==-1)return false;int e=perm[bk];vector rest;rest.reserve(m-1);for(int i=0;i&perm){int m=perm.size();if(m<2)return false;vector diff(m-1),pref(m,0);for(int k=0;k0)g+=ovM[perm[i-1]][perm[j]]-ovM[perm[i-1]][perm[i]];if(jbg){bg=g;bi=i;bj=j;}}if(bi==-1)return false;reverse(perm.begin()+bi,perm.begin()+bj+1);return true;}\nvoid localSearch(vector&perm,int maxP=500){bool imp=true;int pass=0;while(imp&&pass&perm){string s=targets[perm[0]];for(int i=1;i<(int)perm.size();i++)s+=targets[perm[i]].substr(ovM[perm[i-1]][perm[i]]);return s;}\nvector> findPath(const string&s){int L=s.size(),G=N*N;const int INF=1e9;vector dp((L+1)*G,INF),prv((L+1)*G,-1);dp[si*N+sj]=0;for(int i=0;i> path(L);int pos=bp;for(int i=L;i>=1;i--){path[i-1]={pos/N,pos%N};pos=prv[i*G+pos];}return path;}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n auto t0=chrono::steady_clock::now();\n auto ms_el=[&](){return chrono::duration_cast(chrono::steady_clock::now()-t0).count();};\n cin>>N>>M>>si>>sj;\n for(int i=0;i>row;for(int j=0;j>targets[i];\n computeOvMatrix();computeAMD();computeTC();\n vector best;float bestScore=-1e18f;\n for(int s=0;sbestScore){bestScore=sc;best=p;}}\n for(int s=0;sbestScore){bestScore=sc;best=p;}}\n localSearch(best);bestScore=combineScore(best);\n {\n mt19937 rng(42);uniform_real_distribution ud(0.0,1.0);\n vector cur=best;float curScore=bestScore;double T=1.5;\n for(long long it=0;;it++){\n if(it%50000==0&&ms_el()>=1700)break;\n T=max(0.05,T*0.9999998);\n int i=rng()%M,j=rng()%M;if(i==j)continue;if(i>j)swap(i,j);\n float cg=combinedGain(cur,i,j);\n if(cg>0||ud(rng)bestScore){bestScore=curScore;best=cur;}}\n if(it%1000000==999999)curScore=combineScore(cur);\n }\n }\n if(ms_el()<1800)localSearch(best,200);\n string ss=buildString(best);\n auto path=findPath(ss);\n for(auto&[r,c]:path)cout<\nusing namespace std;\nint N,M,MAX_OPS;double eps,coef;int ops=0;\nstruct Field{int d,hi,hj;vector>cells;vectorrp,cp;vector>pos;};\nvectorF;vector>drld;vector>prob,ell;\nvectorrobs,cobs;int nrr=0,nrc=0;\ndouble qdiv(const vector>&c){ops++;cout<<\"q \"<>v;return v;}\nint qdrl(int i,int j){ops++;cout<<\"q 1 \"<>v;drld[i][j]=v;return v;}\nbool qans(const vector>&o){ops++;cout<<\"a \"<>r;return r==1;}\nvoid do_row_col(int reps){for(int rep=0;rep>c;for(int j=0;j>c;for(int i=0;itmr(N,0),tmc(N,0);\n for(int k=0;kkmr(N,0),kmc(N,0);\n for(int p=0;p>drow(N,vector(F[k].hi+1)),dcol(N,vector(F[k].hj+1));\n for(int i=0;ill(np,-1e300);double mx=-1e300;\n for(int p=0;p-1e250)?exp(ll[p]-mx):0.0;s+=prob[k][p];}\n if(s>1e-15)for(int p=0;p1e-15){for(auto&pp:prob[k])pp/=s;}\n else{int cnt=0;for(int p=0;p-1e29)cnt++;\n for(int p=0;p-1e29&&cnt>0)?1.0/cnt:0;\n if(cnt==0){fill(ell[k].begin(),ell[k].end(),0);fill(prob[k].begin(),prob[k].end(),1.0/np);}}}\n }\n}\ndouble field_entropy(int k){double H=0;for(double p:prob[k])if(p>1e-12)H-=p*log(p);return H;}\nvoid do_shape_query(int k){\n if(ops>=MAX_OPS-5)return;int np=(int)F[k].pos.size();\n int p1=-1,p2=-1;for(int p=0;pprob[k][p1]){p2=p1;p1=p;}else if(p2<0||prob[k][p]>prob[k][p2])p2=p;}\n if(p1<0||prob[k][p1]>0.98)return;\n auto[di1,dj1]=F[k].pos[p1];\n vector>S;\n if(p2>=0){auto[di2,dj2]=F[k].pos[p2];set>c2;for(auto[ci,cj]:F[k].cells)c2.insert({di2+ci,dj2+cj});for(auto[ci,cj]:F[k].cells){pairc={di1+ci,dj1+cj};if(!c2.count(c))S.push_back(c);}if((int)S.size()<2){S.clear();for(auto[ci,cj]:F[k].cells)S.push_back({di1+ci,dj1+cj});}}\n else{for(auto[ci,cj]:F[k].cells)S.push_back({di1+ci,dj1+cj});}\n if((int)S.size()<2)return;\n vectorSmap(N*N,false);for(auto[i,j]:S)Smap[i*N+j]=true;\n vectorovl(np,0);for(int p=0;p-1e29)for(int p=0;p-1e29)ell[k][p]-=newmax;\n}\nvector>get_oil_prob(){\n vector>noc(N,vector(N,1.0));\n for(int k=0;k>cvk(N,vector(N,0));for(int p=0;p<(int)F[k].pos.size();p++){double pp=prob[k][p];if(pp<1e-12)continue;auto[di,dj]=F[k].pos[p];for(auto[ci,cj]:F[k].cells)cvk[di+ci][dj+cj]+=pp;}for(int i=0;i>op(N,vector(N));for(int i=0;i>make_guess(const vector>&op,double thr=0.5){\n vector>res;for(int i=0;i0)||(drld[i][j]<0&&op[i][j]>thr);if(oil)res.push_back({i,j});}return res;\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>N>>M>>eps;MAX_OPS=2*N*N;coef=1.0-2.0*eps;\n drld.assign(N,vector(N,-1));robs.assign(N,0.0);cobs.assign(N,0.0);\n F.resize(M);\n for(int k=0;k>F[k].d;F[k].cells.resize(F[k].d);F[k].hi=F[k].hj=0;\n for(int t=0;t>F[k].cells[t].first>>F[k].cells[t].second;F[k].hi=max(F[k].hi,F[k].cells[t].first);F[k].hj=max(F[k].hj,F[k].cells[t].second);}\n F[k].rp.assign(F[k].hi+1,0);F[k].cp.assign(F[k].hj+1,0);for(auto[ci,cj]:F[k].cells){F[k].rp[ci]++;F[k].cp[cj]++;}\n for(int di=0;di+F[k].hi=0.15)?3:(eps>=0.08)?2:1;\n do_row_col(n_reps);\n run_mf(200);\n {int qb=min(60,MAX_OPS-ops-20);\n for(int q=0;qbe){be=h;bk=k;}}\n if(be<0.1)break;do_shape_query(bk);run_mf(15);}}\n apply_constraints();run_mf(100);\n while(ops=0)continue;double pu=min(op[i][j],1.0-op[i][j]);if(pu>bunc){bunc=pu;bi=i;bj=j;}}\n if(bunc<0.05||bi<0){for(int i=0;i0.05&&op[i][j]<0.95)qdrl(i,j);break;}\n qdrl(bi,bj);apply_constraints();run_mf(20);}\n {auto op=get_oil_prob();auto g=make_guess(op);if(ops\nusing namespace std;\ntypedef long long ll;\ntypedef tuple T3;\nint W,D,N;\nvector>a;\nstruct CS{\nint s0,st,nc,cw;\nint r(int d,int k)const{return a[d][s0+k*st];}\nvectorch(const vector&days)const{\n vectorh(nc,1);\n auto be=[&](int k,int cur)->ll{ll b=0;for(int d:days){int df=r(d,k)-cur*cw;if(df>0)b+=(ll)min(cw,df);}return b;};\n priority_queuepq;\n for(int k=0;k0)pq.push({b,k,1});}\n for(int rem=W-nc;rem>0&&!pq.empty();){auto[b,kk,cu]=pq.top();pq.pop();if(b<=0)break;h[kk]++;rem--;ll nb=be(kk,h[kk]);if(nb>0)pq.push({nb,kk,h[kk]});}\n sort(h.begin(),h.end());return h;\n}\nll ac(int d,const vector&h)const{ll c=0;for(int k=0;k0)c+=(ll)df*100;}return c;}\nsetgb(const vector&arr)const{setS;int y=0;for(int i=0;i+1<(int)arr.size();i++){y+=arr[i];S.insert(y);}return S;}\nll bd(const set&A,const set&B)const{ll c=0;for(int x:A)if(!B.count(x))c++;for(int x:B)if(!A.count(x))c++;return c*(ll)cw;}\nvectorag(const vector&h,const set&t)const{\n vectortg(t.begin(),t.end());multisetav(h.begin(),h.end());\n vectorarr;int S=0,j=0,nt=(int)tg.size();\n while(!av.empty()){while(j=tg[j])j++;if(j>=nt){for(int x:av)arr.push_back(x);break;}\n int nd=tg[j]-S;auto it=av.find(nd);\n if(it!=av.end()){arr.push_back(nd);S+=nd;av.erase(it);j++;}\n else{auto ub=av.upper_bound(nd);\n if(ub!=av.begin()){--ub;arr.push_back(*ub);S+=*ub;av.erase(ub);while(j=tg[j])j++;}\n else{it=av.begin();arr.push_back(*it);S+=*it;av.erase(it);while(j=tg[j])j++;}\n }\n }return arr;\n}\nvectorhc(vectorarr,const set&t)const{\n if(t.empty()||(int)arr.size()<=1)return arr;\n int n2=arr.size();vectorps(n2+1,0);for(int i=0;i0){swap(arr[i],arr[j]);for(int k=i+1;k<=j;k++)ps[k]+=dl;im=true;}\n }}return arr;\n}\npair>>solve()const{\n vector>C;vectorai(D);iota(ai.begin(),ai.end(),0);\n C.push_back(ch(ai));\n for(int d=0;d>SS(NC);for(int L=0;L>AR(D,vector(NC));\n for(int d=0;d>pcg(NC,vector(NC,0));\n for(int L1=0;L1>dp(D,vector(NC,INF));vector>frm(D,vector(NC,-1));\n for(int L=0;Ldpseq(D);dpseq[D-1]=bL;for(int d=D-2;d>=0;d--)dpseq[d]=frm[d+1][dpseq[d+1]];\n auto dls=[&](vectors)->vector{\n vector>Sv(D);vectordc(D,0);\n auto rb=[&](int from){for(int d=from;dpv=(d>0)?Sv[d-1]:set();\n if(d>0&&s[d]==s[d-1]){Sv[d]=Sv[d-1];dc[d]=AR[d][s[d]];}\n else{auto a2=ag(C[s[d]],pv);Sv[d]=gb(a2);dc[d]=AR[d][s[d]]+(d>0?bd(pv,Sv[d]):0LL);}}};\n rb(0);\n for(int it=0;it<15;it++){bool any=false;\n for(int d=0;dpv=(d>0)?Sv[d-1]:set();auto na=ag(C[L],pv);auto nSd=gb(na);\n ll nd2=AR[d][L]+(d>0?bd(pv,nSd):0LL);ll nd21=0;\n if(d+1&s)->pair>>{\n vector>arrs(D);ll cost=0;\n arrs[0]=C[s[0]];cost+=AR[0][s[0]];setcur=gb(arrs[0]);\n for(int d=1;dns=gb(arrs[d]);cost+=AR[d][s[d]]+bd(cur,ns);cur=ns;}}\n return{cost,arrs};\n };\n auto[c1,a1]=fs(dls(dpseq));\n vectorgseq(D);{\n vector>Sv(D);int L0=0;for(int L=0;Lapseq(D);for(int d=0;d>W>>D>>N;a.resize(D,vector(N));\n for(int d=0;d>a[d][k];\n ll best=2e18;int bK=1;\n vector>>>bcr;\n for(int K=1;K<=N&&K<=10;K++){\n if(N%K!=0||W%K!=0)continue;\n int npc=N/K,cw=W/K;\n vector>>>cr(K);ll tc=0;\n for(int c=0;c>rects(N);\n for(int c=0;cy(npc+1);y[0]=0;for(int j=0;j>strips(npc);for(int j=0;j\nusing namespace std;\nusing namespace chrono;\nconstexpr long long MOD=998244353;\nint N,M,K;long long sv[20][3][3],b[9][9],cur_score;\ninline long long add_mod(long long a,long long c){long long s=a+c;return s>=MOD?s-MOD:s;}\ninline long long sub_mod(long long a,long long c){return a>=c?a-c:a-c+MOD;}\nvoid apply_s(int m,int p,int q){for(int i=0;i<3;i++)for(int j=0;j<3;j++){long long&c=b[p+i][q+j];long long nv=add_mod(c,sv[m][i][j]);cur_score+=nv-c;c=nv;}}\nvoid undo_s(int m,int p,int q){for(int i=0;i<3;i++)for(int j=0;j<3;j++){long long&c=b[p+i][q+j];long long nv=sub_mod(c,sv[m][i][j]);cur_score+=nv-c;c=nv;}}\nstruct Op{int m,p,q;};\nconst int TK=15;\nlong long gdtv[3][3],gdts,gdtbest;int gdbs[9],gdcs[9],gdord[20],gdfl;bool gdto;steady_clock::time_point gddl;\nvoid tile_dfs(int dep,int mi){\n if(gdto)return;\n if(dep==9){if(++gdfl%200000==0&&steady_clock::now()>=gddl){gdto=true;return;}if(gdts>gdtbest){gdtbest=gdts;for(int d=0;d<9;d++)gdbs[d]=gdord[gdcs[d]];}return;}\n long long ub=gdts;for(int i=0;i<3;i++)for(int j=0;j<3;j++)ub+=(MOD-1)-gdtv[i][j];if(ub<=gdtbest)return;\n for(int idx=mi;idx>N>>M>>K;cur_score=0;\n for(int i=0;i>b[i][j];b[i][j]%=MOD;cur_score+=b[i][j];}\n for(int m=0;m>sv[m][i][j];\n auto t0=steady_clock::now();const long long TL_US=1850000;\n vectorops;ops.reserve(K);\n const int tpos[9][2]={{0,0},{0,3},{0,6},{3,0},{3,3},{3,6},{6,0},{6,3},{6,6}};\n gdfl=0;gdto=false;gddl=t0+milliseconds(1300);\n for(int tile=0;tile<9;tile++){\n int p=tpos[tile][0],q=tpos[tile][1];long long itv[3][3];long long its=0;\n for(int i=0;i<3;i++)for(int j=0;j<3;j++){itv[i][j]=b[p+i][q+j];its+=itv[i][j];}\n long long gn[20];int ord[20];iota(ord,ord+20,0);\n for(int m=0;mgn[b_];});\n long long grtv[3][3];memcpy(grtv,itv,sizeof(itv));long long grts=its;int grs[9];\n for(int d=0;d<9;d++){long long bg=0;int bm=0;for(int m=0;mbg){bg=g;bm=m;}}grs[d]=bm;for(int i=0;i<3;i++)for(int j=0;j<3;j++){long long nv=add_mod(grtv[i][j],sv[bm][i][j]);grts+=nv-grtv[i][j];grtv[i][j]=nv;}}\n memcpy(gdtv,itv,sizeof(itv));gdts=its;gdtbest=grts;for(int d=0;d<9;d++)gdbs[d]=grs[d];for(int m=0;m<20;m++)gdord[m]=ord[m];\n tile_dfs(0,0);\n int best_s[9];memcpy(best_s,gdbs,sizeof(gdbs));long long best_ts=gdtbest;\n bool imp=true;\n while(imp){imp=false;for(int d=0;d<9;d++){int om=best_s[d];for(int m=0;mbest_ts){best_ts=ts;memcpy(best_s,tmp,sizeof(tmp));imp=true;}}}}\n // 2-opt refinement\n bool imp2=true;\n while(imp2){\n imp2=false;long long b2ts=best_ts;int bd1=-1,bd2=-1,bm1=-1,bm2=-1;\n for(int d1=0;d1<9;d1++)for(int d2=d1+1;d2<9;d2++)for(int m1=0;m1b2ts){b2ts=ts;bd1=d1;bd2=d2;bm1=m1;bm2=m2;}\n }\n if(bd1>=0){best_ts=b2ts;best_s[bd1]=bm1;best_s[bd2]=bm2;imp2=true;}\n }\n for(int d=0;d<9;d++){apply_s(best_s[d],p,q);ops.push_back({best_s[d],p,q});}\n }\n long long best_score=cur_score;vectorbest_ops=ops;\n mt19937 rng(42);const int POS=N-2;\n auto rand_op=[&]()->Op{return{(int)(rng()%M),(int)(rng()%POS),(int)(rng()%POS)};};\n double T_start=1e8;\n if(!ops.empty()){long long sumd=0;int cnt=0;for(int i=0;i<3000;i++){int L=ops.size();if(!L)break;int idx=rng()%L;Op oo=ops[idx],no=rand_op();long long s0=cur_score;undo_s(oo.m,oo.p,oo.q);apply_s(no.m,no.p,no.q);long long d=cur_score-s0;sumd+=(d<0?-d:d);cnt++;undo_s(no.m,no.p,no.q);apply_s(oo.m,oo.p,oo.q);}if(cnt>0)T_start=max(1.0,(double)sumd/cnt);}\n double T=T_start,T_end=max(T_start*1e-7,1.0);\n for(long long it=0;;it++){\n if(it%50000==0){long long el=duration_cast(steady_clock::now()-t0).count();if(el>=TL_US)break;T=T_start*pow(T_end/T_start,(double)el/TL_US);}\n int L=ops.size();Op n1=rand_op(),o1{},o2{},n2{};int i1=-1,i2=-1,mt;\n if(L==0){mt=0;}else{int r=rng()%10;if(L==K)mt=(r<2)?1:(r<7)?2:3;else mt=(r<2)?0:(r<3)?1:(r<7)?2:3;if(mt==3&&L<2)mt=2;}\n if(mt==1||mt==2){i1=rng()%L;o1=ops[i1];}\n if(mt==3){i1=rng()%L;do{i2=rng()%L;}while(i2==i1);o1=ops[i1];o2=ops[i2];n2=rand_op();}\n long long s0=cur_score;\n switch(mt){case 0:apply_s(n1.m,n1.p,n1.q);break;case 1:undo_s(o1.m,o1.p,o1.q);break;case 2:undo_s(o1.m,o1.p,o1.q);apply_s(n1.m,n1.p,n1.q);break;case 3:undo_s(o1.m,o1.p,o1.q);undo_s(o2.m,o2.p,o2.q);apply_s(n1.m,n1.p,n1.q);apply_s(n2.m,n2.p,n2.q);break;}\n long long delta=cur_score-s0;bool acc=(delta>=0)||(T>0.5&&(double)(rng()%1000000)best_score){best_score=cur_score;best_ops=ops;}}\n else{switch(mt){case 0:undo_s(n1.m,n1.p,n1.q);break;case 1:apply_s(o1.m,o1.p,o1.q);break;case 2:undo_s(n1.m,n1.p,n1.q);apply_s(o1.m,o1.p,o1.q);break;case 3:undo_s(n2.m,n2.p,n2.q);undo_s(n1.m,n1.p,n1.q);apply_s(o2.m,o2.p,o2.q);apply_s(o1.m,o1.p,o1.q);break;}}\n }\n cout<\nusing namespace std;\nconst int N=5;\nint A[N][N],posR[N*N],posP[N*N],grid[N][N];\nint craneR,craneC,craneContainer;\nbool craneHolding;\nint recvSent[N],recvPickedUp[N],dispatchCount[N];\nmap> bufPos;\nset> usedBufs;\nbool done_[N*N];\nstring result;\nvoid sRecv(){for(int r=0;rtr)turn_('U');else if(craneC freeBuf(int tR=-1){\n if(tR>=0)for(int c=N-2;c>=1;c--){auto p=make_pair(tR,c);if(!usedBufs.count(p)&&grid[tR][c]==-1)return p;}\n for(int c=N-2;c>=1;c--)for(int r=0;r plan(){\n const int ND=N+1;int DB=1;for(int i=0;id,int r,int c)->int{int s=0;for(int i=0;i&d,int&r,int&c){c=s%N;s/=N;r=s%N;s/=N;for(int i=N-1;i>=0;i--){d[i]=s%ND;s/=ND;}};\n vectordist(NS,INT_MAX/2),pS(NS,-1),pG(NS,-1);\n priority_queue,vector>,greater<>>pq;\n arrayd0{};int s0=enc(d0,0,0);dist[s0]=0;pq.push({0,s0});\n while(!pq.empty()){auto[w,s]=pq.top();pq.pop();if(w>dist[s])continue;arrayd;int r,c;dec(s,d,r,c);\n for(int g=0;g=N)continue;int k=N*g+d[g],sR=posR[k];\n int tc=abs(r-sR)+c+abs(sR-g)+(N-1)+2+posP[k]*5;\n auto nd=d;nd[g]++;int ns=enc(nd,g,N-1);\n if(dist[s]+tcgD;gD.fill(N);int best=-1,bd=INT_MAX;\n for(int r=0;rord;if(best!=-1)for(int s=best;pS[s]!=-1;s=pS[s])ord.push_back(pG[s]);\n reverse(ord.begin(),ord.end());return ord;\n}\nvoid solve(){\n for(int r=0;r=0)deliver_(bSR,bSC,bBuf,!bBuf,bK/N);\n else{int bG=-1,bD=INT_MAX;\n for(int g=0;g=0)clearB_(posR[nNext(bG)]);}\n }\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n int n;cin>>n;for(int r=0;r>A[r][p];\n solve();cout<\nusing namespace std;\n\nint N;\nint h[20][20];\nint curR, curC, curLoad;\nvector ops;\n\nvoid doLoad(int d) { if (d<=0) return; ops.push_back(\"+\"+to_string(d)); h[curR][curC]-=d; curLoad+=d; }\nvoid doUnload(int d) { d=min(d,curLoad); if(d<=0) return; ops.push_back(\"-\"+to_string(d)); h[curR][curC]+=d; curLoad-=d; }\n\nvoid moveStep(char dir, int dr, int dc) {\n curR+=dr; curC+=dc; ops.push_back(string(1,dir));\n if (h[curR][curC]>0) doLoad(h[curR][curC]);\n else if (h[curR][curC]<0 && curLoad>0) doUnload(min(curLoad,-h[curR][curC]));\n}\n\nvoid moveTo(int tr, int tc) {\n while (curR!=tr || curC!=tc) {\n bool canR=(curR!=tr), canC=(curC!=tc);\n if (canR && canC) {\n int dr=curR0) { vR=abs(nRh); vC=abs(nCh); }\n else { vR=max(0,nRh); vC=max(0,nCh); if(!vR&&!vC){vR=abs(nRh);vC=abs(nCh);} }\n if (vR>=vC) moveStep(dr>0?'D':'U',dr,0); else moveStep(dc>0?'R':'L',0,dc);\n } else if (canR) { int dr=curR0?'D':'U',dr,0); }\n else { int dc=curC0?'R':'L',0,dc); }\n }\n}\n\nbool allZero() { for(int i=0;i>N;\n for(int i=0;i>h[i][j];\n curR=curC=curLoad=0;\n if(h[0][0]>0) doLoad(h[0][0]);\n \n while (!allZero() && (int)ops.size()<95000) {\n auto mhdist=[&](int i,int j){return abs(i-curR)+abs(j-curC);};\n \n int nearestD=INT_MAX, di=-1, dj=-1;\n for(int i=0;i0){double sc=(double)h[i][j]/(mhdist(i,j)+1); if(sc>bs){bs=sc;bi=i;bj=j;}}\n if(bi<0) break;\n moveTo(bi,bj);\n if(h[bi][bj]>0) doLoad(h[bi][bj]);\n } else {\n // Find best economically feasible supply: d*curLoad < nearestD*100\n double bestFS=-1; int fsi=-1,fsj=-1;\n for(int i=0;i=(long long)nearestD*100) continue;\n double sc=(double)h[i][j]/(d+1);\n if(sc>bestFS){bestFS=sc;fsi=i;fsj=j;}\n }\n if(fsi>=0) {\n moveTo(fsi,fsj);\n if(h[fsi][fsj]>0) doLoad(h[fsi][fsj]);\n } else if(di>=0) {\n moveTo(di,dj);\n if(h[di][dj]<0 && curLoad>0) doUnload(min(curLoad,-h[di][dj]));\n } else break;\n }\n }\n \n for(const auto& op:ops) cout<\nusing namespace std;\nint main(){\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int N,M,T; cin>>N>>M>>T;\n const int SC=2*N*(N-1),nn=N*N;\n vector> X(SC,vector(M));\n for(int i=0;i>X[i][j];\n mt19937 rng(42);\n vector> nbr(nn); vector ndeg(nn,0);\n for(int p=0;p0)nbr[p][ndeg[p]++]=p-N;if(r0)nbr[p][ndeg[p]++]=p-1;if(c vals(SC,0);\n for(int k=0;k ins(SC,false); vector sel;\n for(int l=0;lX[bk][l])bk=k;if(!ins[bk]){ins[bk]=true;sel.push_back(bk);}}\n {vector ord(SC);iota(ord.begin(),ord.end(),0);sort(ord.begin(),ord.end(),[&](int a,int b){return vals[a]>vals[b];});for(int k:ord){if((int)sel.size()>=nn)break;if(!ins[k]){ins[k]=true;sel.push_back(k);}}}\n vector pst(nn*nn);\n for(int i=0;i psum(nn,0);\n for(int i=0;i&g,int p)->int{int v=0;for(int d=0;d&g)->int{int s=0;for(int p=0;p g)->vector{bool imp=true;while(imp){imp=false;for(int a=0;abef)imp=true;else swap(g[a],g[b]);}}return g;};\n auto grinit=[&]()->vector{vector g(nn,-1);vector used(nn,false);for(int pos=0;pos0)cv+=pst[s*nn+g[pos-N]];if(c>0)cv+=pst[s*nn+g[pos-1]];int64_t ev=(int64_t)cv*1000000LL+psum[s];if(ev>bv){bv=ev;bs=s;}}g[pos]=bs;used[bs]=true;}return g;};\n int gbest=-1; vector bg;\n for(int rest=0;rest<3;rest++){\n double rt0=chrono::duration(chrono::steady_clock::now()-ts).count();\n if(rt0>=0.185) break;\n double tl=(0.185-rt0)/(3-rest),tend=rt0+tl;\n vector g(nn); double T0;\n if(rest==0){g=grinit();T0=200.0;}else{iota(g.begin(),g.end(),0);shuffle(g.begin(),g.end(),rng);T0=1000.0;}\n int cur=totsc(g),lb=cur; vector lg=g; double temp=T0;\n for(int it=0;;it++){\n if((it&0x7FF)==0){double now=chrono::duration(chrono::steady_clock::now()-ts).count();if(now>=tend)break;temp=T0*pow(0.1/T0,(now-rt0)/tl);}\n int p1=rng()%nn,p2=rng()%nn; if(p1==p2)continue;\n int bef=ctrb(g,p1)+ctrb(g,p2); swap(g[p1],g[p2]); int aft=ctrb(g,p1)+ctrb(g,p2); int d=aft-bef;\n if(d>=0||(rng()%1000000)<(int)(1e6*exp((double)d/temp))){cur+=d;if(cur>lb){lb=cur;lg=g;}}else swap(g[p1],g[p2]);\n }\n lg=locsrch(lg); int sc=totsc(lg); if(sc>gbest){gbest=sc;bg=lg;}\n }\n for(int i=0;i>X[i][j];\n }\n return 0;\n}","ahc038":"#include \nusing namespace std;\nint N,M,V;\nconst int DR[]={0,1,0,-1},DC[]={1,0,-1,0};\nint rx,ry,nfp,Vp,rfp=-1;\nint fpd[4],hld[4];\nstruct Del{int sr,sc,tr,tc;bool done;};\nvectorP;int np;\nvector>g;\nmap,int>sm;\nvectorops;\nbool navto(int tr,int tc,int pk,int td){\n while((rx!=tr||ry!=tc||fpd[pk]!=td)&&(int)ops.size()<99990){\n char mv='.';\n if(rx!=tr||ry!=tc){if(rxtr)mv='U';else if(ry=N||fc<0||fc>=N)continue;\n if(hld[k]<0){if(k==rfp)continue;auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}}\n else{int di=hld[k];if(P[di].tr==fr&&P[di].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di].done=true;hld[k]=-1;op[Vp+1+k]='P';}}\n }\n ops.push_back(op);\n }\n return rx==tr&&ry==tc&&fpd[pk]==td;\n}\nint pickfp(int di,int r,int c){\n sm.erase({r,c});\n int bk=-1,br=-1,bc=-1,bdir=-1,bv=INT_MAX;\n for(int k=0;k=0)continue;\n for(int d=0;d<4;d++){\n int ar=r-DR[d],ac=c-DC[d];if(ar<0||ar>=N||ac<0||ac>=N)continue;\n int md=abs(rx-ar)+abs(ry-ac),rot=min((d-fpd[k]+4)%4,(fpd[k]-d+4)%4),v=max(md,rot);\n if(v=99990){sm[{r,c}]=di;return -1;}\n string op(2*Vp,'.');bool picked=false;\n for(int k=0;k=N||fc<0||fc>=N)continue;\n if(k==bk&&fr==r&&fc==c&&g[r][c]==1&&hld[k]<0){hld[k]=di;g[r][c]=0;op[Vp+1+k]='P';picked=true;}\n else if(hld[k]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}}\n else if(hld[k]>=0){int di2=hld[k];if(P[di2].tr==fr&&P[di2].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di2].done=true;hld[k]=-1;op[Vp+1+k]='P';}}\n }\n ops.push_back(op);if(!picked){sm[{r,c}]=di;return -1;}return bk;\n}\nbool dropfp(int k,int di){\n if(hld[k]!=di)return true;\n int r=P[di].tr,c=P[di].tc;\n int bdir=-1,bar=-1,bac=-1,bv=INT_MAX;\n for(int d=0;d<4;d++){\n int ar=r-DR[d],ac=c-DC[d];if(ar<0||ar>=N||ac<0||ac>=N)continue;\n int md=abs(rx-ar)+abs(ry-ac),rot=min((d-fpd[k]+4)%4,(fpd[k]-d+4)%4),v=max(md,rot);\n if(v=99990)return false;\n string op(2*Vp,'.');bool ok=false;\n for(int k2=0;k2=N||fc<0||fc>=N)continue;\n if(k2==k&&fr==r&&fc==c&&g[r][c]==0&&hld[k2]==di){g[r][c]=1;P[di].done=true;hld[k2]=-1;op[Vp+1+k2]='P';ok=true;}\n else if(hld[k2]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k2]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k2]='P';}}\n else if(hld[k2]>=0){int di2=hld[k2];if(P[di2].tr==fr&&P[di2].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di2].done=true;hld[k2]=-1;op[Vp+1+k2]='P';}}\n }\n ops.push_back(op);return ok;\n}\nbool cbh(int bk){\n if(hld[bk]<0)return false;int di=hld[bk];\n pairtmp={-1,-1};\n {set>ts;for(auto&d:P)if(!d.done)ts.insert({d.tr,d.tc});\n auto val=[&](int r,int c)->bool{for(int d=0;d<4;d++){int a=r-DR[d],b=c-DC[d];if(a>=0&&a=0&&b>N>>M>>V;\n vectorsg(N),tg(N);for(auto&s:sg)cin>>s;for(auto&s:tg)cin>>s;\n vector>S,T;g.assign(N,vector(N,0));\n for(int i=0;imt(m,-1);\n {vectorsu(m,false),tu(m,false);\n for(int i=0;i=N||fc<0||fc>=N)continue;if(hld[k]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}}else{int di=hld[k];if(P[di].tr==fr&&P[di].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di].done=true;hld[k]=-1;op[Vp+1+k]='P';}}}};\n if(nfp>=2){string op(2*Vp,'.');if(nfp>=2){op[2]='R';fpd[1]=1;}if(nfp>=3){op[3]='R';fpd[2]=1;}if(nfp>=4){op[4]='L';fpd[3]=3;}orient_check(op);ops.push_back(op);}\n if(nfp>=3){string op(2*Vp,'.');op[3]='R';fpd[2]=2;orient_check(op);ops.push_back(op);}\n vectortsp(np);\n if(np>0){\n {vectorused(np,false);int cr=0,cc=0;for(int s=0;sint{if(b<0||b>=np)return 0;int r0=(a<0||a>=np)?0:P[tsp[a]].tr,c0=(a<0||a>=np)?0:P[tsp[a]].tc;return abs(r0-P[tsp[b]].sr)+abs(c0-P[tsp[b]].sc);};\n {bool imp=true;while(imp){imp=false;for(int i=0;i=0){imp=true;int val=tsp[bi];if(bj>bi){tsp.erase(tsp.begin()+bi);tsp.insert(tsp.begin()+bj,val);}else{tsp.erase(tsp.begin()+bi);tsp.insert(tsp.begin()+bj+1,val);}}}}\n }\n int stall=0,tsp_idx=0;\n while((int)ops.size()<97000){\n int tdone=0;for(auto&d:P)if(d.done)tdone++;if(tdone==np)break;\n bool prog=false;\n {int bk=-1,bd=INT_MAX;for(int k=0;k=0){if(!dropfp(bk,hld[bk]))cbh(bk);prog=true;}}\n if(!prog){\n while(tsp_idx=0){int k=pickfp(fi,P[fi].sr,P[fi].sc);if(k>=0){if(!dropfp(k,fi))cbh(k);prog=true;if(tsp_idx=0){if(cbh(k))prog=true;break;}\n if(!prog){int ci=-1,bd=INT_MAX;for(auto&[src,di]:sm){int d=abs(rx-src.first)+abs(ry-src.second);if(d=0){int k=pickfp(ci,P[ci].sr,P[ci].sc);if(k>=0&&cbh(k))prog=true;}}}\n if(prog)stall=0;\n else{stall++;if(stall>300)break;string op(2*Vp,'.');for(int k=0;k=N||fc<0||fc>=N)continue;if(hld[k]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}}else{int di=hld[k];if(P[di].tr==fr&&P[di].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di].done=true;hld[k]=-1;op[Vp+1+k]='P';}}}ops.push_back(op);}\n }\n for(auto&op:ops)cout<\nusing namespace std;\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(NULL);\n using Clock = chrono::steady_clock;\n auto t0 = Clock::now();\n auto elapsedMs = [&]() {\n return (long long)chrono::duration_cast(Clock::now()-t0).count();\n };\n int N; cin >> N;\n int M = 2*N;\n vector X(M), Y(M), W(M);\n for (int i=0; i>X[i]>>Y[i]; W[i]=(ix2)swap(x1,x2);if(y1>y2)swap(y1,y2);\n cout<<4<<\"\\n\"< bx(M),by(M);\n {\n vector idx(M); iota(idx.begin(),idx.end(),0);\n sort(idx.begin(),idx.end(),[&](int a,int b){return X[a]&fish,int lo,int hi)->pair{\n int cur=0,cs=-1,mx=0,blo=-1,bhi=-1;bool ir=false;\n for(int i=0,n=(int)fish.size();i=lo&&fish[i].other<=hi)gs+=fish[i].w;i++;}\n if(!ir){if(gs>0){cs=xv;cur=gs;ir=true;if(cur>mx){mx=cur;blo=cs;bhi=xv;}}}\n else{cur+=gs;if(cur>mx){mx=cur;blo=cs;bhi=xv;}if(cur<0){cur=0;ir=false;}}\n }\n return{blo,bhi};\n };\n auto evalRect=[&](int x1,int x2,int y1,int y2){\n int s=0;\n for(int i=0;i=x1&&X[i]<=x2&&Y[i]>=y1&&Y[i]<=y2)s+=W[i];\n return s;\n };\n auto coordDescent=[&](int x1,int x2,int y1,int y2)->tuple{\n x1=max(0,min(CMAX,x1));x2=max(0,min(CMAX,x2));\n y1=max(0,min(CMAX,y1));y2=max(0,min(CMAX,y2));\n if(x1>x2)swap(x1,x2);if(y1>y2)swap(y1,y2);\n int px1=-1,px2=-1,py1=-1,py2=-1;\n for(int it=0;it<20;it++){\n if(x1==px1&&x2==px2&&y1==py1&&y2==py2)break;\n px1=x1;px2=x2;py1=y1;py2=y2;\n auto[nx1,nx2]=kadane(bx,y1,y2);if(nx1>=0){x1=nx1;x2=nx2;}\n auto[ny1,ny2]=kadane(by,x1,x2);if(ny1>=0){y1=ny1;y2=ny2;}\n }\n return make_tuple(evalRect(x1,x2,y1,y2),x1,x2,y1,y2);\n };\n // Grid Kadane's\n const int G=200,step=CMAX/G;\n vector> grid(G,vector(G,0));\n for(int i=0;i cs(G,0);\n for(int gx2=gx1;gx2mx){mx=cur;ms=cst;me=gy;}if(cur<0){cur=0;cst=gy+1;}}\n if(me>=0&&mx>bgs){bgs=mx;bgx1=gx1;bgx2=gx2;bgy1=ms;bgy2=me;}\n }\n }\n int ix1=bgx1*step,ix2=min((bgx2+1)*step,CMAX);\n int iy1=bgy1*step,iy2=min((bgy2+1)*step,CMAX);\n int gscore=-1,rx1=0,rx2=1,ry1=0,ry2=1;\n auto tryRun=[&](int x1,int x2,int y1,int y2){\n auto[s,a,b,c,d]=coordDescent(x1,x2,y1,y2);\n if(s>gscore){gscore=s;rx1=a;rx2=b;ry1=c;ry2=d;}\n };\n tryRun(ix1,ix2,iy1,iy2);\n tryRun(0,CMAX,0,CMAX);\n {\n long long cx=0,cy=0;\n for(int i=0;i1500)break;\n int seed=rng()%N;\n int hx=200+(int)(rng()%50000),hy=200+(int)(rng()%50000);\n tryRun(X[seed]-hx,X[seed]+hx,Y[seed]-hy,Y[seed]+hy);\n }\n // ARM SEARCH\n // findArm: sweep along one direction, Kadane's on cross-section\n // fish_sorted: (sweep_coord, cross_coord, weight), cross in [clo,chi]\n // Returns (score, cross1, cross2, sweep_end)\n auto findArm=[&](const vector>&fish_sorted,int clo,int chi)\n ->tuple{\n vector xs;\n for(auto&[sw,cr,w]:fish_sorted)if(cr>=clo&&cr<=chi)xs.push_back(cr);\n sort(xs.begin(),xs.end());xs.erase(unique(xs.begin(),xs.end()),xs.end());\n if(xs.empty())return{0,-1,-1,0};\n int kx=(int)xs.size();\n vector cum(kx,0);\n int bsc=0,bc1=-1,bc2=-1,bsw=0;\n int i=0,n=(int)fish_sorted.size();\n while(i(fish_sorted[i]);\n while(i(fish_sorted[i])==csw){\n auto&[sw,cr,w]=fish_sorted[i];\n if(cr>=clo&&cr<=chi){\n int idx=(int)(lower_bound(xs.begin(),xs.end(),cr)-xs.begin());\n cum[idx]+=w;\n }\n i++;\n }\n int cur=0,cs=-1,mx=0,blo=-1,bhi=-1;bool ir=false;\n for(int j=0;j0){cs=xs[j];cur=gs;ir=true;if(cur>mx){mx=cur;blo=cs;bhi=xs[j];}}}\n else{cur+=gs;if(cur>mx){mx=cur;blo=cs;bhi=xs[j];}if(cur<0){cur=0;ir=false;}}\n }\n if(mx>bsc){bsc=mx;bc1=blo;bc2=bhi;bsw=csw;}\n }\n return{bsc,bc1,bc2,bsw};\n };\n // Build sorted fish for 4 arm directions (restricted to base cross-section)\n vector> ft,fb,fright,fl;\n for(int i=0;iry2&&X[i]>=rx1&&X[i]<=rx2)ft.emplace_back(Y[i],X[i],W[i]);\n if(Y[i]=rx1&&X[i]<=rx2)fb.emplace_back(-Y[i],X[i],W[i]);\n if(X[i]>rx2&&Y[i]>=ry1&&Y[i]<=ry2)fright.emplace_back(X[i],Y[i],W[i]);\n if(X[i]=ry1&&Y[i]<=ry2)fl.emplace_back(-X[i],Y[i],W[i]);\n }\n sort(ft.begin(),ft.end());sort(fb.begin(),fb.end());\n sort(fright.begin(),fright.end());sort(fl.begin(),fl.end());\n auto[ts,tax1,tax2,tay2]=findArm(ft,rx1,rx2);\n auto[bms,bax1,bax2,neg_bay]=findArm(fb,rx1,rx2); int bay1=-neg_bay;\n auto[rms,ray1,ray2,rax2]=findArm(fright,ry1,ry2);\n auto[ls,lay1,lay2,neg_lax]=findArm(fl,ry1,ry2); int lax1=-neg_lax;\n // Perimeter budget\n int P_base=2*(rx2-rx1)+2*(ry2-ry1);\n int budget=400000-P_base;\n // Arm validity (strict interior to avoid duplicate vertices)\n bool ht=ts>0&&tax1>rx1&&tax2ry2;\n bool hb=bms>0&&bax1>rx1&&bax20&&ray1>ry1&&ray2rx2;\n bool hl=ls>0&&lay1>ry1&&lay2budget){\n vector> eff;\n if(ht&&ct>0)eff.push_back({(double)ts/ct,0});\n if(hb&&cb>0)eff.push_back({(double)bms/cb,1});\n if(hr&&cr2>0)eff.push_back({(double)rms/cr2,2});\n if(hl&&cl>0)eff.push_back({(double)ls/cl,3});\n sort(eff.begin(),eff.end());\n for(auto&[e,idx]:eff){\n if(total_cost<=budget)break;\n if(idx==0){ht=false;total_cost-=ct;}\n else if(idx==1){hb=false;total_cost-=cb;}\n else if(idx==2){hr=false;total_cost-=cr2;}\n else{hl=false;total_cost-=cl;}\n }\n }\n int combined=gscore+(ht?ts:0)+(hb?bms:0)+(hr?rms:0)+(hl?ls:0);\n if(combined>=1){\n vector> v;\n // Bottom edge\n v.push_back({rx1,ry1});\n if(hb){if(bax1>rx1)v.push_back({bax1,ry1});v.push_back({bax1,bay1});v.push_back({bax2,bay1});if(bax2ry1)v.push_back({rx2,ray1});v.push_back({rax2,ray1});v.push_back({rax2,ray2});if(ray2rx1)v.push_back({tax1,ry2});}\n v.push_back({rx1,ry2});\n // Left edge (going down)\n if(hl){if(lay2ry1)v.push_back({rx1,lay1});}\n // Remove consecutive duplicates\n vector> res;\n for(auto&p:v){if(res.empty()||res.back()!=p)res.push_back(p);}\n while(res.size()>1&&res.front()==res.back())res.pop_back();\n // Check all distinct\n set> vs(res.begin(),res.end());\n bool ok=(int)vs.size()==(int)res.size()&&(int)res.size()>=4;\n if(ok){\n cout<<(int)res.size()<<\"\\n\";\n for(auto&[x,y]:res)cout<=1){\n if(rx1>=rx2){if(rx2=ry2){if(ry2\nusing namespace std;\ntypedef long long ll;\n\nint N, T;\nvector W, H;\ndouble sW, sH, mxW, mxH, totA;\n\nstruct Op { int p, r; char d; int b; };\n\npair simulate(const vector& ops) {\n vector x0(N,0),y0(N,0),x1(N,0),y1(N,0);\n vector pl(N,false);\n for (const auto& o : ops) {\n int p = o.p;\n ll w = max(1LL, llround(o.r ? H[p] : W[p]));\n ll h = max(1LL, llround(o.r ? W[p] : H[p]));\n if (o.d == 'U') {\n ll xl = o.b >= 0 ? x1[o.b] : 0LL;\n ll yt = 0;\n for (int i = 0; i < N; i++)\n if (pl[i] && x0[i] < xl+w && x1[i] > xl)\n yt = max(yt, y1[i]);\n x0[p]=xl; y0[p]=yt; x1[p]=xl+w; y1[p]=yt+h;\n } else {\n ll yt = o.b >= 0 ? y1[o.b] : 0LL;\n ll xl = 0;\n for (int i = 0; i < N; i++)\n if (pl[i] && y0[i] < yt+h && y1[i] > yt)\n xl = max(xl, x1[i]);\n x0[p]=xl; y0[p]=yt; x1[p]=xl+w; y1[p]=yt+h;\n }\n pl[p] = true;\n }\n ll rW=0, rH=0;\n for (int i = 0; i < N; i++)\n if (pl[i]) { rW=max(rW,x1[i]); rH=max(rH,y1[i]); }\n return {rW, rH};\n}\n\n// col=false: shelf packing (rows); col=true: column packing\n// For col=false, line0 uses U, rest use L\n// For col=true, line0 uses L, rest use U\nvector make_pack(const vector& rot, double tgt, bool col) {\n vector ops; ops.reserve(N);\n int cl = -1; double cm = 0;\n vector lr; vector lc;\n int p0 = -1;\n for (int i = 0; i < N; i++) {\n double m = col ? (rot[i] ? W[i] : H[i]) : (rot[i] ? H[i] : W[i]);\n double c = col ? (rot[i] ? H[i] : W[i]) : (rot[i] ? W[i] : H[i]);\n if (cl < 0 || cm + m > tgt) {\n cl++; cm = m;\n lr.push_back(i); lc.push_back(c);\n if (cl == 0) {\n ops.push_back({i, rot[i], col?'L':'U', -1});\n p0 = i;\n } else {\n ops.push_back({i, rot[i], col?'U':'L', lr[cl-1]});\n }\n } else {\n cm += m;\n if (c > lc[cl]) { lc[cl]=c; lr[cl]=i; }\n if (cl == 0) {\n ops.push_back({i, rot[i], col?'L':'U', p0});\n p0 = i;\n } else {\n ops.push_back({i, rot[i], col?'U':'L', lr[cl-1]});\n }\n }\n }\n return ops;\n}\n\ndouble calc_score(const vector& rot, double tgt, bool col) {\n auto [a,b] = simulate(make_pack(rot, tgt, col));\n return (double)(a+b);\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n\n double sigma;\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 sW=sH=mxW=mxH=totA=0;\n for (int i = 0; i < N; i++) {\n sW+=W[i]; sH+=H[i];\n mxW=max(mxW,W[i]); mxH=max(mxH,H[i]);\n totA+=W[i]*H[i];\n }\n\n const double BUDGET = 2600.0;\n auto t0 = chrono::steady_clock::now();\n auto now = [&]() {\n return chrono::duration(chrono::steady_clock::now()-t0).count();\n };\n\n vector g_rot;\n double g_tgt=0, g_score=1e18;\n bool g_col=false;\n\n for (int t = 0; t < T; t++) {\n double ts = now();\n double per = max(1.0, (BUDGET - ts) / (T - t));\n double dl = ts + per * 0.95;\n\n mt19937 rng(t * 1234567891u ^ 987654321u);\n uniform_real_distribution uni(0,1);\n\n bool col;\n double lo, hi, tgt;\n vector rot(N);\n\n if (t < (T+1)/2) {\n col = (t & 1);\n lo = col ? mxH : mxW;\n hi = col ? sH : sW;\n tgt = max(lo, min(hi, sqrt(totA)));\n // Init rotation: minimize cross-dim\n for (int i = 0; i < N; i++)\n rot[i] = col ? (H[i] br=rot;\n double bt=tgt;\n bool bc=col;\n double bs=cur;\n\n double Th = cur*0.05+1.0;\n double Tl = max(1.0, cur*1e-5);\n\n // Simulated Annealing\n for (int it=0; ; it++) {\n if ((it&63)==0 && now()>=dl) break;\n double frac = max(0.0, min(1.0, (now()-ts)/per));\n double Tc = max(Tl, Th * pow(Tl/Th, frac));\n\n int mv = rng()%10, fi=-1;\n double ot=tgt;\n bool oc=col;\n double olo=lo, ohi=hi;\n\n if (mv < 7) {\n fi = rng()%N;\n rot[fi] ^= 1;\n } else if (mv < 9) {\n tgt = max(lo, min(hi, tgt * exp((uni(rng)*2-1)*0.35)));\n } else {\n col ^= 1;\n lo = col ? mxH : mxW;\n hi = col ? sH : sW;\n tgt = max(lo, min(hi, ot));\n }\n\n double ns = calc_score(rot, tgt, col);\n double d = ns - cur;\n if (d <= 0 || uni(rng) < exp(-d/Tc)) {\n cur = ns;\n if (ns < bs) { bs=ns; br=rot; bt=tgt; bc=col; }\n } else {\n if (fi >= 0) rot[fi] ^= 1;\n else if (mv < 9) tgt = ot;\n else { col=oc; lo=olo; hi=ohi; tgt=ot; }\n }\n }\n\n // Final greedy passes\n for (int pass=0; pass<3; pass++) {\n bool imp=false;\n for (int i=0; i> Wf >> Hf;\n }\n\n return 0;\n}","ahc041":"#include \nusing namespace std;\ntypedef long long ll;\nint N,M,H,A[1000];\nvectorG[1000];\nint par[1000],dep[1000],ssm[1000],mdn[1000];\nvectorch[1000];\nvoid dfs_init(int v){ssm[v]=A[v];mdn[v]=0;for(int c:ch[v]){dfs_init(c);ssm[v]+=ssm[c];mdn[v]=max(mdn[v],mdn[c]+1);}}\nvoid push_dep(int v,int d){dep[v]=d;for(int c:ch[v])push_dep(c,d+1);}\nbool in_sub(int w,int v){for(;w!=-1;w=par[w])if(w==v)return true;return false;}\nvoid pull_ssm(int v){for(;v!=-1;v=par[v]){int s=A[v];for(int c:ch[v])s+=ssm[c];ssm[v]=s;}}\nvoid pull_mdn(int v){for(;v!=-1;v=par[v]){int m=0;for(int c:ch[v])m=max(m,mdn[c]+1);mdn[v]=m;}}\nvoid do_move(int v,int np){int op=par[v];if(op!=-1){auto&c=ch[op];c.erase(find(c.begin(),c.end(),v));}par[v]=np;if(np!=-1){ch[np].push_back(v);push_dep(v,dep[np]+1);}else push_dep(v,0);if(op!=-1){pull_ssm(op);pull_mdn(op);}if(np!=-1){pull_ssm(np);pull_mdn(np);}}\nvoid rebuild(){for(int i=0;iq;q.push(v);while(!q.empty()){int u=q.front();q.pop();for(int c:ch[u]){dep[c]=dep[u]+1;q.push(c);}}}for(int v=0;vp(N);iota(p.begin(),p.end(),0);shuffle(p.begin(),p.end(),rng);for(int v:p){int lim=H-1-mdn[v];if(lim<0)continue;int bp=par[v];ll bg=0;for(int w:G[v]){if(dep[w]>lim||in_sub(w,v))continue;ll g=(ll)(dep[w]+1-dep[v])*ssm[v];if(g>bg){bg=g;bp=w;}}if(bg>0){do_move(v,bp);ok=true;}}if(!ok)break;}}\nvoid build_bfs(vector&ord){fill(par,par+N,-1);fill(dep,dep+N,0);for(int i=0;ivis(N,false);for(int s:ord){if(vis[s])continue;queueq;q.push(s);vis[s]=true;while(!q.empty()){int v=q.front();q.pop();if(dep[v]>=H)continue;for(int u:G[v])if(!vis[u]){vis[u]=true;par[u]=v;dep[u]=dep[v]+1;ch[v].push_back(u);q.push(u);}}}for(int v=0;v>N>>M>>H;for(int i=0;i>A[i];\n for(int i=0;i>u>>v;G[u].push_back(v);G[v].push_back(u);}\n for(int i=0;i>x>>y;}\n auto t0=chrono::steady_clock::now();\n mt19937 rng(42);\n ll best_sc=-1;vectorbest_par(N);\n for(int trial=0;;trial++){\n if(chrono::duration(chrono::steady_clock::now()-t0).count()>0.3)break;\n vectorord(N);iota(ord.begin(),ord.end(),0);\n if(trial==0)sort(ord.begin(),ord.end(),[](int a,int b){return A[a]best_sc){best_sc=sc;copy(par,par+N,best_par.begin());}\n }\n copy(best_par.begin(),best_par.end(),par);rebuild();\n ll cur=best_sc;\n uniform_real_distributionuni(0,1);\n auto ts=chrono::steady_clock::now();\n double sa_t=1.80-chrono::duration(ts-t0).count();\n if(sa_t<0.05)sa_t=0.05;\n double T=1000;\n for(long long step=0;;step++){\n if(step%10000==0){double t=chrono::duration(chrono::steady_clock::now()-ts).count();if(t>=sa_t)break;T=1000*pow(0.001,t/sa_t);}\n int v=rng()%N;int lim=H-1-mdn[v];if(lim<0)continue;\n if(G[v].empty())continue;int w=G[v][rng()%G[v].size()];\n if(w==par[v]||dep[w]>lim||in_sub(w,v))continue;\n ll gain=(ll)(dep[w]+1-dep[v])*ssm[v];\n if(gain>0||(T>0.01&&uni(rng)best_sc){best_sc=cur;copy(par,par+N,best_par.begin());}\n }\n }\n for(int v=0;v\nusing namespace std;\nint N,M,OR_[42],OC_[42],ctop_[21],cbot_[21],rleft_[21],rright_[21];\nint gcost(int d,int dep){return(d==0||d==2)?2*(dep+1):2*(N-dep);}\nint odep(int k,int d){return(d<=1)?OR_[k]:OC_[k];}\nint ad_[42],ax_[42];\nvectorgv[4][21];\nvoid ins(int d,int ax,int v){auto&vec=gv[d][ax];vec.insert(lower_bound(vec.begin(),vec.end(),v),v);}\nvoid del(int d,int ax,int v){auto&vec=gv[d][ax];vec.erase(lower_bound(vec.begin(),vec.end(),v));}\nint gcv(int d,int ax){if(gv[d][ax].empty())return 0;return gcost(d,(d==0||d==2)?gv[d][ax].back():gv[d][ax].front());}\nbool vgrp(int k,int d,int ax){int r=OR_[k],c=OC_[k],kd=(d<=1)?r:c;if(d==0)return ax==c&&kdcbot_[ax];if(d==2)return ax==r&&kdrright_[ax];}\nint tc(){int t=0;for(int d=0;d<4;d++)for(int i=0;ico[21],ro[21];\nvoid ls(){bool imp=true;while(imp){imp=false;int bg=0,bt=-1,bk=-1,ba=-1,bb=-1,bd=-1,bx=-1;for(int k=0;kbg){bg=gg;bt=1;bk=k;bd=d;bx=ax;}};if(rcbot_[c])t(1,c);if(crright_[r])t(3,r);}for(int j=0;jbg){bg=gg;bt=2;ba=a;bb=b;bd=d;bx=ax;}};t(0,j);t(1,j);}}for(int i=0;ibg){bg=gg;bt=2;ba=a;bb=b;bd=d;bx=ax;}};t(2,i);t(3,i);}}if(bg>0){if(bt==1)mv1(bk,bd,bx);else mv2(ba,bb,bd,bx);imp=true;}}}\nint main(){ios_base::sync_with_stdio(false);cin.tie(NULL);cin>>N;vectorbrd(N);for(int i=0;i>brd[i];M=0;for(int i=0;i>opts;if(rcbot_[c])opts.push_back({1,c});if(crright_[r])opts.push_back({3,r});int gd,gax;if(trial==0){int bcc=INT_MAX;gd=-1;gax=-1;for(auto[d,ax]:opts){int cc=gcost(d,odep(ki,d));if(cc\nusing namespace std;\nconst int MAXN=100;\nint N,L,T[MAXN],a[MAXN],b[MAXN],cv[MAXN],fv[MAXN],flow[MAXN];\nvoid computeFlow(){fill(flow,flow+N,0);for(int i=0;i0&&!vis[j])return false;return true;}\nbool checkBwd(){if(T[0]==0)return true;static int rl[MAXN][2*MAXN],rc[MAXN];static bool vis[MAXN];int q[MAXN],qh=0,qt=0;fill(rc,rc+N,0);for(int i=0;i0&&!vis[j])return false;return true;}\nvoid fixFwdConn(){for(int pass=0;pass0&&!vis[j]){u=j;break;}if(u<0)break;long long bd=(long long)4e18;int bi=-1;bool bA=false;for(int i=0;i0)?((long long)(abs(flow[oa]-w-T[oa])-abs(flow[oa]-T[oa]))+(long long)(abs(flow[u]+w-T[u])-abs(flow[u]-T[u]))):0LL;if(d0)?((long long)(abs(flow[ob]-w-T[ob])-abs(flow[ob]-T[ob]))+(long long)(abs(flow[u]+w-T[u])-abs(flow[u]-T[u]))):0LL;if(d0){flow[a[bi]]-=cv[bi];flow[u]+=cv[bi];}a[bi]=u;}else{if(fv[bi]>0){flow[b[bi]]-=fv[bi];flow[u]+=fv[bi];}b[bi]=u;}}}\nvoid fixBwdConn(){if(T[0]==0)return;for(int pass=0;pass0&&!vis[j]){u=j;break;}if(u<0)break;long long bd=(long long)4e18;int bk=-1;bool bA=false;for(int k=0;k0)?((long long)(abs(flow[oa]-w-T[oa])-abs(flow[oa]-T[oa]))+(long long)(abs(flow[k]+w-T[k])-abs(flow[k]-T[k]))):0LL;if(d0)?((long long)(abs(flow[ob]-w-T[ob])-abs(flow[ob]-T[ob]))+(long long)(abs(flow[k]+w-T[k])-abs(flow[k]-T[k]))):0LL;if(d0){flow[a[u]]-=cv[u];flow[bk]+=cv[u];}a[u]=bk;}else{if(fv[u]>0){flow[b[u]]-=fv[u];flow[bk]+=fv[u];}b[u]=bk;}}}\n// Fast flow search - NO connectivity check (O(N^3) total)\nvoid flowSearch(){long long ce=flowErr();bool imp=true;while(imp){imp=false;for(int i=0;i0)?((long long)(abs(flow[old]-w-T[old])-abs(flow[old]-T[old]))+(long long)(abs(flow[j]+w-T[j])-abs(flow[j]-T[j]))):0LL;if(d=0){if(w>0){flow[old]-=w;flow[bj]+=w;}ce+=bd;if(t2)b[i]=bj;else a[i]=bj;imp=true;}}}}\nlong long simulateFull(int co[],int od[],int ed[]){int cnt[MAXN]={},vc[MAXN]={};fill(od,od+N,0);fill(ed,ed+N,0);int cur=0;cnt[0]=vc[0]=1;for(int w=2;w<=L;w++){if(vc[cur]&1){od[cur]++;cur=a[cur];}else{ed[cur]++;cur=b[cur];}cnt[cur]++;vc[cur]++;}long long e=0;for(int j=0;j>N>>L;for(int i=0;i>T[i];\n for(int i=0;i>items;\n for(int i=0;i0)rem[0]--;\n priority_queue>pq;for(int j=0;j(chrono::steady_clock::now()-t0).count();};\n struct Cand{long long d;int i,t,j;bool operator<(const Cand&o)const{return dcands;cands.reserve(20001);\n int noImp=0;\n while(el()<1750000LL){\n cands.clear();\n for(int i=0;i0){int oj=a[i];for(int j=0;j0){int oj=b[i];for(int j=0;j0)partial_sort(cands.begin(),cands.begin()+K,cands.end());\n bool found=false;\n for(int k=0;k=15){\n for(int p=0;p<5;p++){int i=rng()%N,t=rng()%2,j=(int)(rng()%N);if(t)b[i]=j;else a[i]=j;}\n if(!checkFwd()){copy(ba,ba+N,a);copy(bb,bb+N,b);}\n curErr=simulateFull(co,od,ed);\n if(curErr\nusing namespace std;\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int N,M,Q,L,W; cin>>N>>M>>Q>>L>>W;\n vector G(M); for(int& g:G) cin>>g;\n vector cx(N),cy(N);\n for(int i=0;i>lx>>rx>>ly>>ry;cx[i]=(lx+rx)/2.0;cy[i]=(ly+ry)/2.0;}\n auto ed2=[&](int a,int b)->double{double dx=cx[a]-cx[b],dy=cy[a]-cy[b];return dx*dx+dy*dy;};\n // Global MST\n vector mpar(N,-1);\n {vector vis(N,false);vector key(N,1e18);key[0]=0;\n for(int it=0;it> mch(N);for(int v=1;v post;{stack> stk;stk.push({0,0});while(!stk.empty()){auto&[v,ci]=stk.top();if(ci<(int)mch[v].size())stk.push({mch[v][ci++],0});else{post.push_back(v);stk.pop();}}}\n // Greedy cut\n vector esz(N);vector scut(N,false);bool use_mst=false;\n {multiset rg(G.begin(),G.end());\n for(int v:post){esz[v]=1;for(int c:mch[v])if(!scut[c])esz[v]+=esz[c];if(v!=0&&rg.count(esz[v])){scut[v]=true;rg.erase(rg.find(esz[v]));}}\n use_mst=(rg.size()==1&&*rg.begin()==esz[0]);}\n // Group assignment\n vector> groups(M);\n {map> sg;for(int i=0;i asn(N,false);\n for(int v:post){if(v==0||!scut[v])continue;int gid=sg[esz[v]].front();sg[esz[v]].pop();queueq;q.push(v);while(!q.empty()){int u=q.front();q.pop();if(asn[u])continue;groups[gid].push_back(u);asn[u]=true;for(int c:mch[u])if(!asn[c])q.push(c);}}\n int gid=sg[esz[0]].front();sg[esz[0]].pop();for(int v=0;vuint64_t{uint64_t r=0;for(int i=0;i<16;i++)r|=((uint64_t)((x>>i)&1))<<(2*i);return r;};\n vector ord(N);iota(ord.begin(),ord.end(),0);sort(ord.begin(),ord.end(),[&](int a,int b){return(eb((uint32_t)cx[a])|(eb((uint32_t)cy[a])<<1))<(eb((uint32_t)cx[b])|(eb((uint32_t)cy[b])<<1));});\n int p=0;for(int i=0;i> sc(M);\n for(int i=0;i used(g,false);int s0=0;for(int k=1;k>>> ae(M);\n auto dq=[&](const vector&qc,int gi){if((int)qc.size()<2||qrem<=0)return;qrem--;cout<<\"? \"<>a>>b;ae[gi].push_back({ed2(a,b),{a,b}});}};\n auto nw=[&](int g)->int{if(g<=1)return 0;if(g<=L)return 1;return(g-2)/(L-1)+1;};\n int tmand=0;for(int i=0;i=g);if(last&&en-st(sc[i].begin()+st,sc[i].begin()+en),i);if(last)break;st+=L-1;}}\n // Extra strided\n {vector lg;for(int i=0;iL)lg.push_back(i);\n if(!lg.empty()&&xtra>0)for(int qi=0;qi0;qi++){int gi=lg[qi%(int)lg.size()];int g=G[gi];int stride=max(1,g/L),off=(qi/(int)lg.size())%stride;vectorwin;for(int k=off;k=2)dq(win,gi);}}\n // Kruskal's\n vector par(N);auto fu=[&](int x)->int{while(par[x]!=x){par[x]=par[par[x]];x=par[x];}return x;};\n vector>> ans(M);\n for(int i=0;i0)cout<<\" \";cout<\nusing namespace std;\nconst int N=20;bool grid[N][N];\nconst int DR[]={-1,1,0,0},DC[]={0,0,-1,1};\ninline bool inB(int r,int c){return(unsigned)r<(unsigned)N&&(unsigned)c<(unsigned)N;}\nconst int NS1=N*N*21*21;static int d1[NS1],p1[NS1],q1[NS1];static uint8_t a1[NS1];\nvector> fp1(int r0,int c0,int tr,int tc){\n memset(d1,-1,sizeof(d1));int S=(r0*N+c0)*441,G=(tr*N+tc)*441;if(S==G)return{};\n d1[S]=0;int qh=0,qt=0;q1[qt++]=S;\n while(qh> res;int r=r0,c=c0;while(r!=tr){res.push_back({'M',r> path;for(int cur=G;cur!=S;cur=p1[cur])path.push_back({\"MSA\"[a1[cur]>>2],\"UDLR\"[a1[cur]&3]});reverse(path.begin(),path.end());return path;}\nconst int NS2=N*N*2*21*21;static int d2[NS2],p2[NS2],q2[NS2];static uint8_t a2[NS2];\nvector> fp2(int r0,int c0,int t1r,int t1c,int t2r,int t2c){\n memset(d2,-1,sizeof(d2));auto E=[](int r,int c,int v,int er,int ec){return (r*N+c)*2*441+v*441+(er+1)*21+(ec+1);};\n int S=E(r0,c0,0,-1,-1),G=E(t2r,t2c,1,-1,-1);d2[S]=0;int qh=0,qt=0;q2[qt++]=S;\n while(qh> path;for(int cur=G;cur!=S;cur=p2[cur])path.push_back({\"MSA\"[a2[cur]>>2],\"UDLR\"[a2[cur]&3]});reverse(path.begin(),path.end());return path;}\nconst int NS3=N*N*3*21*21;static int d3[NS3],p3[NS3],q3[NS3];static uint8_t a3[NS3];\nvector> fp3(int r0,int c0,int t1r,int t1c,int t2r,int t2c,int t3r,int t3c){\n memset(d3,-1,sizeof(d3));auto E=[](int r,int c,int ph,int er,int ec){return (r*N+c)*3*441+ph*441+(er+1)*21+(ec+1);};\n int S=E(r0,c0,0,-1,-1),G=E(t3r,t3c,2,-1,-1);d3[S]=0;int qh=0,qt=0;q3[qt++]=S;\n while(qh> path;for(int cur=G;cur!=S;cur=p3[cur])path.push_back({\"MSA\"[a3[cur]>>2],\"UDLR\"[a3[cur]&3]});reverse(path.begin(),path.end());return path;}\nconst int NS4=N*N*4*21*21;static int d4[NS4],p4[NS4],q4[NS4];static uint8_t a4[NS4];\nvector> fp4(int r0,int c0,int t1r,int t1c,int t2r,int t2c,int t3r,int t3c,int t4r,int t4c){\n memset(d4,-1,sizeof(d4));auto E=[](int r,int c,int ph,int er,int ec){return (r*N+c)*4*441+ph*441+(er+1)*21+(ec+1);};\n int S=E(r0,c0,0,-1,-1),G=E(t4r,t4c,3,-1,-1);d4[S]=0;int qh=0,qt=0;q4[qt++]=S;\n while(qh> path;for(int cur=G;cur!=S;cur=p4[cur])path.push_back({\"MSA\"[a4[cur]>>2],\"UDLR\"[a4[cur]&3]});reverse(path.begin(),path.end());return path;}\nint cr,cc,eebr=-1,eebc=-1;\nvoid execPath(const vector>&path){\n for(auto[a,d]:path){cout<>Nin>>M;vector> pts(M);\n for(int i=0;i>pts[i].first>>pts[i].second;\n memset(grid,0,sizeof(grid));cr=pts[0].first;cc=pts[0].second;eebr=eebc=-1;\n int k=1;\n while(k\nusing namespace std;\nconst int MAXN=205;\nint n,px[MAXN],py[MAXN];long long pr[MAXN];\ndouble score_pi(double si,long long ri){if(si<=0)return 0;double r=(si<=(double)ri)?si/ri:(double)ri/si;return 1-(1-r)*(1-r);}\nstruct Split{int x1,y1,x2,y2,dir,sp,lo,hi;vectorL,R;};\nvectorsplits;int rx1[MAXN],ry1[MAXN],rx2[MAXN],ry2[MAXN];\nvoid recompute(){for(int i=0;icomp,int x1,int y1,int x2,int y2){\n int nc=(int)comp.size();if(nc==1)return;\n long long tr=0;for(int i:comp)tr+=pr[i];long long H=y2-y1,W=x2-x1;\n vectorbx(comp),by(comp);\n sort(bx.begin(),bx.end(),[](int a,int b){return px[a]cands;\n auto ss=[](long long AL,long long RL,int nL,long long AR,long long RR,int nR){double a=(RL<=0||AL>=RL)?(double)nL:nL*(1-pow(1-(double)AL/RL,2));double b=(RR<=0||AR>=RR)?(double)nR:nR*(1-pow(1-(double)AR/RR,2));return a+b;};\n {long long pf=0;for(int k=1;k=px[bx[k]])continue;int lo=max(px[bx[k-1]]+1,x1+1),hi=min(px[bx[k]],x2-1);if(lo>hi)continue;int sp=(int)round(x1+(double)W*pf/tr);sp=max(lo,min(hi,sp));cands.push_back({ss((long long)(sp-x1)*H,pf,k,(long long)(x2-sp)*H,tr-pf,nc-k),0,k,sp,lo,hi});}}\n {long long pf=0;for(int k=1;k=py[by[k]])continue;int lo=max(py[by[k-1]]+1,y1+1),hi=min(py[by[k]],y2-1);if(lo>hi)continue;int sp=(int)round(y1+(double)H*pf/tr);sp=max(lo,min(hi,sp));cands.push_back({ss((long long)(sp-y1)*W,pf,k,(long long)(y2-sp)*W,tr-pf,nc-k),1,k,sp,lo,hi});}}\n if(cands.empty())return;\n sort(cands.begin(),cands.end(),[](const Cand&a,const Cand&b){return a.sc>b.sc;});\n int ch=0;if(p_rand>0&&(int)cands.size()>1){int K=min((int)cands.size(),5);if(uniform_real_distribution(0,1)(rng)=s.hi)continue;int bsp=s.sp;double bs=evalAt(s,s.sp);int lo=s.lo,hi=s.hi;while(hi-lo>=3){int m1=lo+(hi-lo)/3,m2=hi-(hi-lo)/3;double s1=evalAt(s,m1),s2=evalAt(s,m2);if(s1bs){bs=sc;bsp=sp;}}if(bsp!=s.sp){s.sp=bsp;recompute();imp=true;}}return imp;}\ndouble computeScore(){double t=0;for(int i=0;i>n;for(int i=0;i>px[i]>>py[i]>>pr[i];\n vectorall(n);iota(all.begin(),all.end(),0);\n auto t0=chrono::steady_clock::now();\n auto msf=[&](){return(int)chrono::duration_cast(chrono::steady_clock::now()-t0).count();};\n const double prs[]={0.0,0.1,0.2,0.3,0.4,0.5};\n double best=-1;int bx1[MAXN],by1[MAXN],bx2[MAXN],by2[MAXN];\n auto save=[&](){for(int i=0;i>tinfo;\n vector>ph1;\n // Phase 1: Quick 2-pass evaluation\n for(int trial=0;msf()<2200;trial++){\n uint32_t seed=(uint32_t)(trial*7919+12345);\n double pr=prs[trial==0?0:1+(trial-1)%5];\n splits.clear();rng.seed(seed);p_rand=pr;\n doBuild(all,0,0,10000,10000);recompute();\n for(int p=0;p<2&&msf()<2200;p++)if(!lsPass())break;\n double q=computeScore();\n tinfo.emplace_back(seed,pr);\n ph1.emplace_back(q,(int)tinfo.size()-1);\n if(q>best){best=q;save();}\n }\n // Phase 2: Full LS on top trials\n sort(ph1.rbegin(),ph1.rend());\n for(auto&[q,tid]:ph1){\n if(msf()>4500)break;\n splits.clear();rng.seed(tinfo[tid].first);p_rand=tinfo[tid].second;\n doBuild(all,0,0,10000,10000);recompute();\n while(msf()<4500)if(!lsPass())break;\n double sc=computeScore();\n if(sc>best){best=sc;save();}\n }\n for(int i=0;i(long long)H)continue;long long area=(long long)w*hh;double ratio=area<=(long long)ri?(double)area/ri:(double)ri/area;if(ratio>br){br=ratio;bw=w;bh=(int)hh;if(br>=1-1e-9){done=true;break;}}}}\n int a=max(x1,xi+1-bw),b=max(y1,yi+1-bh);\n cout<\nusing namespace std;\ntypedef chrono::steady_clock Clock;\nconst int N=50,MAXM=N*N+1;\nint si,sj,M,tid[N][N],pval[N][N];\nconst int dx[]={-1,1,0,0},dy[]={0,0,-1,1};\nconst char dc[]={'U','D','L','R'};\nmt19937 rng;\nbool tu[MAXM],btu[MAXM];\nint pi_[MAXM],pj_[MAXM],pt_[MAXM],bpi[MAXM],bpj[MAXM],bpt[MAXM];\nchar pmv[MAXM],bpmv[MAXM];\nint plen,blen;long long cscore,bscore;int ci,cj;\nint g_seen[MAXM]={};int g_ts=0;\nvoid save_best(){if(cscore<=bscore)return;bscore=cscore;blen=plen;memcpy(btu,tu,M);memcpy(bpi,pi_,plen*4);memcpy(bpj,pj_,plen*4);memcpy(bpt,pt_,plen*4);if(plen>1)memcpy(bpmv,pmv,plen-1);}\nvoid restore_best(){cscore=bscore;plen=blen;memcpy(tu,btu,M);memcpy(pi_,bpi,plen*4);memcpy(pj_,bpj,plen*4);memcpy(pt_,bpt,plen*4);if(plen>1)memcpy(pmv,bpmv,plen-1);ci=pi_[plen-1];cj=pj_[plen-1];}\nvoid walk_init(){fill(tu,tu+M,false);plen=1;ci=si;cj=sj;pi_[0]=si;pj_[0]=sj;pt_[0]=tid[si][sj];tu[tid[si][sj]]=true;cscore=pval[si][sj];}\nbool walk_step(double a,double b,double g,double g2,double g3){\n int bd=-1;double bh=-1e18;bool g3pos=(g3>0);\n for(int d=0;d<4;d++){\n int ni=ci+dx[d],nj=cj+dy[d];\n if((unsigned)ni>=(unsigned)N||(unsigned)nj>=(unsigned)N)continue;\n int t=tid[ni][nj];if(tu[t])continue;\n tu[t]=true;++g_ts;g_seen[t]=g_ts;\n int cnt=0;double nv=0,nv2=0,nv3=0;\n for(int d2=0;d2<4;d2++){\n int nni=ni+dx[d2],nnj=nj+dy[d2];\n if((unsigned)nni>=(unsigned)N||(unsigned)nnj>=(unsigned)N)continue;\n int t2=tid[nni][nnj];if(tu[t2]||g_seen[t2]==g_ts)continue;\n g_seen[t2]=g_ts;cnt++;nv+=pval[nni][nnj];\n for(int d3=0;d3<4;d3++){\n int n3i=nni+dx[d3],n3j=nnj+dy[d3];\n if((unsigned)n3i>=(unsigned)N||(unsigned)n3j>=(unsigned)N)continue;\n int t3=tid[n3i][n3j];if(tu[t3]||g_seen[t3]==g_ts)continue;\n g_seen[t3]=g_ts;nv2+=pval[n3i][n3j];\n if(g3pos){for(int d4=0;d4<4;d4++){\n int n4i=n3i+dx[d4],n4j=n3j+dy[d4];\n if((unsigned)n4i>=(unsigned)N||(unsigned)n4j>=(unsigned)N)continue;\n int t4=tid[n4i][n4j];if(tu[t4]||g_seen[t4]==g_ts)continue;\n g_seen[t4]=g_ts;nv3+=pval[n4i][n4j];\n }}\n }\n }\n tu[t]=false;\n double h=a*pval[ni][nj]+g*nv+g2*nv2+g3*nv3-b*cnt+(cnt==0?-1e6:0.0)\n +uniform_real_distribution(-0.5,0.5)(rng);\n if(h>bh){bh=h;bd=d;}\n }\n if(bd==-1)return false;\n int ni=ci+dx[bd],nj=cj+dy[bd];\n tu[tid[ni][nj]]=true;cscore+=pval[ni][nj];pmv[plen-1]=dc[bd];\n pi_[plen]=ni;pj_[plen]=nj;pt_[plen]=tid[ni][nj];plen++;ci=ni;cj=nj;return true;\n}\nvoid walk_extend(double a,double b,double g,double g2,double g3){while(walk_step(a,b,g,g2,g3));}\nvoid walk_undo(int s){s=min(s,plen-1);while(s-->0){plen--;tu[pt_[plen]]=false;cscore-=pval[pi_[plen]][pj_[plen]];}ci=pi_[plen-1];cj=pj_[plen-1];}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n rng.seed(chrono::steady_clock::now().time_since_epoch().count());\n cin>>si>>sj;\n for(int i=0;i>tid[i][j];\n for(int i=0;i>pval[i][j];\n M=0;for(int i=0;i=phase2);\n double a=uniform_real_distribution(0.5,2.0)(rng);\n double b=uniform_real_distribution(0,25)(rng);\n double g=uniform_real_distribution(0,1.0)(rng);\n double g2,g3;\n if(!p2){g2=uniform_real_distribution(0,0.1)(rng);g3=0.0;}\n else{g2=uniform_real_distribution(0,0.15)(rng);g3=(rng()%3==0)?0.0:uniform_real_distribution(0,0.02)(rng);}\n if(iter%4==0||blen<=1){walk_init();}\n else{restore_best();int mb=blen-1,back,r=rng()%10;\n if(r<5)back=uniform_int_distribution(1,max(1,mb/10))(rng);\n else if(r<8)back=uniform_int_distribution(max(1,mb/10),max(1,mb/3))(rng);\n else back=uniform_int_distribution(max(1,mb/3),mb)(rng);\n walk_undo(back);}\n walk_extend(a,b,g,g2,g3);save_best();\n }\n cout<\nusing namespace std;\nconst int N=30;\nconst double DELTA_VAR=1e6,INIT_SIG2_R=1e8,INIT_SIG2_E=1e7,MIN_SIG2=1e4;\ndouble mu_row[N],sig2_row[N],mu_col[N],sig2_col[N];\ndouble mu_h[N][N-1],sig2_h[N][N-1],mu_v[N-1][N],sig2_v[N-1][N];\nbool obs_h[N][N-1],obs_v[N-1][N];\ndouble wh(int i,int j){return obs_h[i][j]?mu_h[i][j]:mu_row[i];}\ndouble wv(int i,int j){return obs_v[i][j]?mu_v[i][j]:mu_col[j];}\nstring dijkstra(int sr,int sc,int tr,int tc){\n static double dist[N*N];static int par[N*N];static char pdir[N*N];\n fill(dist,dist+N*N,1e18);\n priority_queue,vector>,greater<>> pq;\n int src=sr*N+sc,dst=tr*N+tc;dist[src]=0;pq.push({0.0,src});\n while(!pq.empty()){\n auto[d,u]=pq.top();pq.pop();\n if(d>dist[u]+1e-9)continue;if(u==dst)break;\n int r=u/N,c=u%N;\n if(r>0){int nv=(r-1)*N+c;double nd=d+wv(r-1,c);if(nd0){int nv=r*N+(c-1);double nd=d+wh(r,c-1);if(nd>sr>>sc>>tr>>tc;\n string path=dijkstra(sr,sc,tr,tc);cout<>obs;\n double noise_var=(double)obs*obs/300.0;\n int kh[N]={},lv[N]={};\n struct E{bool is_h;int i,j;};vector edges;\n int r=sr,c=sc;\n for(char ch:path){\n if(ch=='U'){edges.push_back({false,r-1,c});lv[c]++;r--;}\n else if(ch=='D'){edges.push_back({false,r,c});lv[c]++;r++;}\n else if(ch=='L'){edges.push_back({true,r,c-1});kh[r]++;c--;}\n else{edges.push_back({true,r,c});kh[r]++;c++;}\n }\n double pred_r=0,pvar_r=0;\n for(int i=0;i0){pred_r+=kh[i]*mu_row[i];pvar_r+=(double)kh[i]*kh[i]*sig2_row[i]+kh[i]*DELTA_VAR;}\n for(int j=0;j0){pred_r+=lv[j]*mu_col[j];pvar_r+=(double)lv[j]*lv[j]*sig2_col[j]+lv[j]*DELTA_VAR;}\n double tvr=pvar_r+noise_var,resr=(double)obs-pred_r;\n for(int i=0;i0){double K=sig2_row[i]*kh[i]/tvr;mu_row[i]=clamp(mu_row[i]+K*resr,1000.0,9000.0);sig2_row[i]=max(sig2_row[i]*(1.0-K*kh[i]),MIN_SIG2);}\n for(int j=0;j0){double K=sig2_col[j]*lv[j]/tvr;mu_col[j]=clamp(mu_col[j]+K*resr,1000.0,9000.0);sig2_col[j]=max(sig2_col[j]*(1.0-K*lv[j]),MIN_SIG2);}\n for(auto& e:edges){\n if(e.is_h&&!obs_h[e.i][e.j]){obs_h[e.i][e.j]=true;mu_h[e.i][e.j]=mu_row[e.i];sig2_h[e.i][e.j]=INIT_SIG2_E;}\n else if(!e.is_h&&!obs_v[e.i][e.j]){obs_v[e.i][e.j]=true;mu_v[e.i][e.j]=mu_col[e.j];sig2_v[e.i][e.j]=INIT_SIG2_E;}\n }\n double pred_e=0,pvar_e=0;\n for(auto& e:edges){pred_e+=(e.is_h?mu_h[e.i][e.j]:mu_v[e.i][e.j]);pvar_e+=(e.is_h?sig2_h[e.i][e.j]:sig2_v[e.i][e.j]);}\n double tve=pvar_e+noise_var,rese=(double)obs-pred_e;\n for(auto& e:edges){\n double& mu=e.is_h?mu_h[e.i][e.j]:mu_v[e.i][e.j];\n double& s2=e.is_h?sig2_h[e.i][e.j]:sig2_v[e.i][e.j];\n double K=s2/tve;mu=clamp(mu+K*rese,1000.0,9000.0);s2=max(s2*(1.0-K),MIN_SIG2);\n }\n }\n return 0;\n}","ahc004":"#include \nusing namespace std;\nconst int N=20,MAXM=800,MAXL=12;\nint M,bs,score;\nint8_t grid[N][N],bg[N][N],h_mm[N][MAXM][N],v_mm[N][MAXM][N];\nint match_count[MAXM],slen[MAXM];\nint8_t S[MAXM][MAXL],char_pos[MAXM][8][MAXL],char_pos_cnt[MAXM][8];\nuint8_t char_appears[MAXM];\nint unsat_arr[MAXM],unsat_cnt,unsat_pos[MAXM];\nvoid unsat_remove(int k){int pos=unsat_pos[k];if(pos<0)return;int last=unsat_arr[--unsat_cnt];unsat_arr[pos]=last;unsat_pos[last]=pos;unsat_pos[k]=-1;}\nvoid unsat_add(int k){if(unsat_pos[k]>=0)return;unsat_pos[k]=unsat_cnt;unsat_arr[unsat_cnt++]=k;}\nvoid apply_cell(int r,int c,int oc,int nc){\n uint8_t mask=(1u<0&&nm==0){unsat_add(k);score--;}else if(om==0&&nm>0){unsat_remove(k);score++;}}grid[r][c]=nc;}\nint compute_delta(int r,int c,int oc,int nc){\n uint8_t mask=(1u<0)-(match_count[k]>0);}return d;}\nvoid recompute(){score=0;unsat_cnt=0;fill(unsat_pos,unsat_pos+M,-1);\n for(int r=0;r0)score++;else unsat_add(k);}}\nvoid safe_refresh(){\n int votes[N][N][8];memset(votes,0,sizeof(votes));\n for(int k=0;k=7?slen[k]-4:slen[k]-5));if(bm>rthr)continue;\n for(int p=0;pbv){bv=votes[r][c][ch];bc=ch;}\n if(bv>0&&grid[r][c]!=bc){int d=compute_delta(r,c,grid[r][c],bc);\n if(d>0){apply_cell(r,c,grid[r][c],bc);if(score>bs){bs=score;memcpy(bg,grid,sizeof(grid));}}}}}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n int n;cin>>n>>M;\n for(int k=0;k>s;slen[k]=s.size();char_appears[k]=0;memset(char_pos_cnt[k],0,8);\n for(int p=0;p0){double el=chrono::duration(chrono::steady_clock::now()-t0).count();\n if(el>=0.15||score>=M*2/5)break;\n int k=unsat_arr[rng()%(uint32_t)unsat_cnt];int bm=INT_MAX,br=0,bj=0,bd=0;\n for(int r=0;rbs){bs=score;memcpy(bg,grid,sizeof(grid));}}\n if(score!=bs){memcpy(grid,bg,sizeof(grid));recompute();}}\n double sa0=chrono::duration(chrono::steady_clock::now()-t0).count();\n double sad=max(0.1,TL-sa0);\n double phase1_end=sa0+sad*0.50,phase2_end=sa0+sad*0.75;\n bool p1t=false,p1d=false,p2t=false,p2d=false;\n int bs_last_upd=0;double T=5.0;\n for(int iter=0;;iter++){\n if((iter&0xFFF)==0){\n double el=chrono::duration(chrono::steady_clock::now()-t0).count();\n if(el>=TL)break;\n // First restart at 50% (always, unchanged from 4th submission)\n if(!p1t&&el>=phase1_end){p1t=true;\n if(bs=phase2_end){p2t=true;\n if(bs=100000){p2d=true;\n memcpy(grid,bg,sizeof(grid));recompute();\n for(int i=0;i<2;i++){int r=rng()%N,c=rng()%N,nc=rng()%8;if(nc!=grid[r][c])apply_cell(r,c,grid[r][c],nc);}\n bs_last_upd=iter;}}\n // Temperature\n if(p2d){double prog=min(1.0,max(0.0,(el-phase2_end)/(TL-phase2_end)));T=1.5*pow(0.001/1.5,prog);}\n else if(p1d){double prog=min(1.0,max(0.0,(el-phase1_end)/(sad*0.5)));T=2.0*pow(0.001/2.0,prog);}\n else{double prog=min(1.0,max(0.0,(el-sa0)/sad));T=5.0*pow(0.001/5.0,prog);}\n }\n if(iter>0&&(iter%100000)==0&&bspb)bs_last_upd=iter;}\n bool guided=false;int r,c,nc,oc;\n if(unsat_cnt>0&&rng()%(uint32_t)M<(uint32_t)unsat_cnt){\n int k=unsat_arr[rng()%(uint32_t)unsat_cnt];int bm=INT_MAX,br=0,bj=0,bd=0;\n for(int rr=0;rr=7?slen[k]-4:slen[k]-5));\n if(bm>=1&&bm<=thr)for(int p=0;p=0||(double)rng()bs){bs=score;memcpy(bg,grid,sizeof(grid));bs_last_upd=iter;}}\n }\n for(int i=0;i\nusing namespace std;\nint N,si,sj;vector grid;\nbool isRoad(int r,int c){return r>=0&&r=0&&c,vector> dijkstra(int src){\n vector d(N*N,INF),p(N*N,-1);\n priority_queue,vector>,greater<>> pq;\n d[src]=0;pq.push({0,src});const int DR[]={-1,1,0,0},DC[]={0,0,-1,1};\n while(!pq.empty()){auto[dd,u]=pq.top();pq.pop();if(dd>d[u])continue;int r=u/N,c=u%N;for(int i=0;i<4;i++){int nr=r+DR[i],nc=c+DC[i];if(!isRoad(nr,nc))continue;int v=nr*N+nc,nd=dd+(grid[nr][nc]-'0');if(nd>N>>si>>sj;grid.resize(N);for(int i=0;i>grid[i];\n vector roads;vector rIdx(N*N,-1);\n for(int r=0;r> vis(R);\n for(int i=0;i=0&&isRoad(r,c-d);d++)vis[i].push_back(rIdx[r*N+(c-d)]);\n for(int d=1;r+d=0&&isRoad(r-d,c);d++)vis[i].push_back(rIdx[(r-d)*N+c]);}\n vector cov(R,false);int uncov=R;\n vector cnt(R);for(int i=0;i> pqsc;for(int i=0;i sents;\n while(uncov>0){\n int best=-1;\n while(!pqsc.empty()){auto[cv,id]=pqsc.top();pqsc.pop();if(cv==cnt[id]){best=id;break;}}\n if(best<0)break;\n sents.push_back(roads[best]);\n for(int j:vis[best])if(!cov[j]){\n cov[j]=true;uncov--;\n for(int k:vis[j]){cnt[k]--;pqsc.push({cnt[k],k});}\n }\n }\n int stSq=si*N+sj;\n {auto it=find(sents.begin(),sents.end(),stSq);if(it==sents.end())sents.insert(sents.begin(),stSq);else swap(*it,sents[0]);}\n int S=sents.size();\n {\n vector cc(R,0);for(int sq:sents)for(int j:vis[rIdx[sq]])cc[j]++;\n bool ch=true;\n while(ch){ch=false;for(int i=S-1;i>=1;i--){if(sents[i]<0)continue;int idx=rIdx[sents[i]];bool red=true;for(int j:vis[idx])if(cc[j]<=1){red=false;break;}if(red){for(int j:vis[idx])cc[j]--;sents[i]=-1;ch=true;}}}\n sents.erase(remove(sents.begin(),sents.end(),-1),sents.end());S=sents.size();\n }\n vector> aD(S),aP(S);\n for(int i=0;i> dm(S,vector(S,INF));\n for(int i=0;i tour;\n {vector tv(S,false);tour={0};tv[0]=true;\n for(int s=1;sbool{\n int sz=tour.size();int bg=0,bi=-1,bj=-1;\n for(int i=1;ibg){bg=rmv-ins;bi=i;bj=j;}\n }\n }\n if(bi!=-1){int nd=tour[bi];tour.erase(tour.begin()+bi);int ip=(bj path;for(int c=tSq;c!=sSq;c=aP[fi][c])path.push_back(c);\n reverse(path.begin(),path.end());\n int pp=sSq;\n for(int nx:path){\n int pr=pp/N,pc=pp%N,nr=nx/N,nc=nx%N;\n if(nrpr)res+='D';else if(nc\nusing namespace std;\nint N,M,K,R;\nvector> d,succs;\nvector task_st,task_pre,task_w,worker_t,task_sd;\nvector> sk,et;\nvector> lb;\nvector>> obs;\nvector cp;\nint cur_day;double prior_sk;\nvoid upd_et(int w){for(int i=0;i0)ww+=df;}et[i][w]=ww<0.5?1.0:ww;}}\nvoid calc_cp(){cp.assign(N,0.0);for(int i=N-1;i>=0;i--){if(task_st[i]==2)continue;double mn;if(task_st[i]==1){double rem=task_sd[i]+et[i][task_w[i]]-cur_day;mn=max(1.0,rem);}else{mn=et[i][0];for(int j=1;j0)wh+=df;}double tgt=to==1?0.0:(double)to,err=wh-tgt;loss+=err*err;for(int k=0;ksk[w][k])delta[k]+=err;else if(err<-0.5&&d[ti][k]>0)delta[k]+=0.3*err;}}bool ch=false;for(int k=0;k>N>>M>>K>>R;d.assign(N,vector(K));for(int i=0;i>d[i][k];\n succs.assign(N,{});task_pre.assign(N,0);for(int r=0;r>u>>v;u--;v--;succs[u].push_back(v);task_pre[v]++;}\n task_st.assign(N,0);task_w.assign(N,-1);worker_t.assign(M,-1);task_sd.assign(N,0);\n prior_sk=40.0/sqrt((double)K);sk.assign(M,vector(K,prior_sk));lb.assign(M,vector(K,0));obs.resize(M);\n et.assign(N,vector(M));for(int j=0;javail,idle;for(int i=0;iav(avail.begin(),avail.end());sort(av.begin(),av.end(),[](int a,int b){return cp[a]>cp[b];});\n // Reservation heuristic\n mapres_cp;\n if(!av.empty()){double maxcp=cp[av[0]];for(int wb=0;wb1.5)continue;for(int nxt:succs[cur]){if(task_pre[nxt]!=1||task_st[nxt]!=0)continue;if(cp[nxt]1.0)continue;double sec=1e18;for(int j=0;j=3.0){if(!res_cp.count(bw)||res_cp[bw]>asgn;setid=idle;\n for(int t:av){if(id.empty())break;int bw=-1;double bt=1e18;for(int j:id){if(res_cp.count(j)&&cp[t]0&&!av.empty()){\n setasgn_set;for(auto&[w,t]:asgn)asgn_set.insert(t);\n for(int i=0;i1.0)continue;\n double rcp_tj=0;for(int v:succs[tj])rcp_tj=max(rcp_tj,cp[v]);\n double ncost=et[tj][wi]+rcp_tj;\n if(ncost=2){\n vectorrcp_a(na,0.0);for(int i=0;i>nc;if(nc==-1)break;\n for(int i=0;i>w;w--;int t=worker_t[w];int tk=cur_day-task_sd[t]+1;obs[w].push_back({t,tk});if(tk==1)for(int k=0;k\nusing namespace std;\nconst int OX=400,OY=400,TOT=1000,K=50,NN=2*K+1;\nint A[TOT],B[TOT],C[TOT],D[TOT],sel[K],NX[NN],NY[NN];\nint md(int x1,int y1,int x2,int y2){return abs(x1-x2)+abs(y1-y2);}\nint ec(int u,int v){return md(NX[u],NY[u],NX[v],NY[v]);}\nvoid refresh(){NX[0]=OX;NY[0]=OY;for(int i=0;i&r){int s=0;for(int i=0;i+1<(int)r.size();i++)s+=ec(r[i],r[i+1]);return s;}\nbool feasible(const vector&r){bool p[K+1]={};for(int v:r){if(v>=1&&v<=K)p[v]=true;else if(v>K&&!p[v-K])return false;}return true;}\nvector build_nn(){bool vis[NN]={},has[K+1]={};vector r={0};vis[0]=true;for(int s=0;s<2*K;s++){int cur=r.back(),bv=-1,bd=INT_MAX;for(int v=1;vK&&!has[v-K]))continue;int dd=ec(cur,v);if(dd&r){int n=r.size();bool any=false;for(int i=1;i&r){int n=r.size();bool any=false;for(int i=1;ibd){bd=rem-ins;bj=j;}}if(bj<0)continue;vector nr;nr.reserve(n);for(int k=0;k&r){int n=r.size();bool any=false;for(int i=1;ibd){bd=rem-ins;bj=j;}}if(bj<0)continue;vector nr;nr.reserve(n);for(int k=0;k&r){for(;;){bool a=two_opt_pass(r),b=or1_pass(r),c=or2_pass(r);if(!a&&!b&&!c)break;}}\nvoid quick_search(vector&r,int it=5){for(int i=0;i build_perturbed(const vector&base,int si){int pi=si+1,di=K+si+1;vector r;r.reserve(base.size()-2);for(int v:base)if(v!=pi&&v!=di)r.push_back(v);int n=r.size();int bc=INT_MAX,bp=0,bd2=1;for(int p=0;p res=r;res.insert(res.begin()+bp+1,pi);res.insert(res.begin()+bd2+1,di);return res;}\nvector double_bridge(const vector&r,mt19937&rng){int n=r.size();if(n<8)return r;int pos[4];do{for(int i=0;i<4;i++)pos[i]=1+rng()%(n-2);}while(pos[0]==pos[1]||pos[0]==pos[2]||pos[0]==pos[3]||pos[1]==pos[2]||pos[1]==pos[3]||pos[2]==pos[3]);sort(pos,pos+4);int a=pos[0],b=pos[1],c=pos[2],d=pos[3];vector nr;nr.reserve(n);for(int i=0;i&r){cout<(Clk::now()-T0).count();}\nint bcost=INT_MAX;vector broute;int bsel[K];bool inS[TOT]={};\nvoid trysel(){refresh();auto r=build_nn();full_search(r);int c=tcost(r);if(c pos(NN,-1);for(int i=0;i rem(K);for(int i=0;i> cands;for(int j=0;j0)cands.emplace_back(g,si,j);}}\nif(cands.empty())return false;int tk=min(10,(int)cands.size());partial_sort(cands.begin(),cands.begin()+tk,cands.end(),greater>());for(int ci=0;ci>A[i]>>B[i]>>C[i]>>D[i];\n {vector> sc(TOT);for(int i=0;i> sc(TOT);for(int i=0;i> sc(TOT);for(int i=0;i1.95)break;bool a=two_opt_pass(broute),b=or1_pass(broute),c=or2_pass(broute);if(!a&&!b&&!c)break;}\n emit(broute);\n return 0;\n}","ahc007":"#include \nusing namespace std;\nconst int N=400,M=1995;\nint px[N],py[N],eu[M],ev[M];\nlong long ed[M];\nstruct UF{int p[N],r[N];\nvoid init(){for(int i=0;i>>cadj(nc);\n for(int j=ie+1;j0&&((a==src&&b==dst)||(a==dst&&b==src)))continue;\n double w=2.0*ed[j];cadj[a].push_back({b,w});cadj[b].push_back({a,w});\n }\n vectordist(nc,1e18);vectorhops(nc,0);\n {priority_queue,vector>,greater<>>pq;\n dist[src]=0;pq.push({0.0,src});\n while(!pq.empty()){auto[dv,u]=pq.top();pq.pop();\n if(dv>dist[u]+1e-9)continue;if(u==dst)break;\n for(auto&[v,w]:cadj[u]){double nd=dist[u]+w;if(ndbn(nc,1e18);\n {priority_queue,vector>,greater<>>pq;\n bn[src]=0;pq.push({0.0,src});\n while(!pq.empty()){auto[bv,u]=pq.top();pq.pop();\n if(bv>bn[u]+1e-9)continue;if(u==dst)break;\n for(auto&[v,w]:cadj[u]){double nb=max(bn[u],w);if(nb0)sum_thr=dist[dst]*(3.0*n+1.0)/(2.0*n*(n+1.0));}\n double bn_thr=(bn[dst]<1e17)?bn[dst]:1e18;\n double indir=min(sum_thr,bn_thr);\n if(k==0)return(indir<1e17)?indir:2.0*ed[ie];\n double ft=(double)mn*(1.0+2.0/(k+1.0));\n return(indir<1e17)?min(ft,indir):ft;\n}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n for(int i=0;i>px[i]>>py[i];\n for(int i=0;i>eu[i]>>ev[i];double dx=px[eu[i]]-px[ev[i]],dy=py[eu[i]]-py[ev[i]];ed[i]=llround(sqrt(dx*dx+dy*dy));}\n uf.init();\n for(int i=0;i>l;\n if(uf.same(eu[i],ev[i])){cout<<0<1){cout<<1<\nusing namespace std;\nconst int G=30;\nint N,M,px[20],py[20],hx[10],hy[10];\nbool wall[G+2][G+2];\nint spx[20],spy[20],shx[10],shy[10];\nconst int ddx[]={-1,1,0,0},ddy[]={0,0,-1,1};\nconst char DIRS[]=\"UDLR\",WDIRS[]=\"udlr\";\nbool inb(int x,int y){return x>=1&&x<=G&&y>=1&&y<=G;}\nint dbuf[G+2][G+2];\nvoid bfs(int tx,int ty){\n for(int i=0;i<=G+1;i++)fill(dbuf[i],dbuf[i]+G+2,-1);\n dbuf[tx][ty]=0;queue>q;q.push({tx,ty});\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int d=0;d<4;d++){int nx=x+ddx[d],ny=y+ddy[d];if(!inb(nx,ny)||wall[nx][ny]||dbuf[nx][ny]!=-1)continue;dbuf[nx][ny]=dbuf[x][y]+1;q.push({nx,ny});}}\n}\nchar gmv(int sx,int sy,int tx,int ty){\n if(sx==tx&&sy==ty)return '.';bfs(tx,ty);if(dbuf[sx][sy]==-1)return '.';\n for(int d=0;d<4;d++){int nx=sx+ddx[d],ny=sy+ddy[d];if(!inb(nx,ny)||wall[nx][ny])continue;if(dbuf[nx][ny]==dbuf[sx][sy]-1)return DIRS[d];}return '.';\n}\nbool cpl(int wx,int wy){\n if(!inb(wx,wy)||wall[wx][wy])return false;\n for(int i=0;i tsk[2];\nvector te[2],ct[2];\nint phase=1;\nbool on_side1(int h){return wt[0]==0?(hp[0]?hy[h]=wp[0]):(hp[0]?hx[h]=wp[0]);}\nbool on_side(int h){\n if(!on_side1(h))return false;\n if(phase==1)return true;\n return wt[1]==0?(hp[1]?hy[h]=wp[1]):(hp[1]?hx[h]=wp[1]);\n}\nvoid setup_phase2(){\n int pr1,pr2,pc1,pc2;\n if(wt[0]==0){pr1=1;pr2=G;pc1=hp[0]?1:wp[0];pc2=hp[0]?wp[0]-1:G;}\n else{pr1=hp[0]?1:wp[0];pr2=hp[0]?wp[0]-1:G;pc1=1;pc2=G;}\n auto cp=[&](int r1,int c1,int r2,int c2)->int{int cnt=0;for(int i=0;i=r1&&px[i]<=r2&&py[i]>=c1&&py[i]<=c2)cnt++;return cnt;};\n auto ch=[&](int r1,int c1,int r2,int c2)->int{int cnt=0;for(int i=0;i=r1&&hx[i]<=r2&&hy[i]>=c1&&hy[i]<=c2)cnt++;return cnt;};\n if(cp(pr1,pc1,pr2,pc2)<2){phase=3;return;}\n auto ev=[&](int area,int n,int hin)->double{return (double)area/900.0*pow(2.0,-(double)n)*(0.7+0.3*(double)hin/M);};\n double bv=-1e18;wt[1]=-1;wp[1]=-1;hp[1]=true;\n for(int c=pc1+1;c<=pc2;c++){\n int lp=cp(pr1,pc1,pr2,c-1),rp=cp(pr1,c,pr2,pc2);\n int lh=ch(pr1,pc1,pr2,c-1),rh=ch(pr1,c,pr2,pc2);\n double vl=ev((c-pc1)*(pr2-pr1+1),lp,lh),vr=ev((pc2-c+1)*(pr2-pr1+1),rp,rh);\n if(vl>bv){bv=vl;wt[1]=0;wp[1]=c;hp[1]=true;}if(vr>bv){bv=vr;wt[1]=0;wp[1]=c;hp[1]=false;}\n }\n for(int r=pr1+1;r<=pr2;r++){\n int tp=cp(pr1,pc1,r-1,pc2),bp=cp(r,pc1,pr2,pc2);\n int th=ch(pr1,pc1,r-1,pc2),bh=ch(r,pc1,pr2,pc2);\n double vt=ev((r-pr1)*(pc2-pc1+1),tp,th),vb=ev((pr2-r+1)*(pc2-pc1+1),bp,bh);\n if(vt>bv){bv=vt;wt[1]=1;wp[1]=r;hp[1]=true;}if(vb>bv){bv=vb;wt[1]=1;wp[1]=r;hp[1]=false;}\n }\n if(wt[1]<0){phase=3;return;}\n tsk[1].clear();\n if(wt[1]==0){if(hp[1])for(int r=pr1;r<=pr2;r++)tsk[1].push_back({r,wp[1],r,wp[1]-1,3});else for(int r=pr1;r<=pr2;r++)tsk[1].push_back({r,wp[1]-1,r,wp[1],2});}\n else{if(hp[1])for(int c=pc1;c<=pc2;c++)tsk[1].push_back({wp[1],c,wp[1]-1,c,1});else for(int c=pc1;c<=pc2;c++)tsk[1].push_back({wp[1]-1,c,wp[1],c,0});}\n int TT2=tsk[1].size();\n vectorhord(M);iota(hord.begin(),hord.end(),0);\n if(wt[1]==0)sort(hord.begin(),hord.end(),[](int a,int b){return a>N;for(int i=0;i>px[i]>>py[i]>>t;}\n cin>>M;for(int i=0;i>hx[i]>>hy[i];\n auto ch0=[&](int wtt,int wpp,bool hhp)->int{int c=0;for(int i=0;i=wpp):(hhp?hx[i]=wpp);if(ok)c++;}return c;};\n auto ev0=[&](int area,int n,int wtt,int wpp,bool hhp)->double{return (double)area/900.0*pow(2.0,-(double)n)*(0.7+0.3*(double)ch0(wtt,wpp,hhp)/M);};\n double bv=-1e18;wt[0]=0;wp[0]=16;hp[0]=true;\n for(int c=2;c<=G;c++){int lp=0,rp=0;for(int i=0;ibv){bv=vl;wt[0]=0;wp[0]=c;hp[0]=true;}if(vr>bv){bv=vr;wt[0]=0;wp[0]=c;hp[0]=false;}}\n for(int r=2;r<=G;r++){int tp=0,bp=0;for(int i=0;ibv){bv=vt;wt[0]=1;wp[0]=r;hp[0]=true;}if(vb>bv){bv=vb;wt[0]=1;wp[0]=r;hp[0]=false;}}\n tsk[0].resize(G);\n if(wt[0]==0){if(hp[0])for(int r=1;r<=G;r++)tsk[0][r-1]={r,wp[0],r,wp[0]-1,3};else for(int r=1;r<=G;r++)tsk[0][r-1]={r,wp[0]-1,r,wp[0],2};}\n else{if(hp[0])for(int c=1;c<=G;c++)tsk[0][c-1]={wp[0],c,wp[0]-1,c,1};else for(int c=1;c<=G;c++)tsk[0][c-1]={wp[0]-1,c,wp[0],c,0};}\n vectorhord0(M);iota(hord0.begin(),hord0.end(),0);\n if(wt[0]==0)sort(hord0.begin(),hord0.end(),[&](int a,int b){return hx[a]>pw;vectorisp(M,false);\n for(int h=0;h=(int)tes[h])continue;\n Task&t=tsks[cts[h]];bool ig=(cts[h]==TT-1)&&!all_safe;\n if(hx[h]==t.sx&&hy[h]==t.sy&&!ig&&cpl(t.wx,t.wy)&&!pw.count({t.wx,t.wy})){acts[h]=WDIRS[t.wd];pw.insert({t.wx,t.wy});wall[t.wx][t.wy]=true;cts[h]++;isp[h]=true;}\n }\n for(int h=0;h=(int)tes[h]){\n if(!on_side(h)){\n int tx,ty;int p=phase-1;\n if(wt[p]==0){tx=hx[h];ty=hp[p]?wp[p]-1:wp[p];}\n else{tx=hp[p]?wp[p]-1:wp[p];ty=hy[h];}\n char mv=gmv(hx[h],hy[h],tx,ty);acts[h]=mv;if(mv!='.')for(int d=0;d<4;d++)if(DIRS[d]==mv){hx[h]+=ddx[d];hy[h]+=ddy[d];break;}\n }\n continue;\n }\n Task&t=tsks[cts[h]];\n if(hx[h]==t.sx&&hy[h]==t.sy){acts[h]='.';continue;}\n char mv=gmv(hx[h],hy[h],t.sx,t.sy);acts[h]=mv;if(mv!='.')for(int d=0;d<4;d++)if(DIRS[d]==mv){hx[h]+=ddx[d];hy[h]+=ddy[d];break;}\n }\n if(phase==2){bool done=true;for(auto&t:tsk[1])if(!wall[t.wx][t.wy]){done=false;break;}if(done)phase=3;}\n }\n cout<>s;for(char c:s){if(c=='U')px[i]--;else if(c=='D')px[i]++;else if(c=='L')py[i]--;else if(c=='R')py[i]++;}}\n }\n return 0;\n}","ahc009":"#include \nusing namespace std;\nint si,sj,ti,tj; double pf;\nbool H[20][19],V[19][20];\nint nb[400][4],G;\ndouble PP[201][400],PE[201];\ndouble VA[201][400];\nvoid initNb(){for(int i=0;i<20;i++)for(int j=0;j<20;j++){int c=i*20+j;nb[c][0]=(i>0&&!V[i-1][j])?(i-1)*20+j:c;nb[c][1]=(i<19&&!V[i][j])?(i+1)*20+j:c;nb[c][2]=(j>0&&!H[i][j-1])?i*20+(j-1):c;nb[c][3]=(j<19&&!H[i][j])?i*20+(j+1):c;}}\nint dc(char c){return c=='U'?0:c=='D'?1:c=='L'?2:3;}\nvoid computeVA(){memset(VA,0,sizeof(VA));for(int t=199;t>=0;t--)for(int c=0;c<400;c++){if(c==G)continue;double best=-1e18;for(int d=0;d<4;d++){int nk=nb[c][d];double v=pf*VA[t+1][c]+(nk==G?(1-pf)*(400.-t):(1-pf)*VA[t+1][nk]);if(v>best)best=v;}VA[t][c]=best;}}\nvoid buildP(const string&s,int fr){for(int t=fr;t<200;t++){int d=dc(s[t]);double*a=PP[t],*b=PP[t+1];memset(b,0,3200);for(int k=0;k<400;k++){double v=a[k];if(v<1e-15)continue;b[k]+=v*pf;b[nb[k][d]]+=v*(1-pf);}double e=b[G]*(401.-(t+1));b[G]=0;PE[t+1]=PE[t]+e;}}\ndouble evalF(const string&s,int fr){double p[400],q[400];memcpy(p,PP[fr],3200);double E=PE[fr];for(int t=fr;t<200;t++){int d=dc(s[t]);memset(q,0,3200);for(int k=0;k<400;k++){double v=p[k];if(v<1e-15)continue;q[k]+=v*pf;q[nb[k][d]]+=v*(1-pf);}E+=q[G]*(401.-(t+1));q[G]=0;memcpy(p,q,3200);}return E;}\nvoid setP(const string&s){memset(PP[0],0,3200);PP[0][si*20+sj]=1;PE[0]=0;buildP(s,0);}\nchrono::time_pointT0;\ndouble el(){return chrono::duration(chrono::steady_clock::now()-T0).count();}\ndouble hc(string&s,double E0,double tl){double be=E0;for(;;){if(el()>tl)break;bool imp=false;for(int t=0;t<200;t++){int od=dc(s[t]);for(int d=0;d<4;d++){if(d==od)continue;s[t]=\"UDLR\"[d];double e=evalF(s,t);if(e>be+1e-12){be=e;od=d;buildP(s,t);imp=true;}else s[t]=\"UDLR\"[od];}}if(!imp)break;}return be;}\nstring bfsPath(){int ds[400];fill(ds,ds+400,-1);int pr[400],pd[400];int src=si*20+sj;queueq;q.push(src);ds[src]=0;while(!q.empty()){int k=q.front();q.pop();for(int d=0;d<4;d++){int nk=nb[k][d];if(nk==k||ds[nk]!=-1)continue;ds[nk]=ds[k]+1;pr[nk]=k;pd[nk]=d;q.push(nk);}}string r;for(int c=G;c!=src;c=pr[c])r+=\"UDLR\"[pd[c]];reverse(r.begin(),r.end());return r;}\nstring distanceGreedy(){int bd[400];fill(bd,bd+400,-1);queueq;q.push(G);bd[G]=0;while(!q.empty()){int k=q.front();q.pop();for(int d=0;d<4;d++){int nk=nb[k][d];if(nk==k||bd[nk]!=-1)continue;bd[nk]=bd[k]+1;q.push(nk);}}double prob[400]={},np[400];prob[si*20+sj]=1.0;string s(200,'D');for(int t=0;t<200;t++){double best=-1e18;int bestd=0;for(int d=0;d<4;d++){double g=0;for(int k=0;k<400;k++){if(prob[k]<1e-15)continue;g+=prob[k]*(1-pf)*(bd[k]-bd[nb[k][d]]);}if(g>best){best=g;bestd=d;}}s[t]=\"UDLR\"[bestd];memset(np,0,3200);for(int k=0;k<400;k++){if(prob[k]<1e-15)continue;np[k]+=prob[k]*pf;np[nb[k][bestd]]+=prob[k]*(1-pf);}np[G]=0;memcpy(prob,np,3200);}return s;}\ndouble la_val(const double*prob,int t,int depth){if(depth==0||t>=200){double v=0;for(int k=0;k<400;k++)if(prob[k]>1e-15)v+=prob[k]*(t<200?VA[t][k]:0.);return v;}double best=-1e18,np[400];for(int d=0;d<4;d++){memset(np,0,3200);for(int k=0;k<400;k++){double v=prob[k];if(v<1e-15)continue;np[k]+=v*pf;np[nb[k][d]]+=v*(1-pf);}double sc=np[G]*(400.-t);np[G]=0;double fv=la_val(np,t+1,depth-1);if(sc+fv>best)best=sc+fv;}return best;}\nstring kStepGreedy(int K){double prob[400]={},np[400];prob[si*20+sj]=1.0;string s(200,'D');for(int t=0;t<200;t++){double best=-1e18;int bestd=0;for(int d=0;d<4;d++){memset(np,0,3200);for(int k=0;k<400;k++){double v=prob[k];if(v<1e-15)continue;np[k]+=v*pf;np[nb[k][d]]+=v*(1-pf);}double sc=np[G]*(400.-t);np[G]=0;double fv=la_val(np,t+1,K-1);if(sc+fv>best){best=sc+fv;bestd=d;}}s[t]=\"UDLR\"[bestd];memset(np,0,3200);for(int k=0;k<400;k++){double v=prob[k];if(v<1e-15)continue;np[k]+=v*pf;np[nb[k][bestd]]+=v*(1-pf);}np[G]=0;memcpy(prob,np,3200);}return s;}\nint main(){\n ios::sync_with_stdio(0);cin.tie(0);\n cin>>si>>sj>>ti>>tj>>pf;\n for(int i=0;i<20;i++){string r;cin>>r;for(int j=0;j<19;j++)H[i][j]=(r[j]=='1');}\n for(int i=0;i<19;i++){string r;cin>>r;for(int j=0;j<20;j++)V[i][j]=(r[j]=='1');}\n initNb();G=ti*20+tj;T0=chrono::steady_clock::now();\n computeVA();\n string path=bfsPath();int K=(int)path.size();\n string s1(200,'D');for(int i=0;i<200;i++)s1[i]=path[i%K];\n string s2=kStepGreedy(3);\n string s3=distanceGreedy();\n setP(s1);double e1=hc(s1,PE[200],0.13);\n setP(s2);double e2=hc(s2,PE[200],0.27);\n setP(s3);double e3=hc(s3,PE[200],0.43);\n string gb;double gbE;\n if(e1>=e2&&e1>=e3){gb=s1;gbE=e1;}else if(e2>=e3){gb=s2;gbE=e2;}else{gb=s3;gbE=e3;}\n setP(gb);\n mt19937 rng(42);uniform_real_distributionud(0,1);\n // SA with STEP-BASED cooling - eliminates timing sensitivity\n {string sc=gb;double scE=gbE;double T=2.0;int sa_st=0;\n const int SA_MAX=6000; // calibrated for ~120us/step * 6000 = 720ms\n while(el()<1.2&&sa_st0||ud(rng)gbE){gbE=e;gb=sc;}}\n else sc[t]=\"UDLR\"[od];\n sa_st++;\n if(sa_st%500==0){\n // STEP-BASED cooling: temperature depends only on step count, not elapsed time\n T=2.0*exp(-7.0*(double)sa_st/SA_MAX);\n if(scEgbE+1e-12){gbE=e;gb=p2;}}\n cout<\nusing namespace std;\nconst int N=30,TOTAL=N*N*4;\nconst int to_t[8][4]={{1,0,-1,-1},{3,-1,-1,0},{-1,-1,3,2},{-1,2,1,-1},{1,0,3,2},{3,2,1,0},{2,-1,0,-1},{-1,3,-1,1}};\nconst int di[4]={0,-1,0,1},dj[4]={-1,0,1,0};\nint tiles[N][N],init_t[N][N],rots[N][N],best_rots[N][N];\nlong long global_best=0;\nmt19937 rng(42);int nxt[TOTAL];uint8_t col[TOTAL];\ninline int apply_rot(int t,int r){if(t<=3)return(t+r)&3;if(t<=5)return 4+((t-4+r)&1);return 6+((t-6+r)&1);}\ninline void update_nxt(int i,int j){int base=(i*N+j)*4,t=tiles[i][j];for(int d=0;d<4;d++){int d2=to_t[t][d];if(d2<0){nxt[base+d]=-1;continue;}int ni=i+di[d2],nj=j+dj[d2];if((unsigned)ni>=(unsigned)N||(unsigned)nj>=(unsigned)N){nxt[base+d]=-1;continue;}nxt[base+d]=(ni*N+nj)*4+((d2+2)&3);}}\nlong long evaluate(){memset(col,0,TOTAL);int t1=0,t2=0;for(int s=0;s=0&&!col[c]){col[c]=1;c=nxt[c];}if(c>=0&&col[c]==1){int len=0,cc=c;do{cc=nxt[cc];len++;}while(cc!=c);if(len>t1){t2=t1;t1=len;}else if(len>t2)t2=len;}c=s;while(c>=0&&col[c]==1){col[c]=2;c=nxt[c];}}return(long long)t1*t2;}\nconst auto TS=chrono::steady_clock::now();\ndouble gt(){return chrono::duration(chrono::steady_clock::now()-TS).count();}\nstatic bool dv[TOTAL],dvb[TOTAL];\ntypedef array Pt;\nint dfs_loop(int si,int sj,int sd,const bool*occ){\n memset(dv,0,TOTAL);if(occ&&occ[(si*N+sj)*4+sd])return 0;\n int i=si,j=sj,d=sd,len=0;\n while(len0)?len:0;\n if(occ&&occ[s])return 0;dv[s]=true;\n int base=(i*N+j)*4;\n bool dc=false;for(int p=0;p<4&&!dc;p++)if(p!=d&&dv[base+p])dc=true;\n bool gc=false;if(occ)for(int p=0;p<4&&!gc;p++)if(occ[base+p])gc=true;\n if(dc||gc){int d2=to_t[tiles[i][j]][d];if(d2<0)return 0;int ni=i+di[d2],nj=j+dj[d2];if((unsigned)ni>=(unsigned)N||(unsigned)nj>=(unsigned)N)return 0;int nd=(d2+2)&3;if(occ&&occ[(ni*N+nj)*4+nd])return 0;len++;if(ni==si&&nj==sj&&nd==sd)return len;i=ni;j=nj;d=nd;continue;}\n int ti=init_t[i][j],br=-1,bp=-9999;\n for(int r=0;r<4;r++){int t=apply_rot(ti,r),d2=to_t[t][d];if(d2<0)continue;int ni=i+di[d2],nj=j+dj[d2];if((unsigned)ni>=(unsigned)N||(unsigned)nj>=(unsigned)N)continue;int nd=(d2+2)&3,ns=(ni*N+nj)*4+nd;if(occ&&occ[ns])continue;\n // 1-step lookahead: skip if next committed and incompatible\n int nb=(ni*N+nj)*4;bool nc=false;for(int pp=0;pp<4&&!nc;pp++)if(pp!=nd&&(dv[nb+pp]||(occ&&occ[nb+pp])))nc=true;\n if(nc&&to_t[tiles[ni][nj]][nd]<0)continue;\n int p=(!dv[ns])?100:0;if(ni==si&&nj==sj&&nd==sd&&len>4)p=50;int nti=init_t[ni][nj];if(nti==4||nti==5)p+=5;if(ni>0&&ni0&&njbp){bp=p;br=r;}}\n if(br<0)return 0;\n rots[i][j]=br;tiles[i][j]=apply_rot(ti,br);update_nxt(i,j);\n int d2=to_t[tiles[i][j]][d];int ni=i+di[d2],nj=j+dj[d2],nd=(d2+2)&3;\n if(occ&&occ[(ni*N+nj)*4+nd])return 0;len++;if(ni==si&&nj==sj&&nd==sd)return len;i=ni;j=nj;d=nd;\n }return 0;\n}\nint build_loop(int n,const bool*occ,const vector*sm=nullptr){\n int sr[N][N];memcpy(sr,rots,sizeof(rots));int bl=0,bs[N][N];memcpy(bs,sr,sizeof(sr));memset(dvb,0,TOTAL);\n for(int a=0;aempty()&&(int)(rng()%10)<7){const auto&p=(*sm)[rng()%sm->size()];si=p[0];sj=p[1];sd=p[2];}\n else{si=rng()%N;sj=rng()%N;sd=rng()%4;}\n int l=dfs_loop(si,sj,sd,occ);\n if(l>bl){bl=l;memcpy(bs,rots,sizeof(rots));memcpy(dvb,dv,TOTAL);}\n }\n memcpy(rots,bs,sizeof(rots));for(int i=0;i=(unsigned)N||(unsigned)nj>=(unsigned)N)continue;if(to_t[tiles[ni][nj]][(d+2)%4]>=0)cnt++;}if(cnt>bc){bc=cnt;br=r;}}if(br!=rots[i][j]){rots[i][j]=br;tiles[i][j]=apply_rot(ti,br);update_nxt(i,j);c=true;}}if(!c)break;}}\nvoid run_sa(double Tf,double et){\n long long cur=evaluate();if(cur>global_best){global_best=cur;memcpy(best_rots,rots,sizeof(rots));}\n double si=max(10.0,(double)cur),e=gt(),s0=e;int cnt=0;\n while(e=0||rng()/4294967296.0global_best){global_best=ns;memcpy(best_rots,rots,sizeof(rots));}}\n else{tiles[i][j]=ot;update_nxt(i,j);}\n }\n}\nvoid run_greedy(long long&cur,double et){\n for(bool imp=true;imp&>()bl){bl=ns;bd=dr;}tiles[i][j]=st;update_nxt(i,j);}if(bd){rots[i][j]=(rots[i][j]+bd)&3;tiles[i][j]=apply_rot(ti,rots[i][j]);update_nxt(i,j);cur=bl;if(bl>global_best){global_best=bl;memcpy(best_rots,rots,sizeof(rots));}imp=true;}}}\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n for(int i=0;i>s;for(int j=0;j0){\n bool occ1[TOTAL];memcpy(occ1,dvb,TOTAL);\n vector smart;\n for(int i=0;i0){memcpy(rots,pr,sizeof(rots));for(int i=0;i\nusing namespace std;\nint N,T,board[10][10],board_label[10][10],er,ec,tgt[10][10],avail[16];\nbool fixed_cells[10][10];string out;int total_edges;\nint uf_p[101],uf_rk[101];\nstruct UFCh{int ch,op,rt,ork;};vectoruf_ch;\nvoid uf_init(){for(int i=0;i<=N*N;i++){uf_p[i]=i;uf_rk[i]=0;}}\nint uf_find(int x){while(uf_p[x]!=x)x=uf_p[x];return x;}\nbool uf_union(int a,int b){int ra=uf_find(a),rb=uf_find(b);if(ra==rb)return false;if(uf_rk[ra]sv){UFCh c=uf_ch.back();uf_ch.pop_back();uf_p[c.ch]=c.op;uf_rk[c.rt]=c.ork;}}\nint sb_p[100],sb_sz[100];bool sb_cy[100];\nint sb_find(int x){while(sb_p[x]!=x){sb_p[x]=sb_p[sb_p[x]];x=sb_p[x];}return x;}\nint scoreBoard(){int NN=N*N;for(int i=0;i0&&board[i][j+1]>0&&(board[i][j]&4)&&(board[i][j+1]&1))add(i*N+j,i*N+j+1);for(int i=0;i0&&board[i+1][j]>0&&(board[i][j]&8)&&(board[i+1][j]&2))add(i*N+j,(i+1)*N+j);int best=0;for(int i=0;i0&&sb_find(i)==i&&!sb_cy[i])best=max(best,sb_sz[i]);return best;}\nvoid read_input(){cin>>N>>T;for(int i=0;i>s;for(int j=0;j='0'&&c<='9')?c-'0':c-'a'+10;if(!board[i][j]){er=i;ec=j;}}}}\nbool valid_pos(int v,int i,int j){return!((v&1)&&!j)&&!((v&2)&&!i)&&!((v&4)&&j==N-1)&&!((v&8)&&i==N-1);}\nint g_ops;\nbool find_target(int pos){\n if(++g_ops>5000000)return false;\n if(pos==N*N)return total_edges==N*N-2;\n int i=pos/N,j=pos%N;if(i==N-1&&j==N-1){tgt[i][j]=0;return find_target(pos+1);}\n bool fl=(j>0),nl=fl&&(tgt[i][j-1]&4),fu=(i>0),nu=fu&&(tgt[i-1][j]&8);\n int new_ed=(fl?nl:0)+(fu?nu:0);if(total_edges+new_ed>N*N-2){tgt[i][j]=-1;return false;}\n for(int v=1;v<=15;v++){\n if(!avail[v]||!valid_pos(v,i,j))continue;if(fl&&!!(v&1)!=nl)continue;if(fu&&!!(v&2)!=nu)continue;\n if(j0),nu2=fcu&&(tgt[i-1][nj]&8);for(int u=1;u<=15&&!ok;u++){int cnt=avail[u]-(u==v?1:0);if(cnt<=0||!valid_pos(u,i,nj)||!!(u&1)!=n2||(fcu&&!!(u&2)!=nu2))continue;ok=true;}}if(!ok)continue;}\n if(i>cp[16],tp[16];for(int i=0;i0)cp[board[i][j]].push_back({i,j});if(tgt[i][j]>0)tp[tgt[i][j]].push_back({i,j});}for(int v=1;v<=15;v++){sort(cp[v].begin(),cp[v].end());sort(tp[v].begin(),tp[v].end());for(int k=0;k<(int)cp[v].size();k++){auto[cr,cc]=cp[v][k];auto[tr,tc]=tp[v][k];board_label[cr][cc]=tr*N+tc;}}}\nbool check_solvable(){vectors;for(int i=0;i=0)s.push_back(board_label[i][j]);int inv=0;for(int a=0;a<(int)s.size();a++)for(int b=a+1;b<(int)s.size();b++)if(s[a]>s[b])inv++;if(N%2)return!(inv%2);return(inv+er)%2==1;}\nvoid fix_parity(){if(check_solvable())return;for(int v=1;v<=15;v++){vector>cp;for(int i=0;i=2){swap(board_label[cp[0].first][cp[0].second],board_label[cp[1].first][cp[1].second]);if(check_solvable())return;swap(board_label[cp[0].first][cp[0].second],board_label[cp[1].first][cp[1].second]);}}}\nvoid do_move(char m){int tr=er,tc=ec;if(m=='U')tr--;else if(m=='D')tr++;else if(m=='L')tc--;else tc++;board[er][ec]=board[tr][tc];board_label[er][ec]=board_label[tr][tc];board[tr][tc]=0;board_label[tr][tc]=-1;er=tr;ec=tc;out+=m;}\nstatic int me_prv[100],me_q[100];\nbool move_empty(int gr,int gc){if(er==gr&&ec==gc)return true;if((int)out.size()>=T)return false;if(fixed_cells[gr][gc])return false;int NN=N*N,s=er*N+ec,g=gr*N+gc;fill(me_prv,me_prv+NN,-2);me_prv[s]=-1;int qh=0,qt=0;me_q[qt++]=s;const int dr[]={-1,1,0,0},dc[]={0,0,-1,1};while(qh=N||nc<0||nc>=N||fixed_cells[nr][nc])continue;int nxt=nr*N+nc;if(me_prv[nxt]!=-2)continue;me_prv[nxt]=cur;me_q[qt++]=nxt;}}if(me_prv[g]==-2)return false;static int path[101];int plen=0,cur=g;while(cur!=s){path[plen++]=cur;cur=me_prv[cur];}for(int k=plen-1;k>=0;k--){if((int)out.size()>=T)return false;int nxt=path[k],nr=nxt/N,nc=nxt%N;char m;if(nr==er-1)m='U';else if(nr==er+1)m='D';else if(nc==ec-1)m='L';else m='R';do_move(m);}return true;}\nstatic int bt_prv[10000],bt_q[10001];static char bt_mv[10000],bt_path[10000];\nbool bfs_tile(int&tr,int&tc,int dr,int dc){if(tr==dr&&tc==dc)return true;if((int)out.size()>=T)return false;int NN=N*N,t0=tr*N+tc,e0=er*N+ec,tg=dr*N+dc,tot=NN*NN;memset(bt_prv,-1,tot*sizeof(int));int start=t0*NN+e0;bt_prv[start]=start;int qh=0,qt=0;bt_q[qt++]=start;const int ddr[]={-1,1,0,0},ddc[]={0,0,-1,1};const char dch[]={'U','D','L','R'};int goal=-1;while(qh=N||nc<0||nc>=N||fixed_cells[nr][nc])continue;int np=nr*N+nc,nt=(np==ct)?ce:ct,ne=np;if(nt==ne)continue;int nst=nt*NN+ne;if(nst<0||nst>=tot||bt_prv[nst]!=-1)continue;bt_prv[nst]=cur;bt_mv[nst]=dch[d];bt_q[qt++]=nst;}}if(goal<0){for(int e=0;e=0;k--){if((int)out.size()>=T)return false;do_move(bt_path[k]);}tr=dr;tc=dc;return true;}\npairfind_lbl(int lbl){for(int i=0;i=T)return;for(int col=0;col<=N-3&&(int)out.size()=T)return;auto[ar,ac]=find_lbl(row*N+(N-2));auto[br,bc]=find_lbl(row*N+(N-1));if(ar<0||br<0)return;if(ar==row&&ac==N-2&&br==row&&bc==N-1){fixed_cells[row][N-2]=fixed_cells[row][N-1]=true;return;}bfs_tile(ar,ac,row,N-1);if((int)out.size()>=T)return;auto[br2,bc2]=find_lbl(row*N+(N-1));if(br2<0)return;fixed_cells[row][N-1]=true;bfs_tile(br2,bc2,row+1,N-1);fixed_cells[row][N-1]=false;if((int)out.size()>=T)return;fixed_cells[row][N-1]=fixed_cells[row+1][N-1]=true;move_empty(row,N-2);fixed_cells[row][N-1]=fixed_cells[row+1][N-1]=false;if((int)out.size()=T)return;auto[ar,ac]=find_lbl((N-2)*N+col);auto[br,bc]=find_lbl((N-1)*N+col);if(ar<0||br<0)return;if(ar==N-2&&ac==col&&br==N-1&&bc==col){fixed_cells[N-2][col]=fixed_cells[N-1][col]=true;return;}bfs_tile(ar,ac,N-1,col);if((int)out.size()>=T)return;auto[br2,bc2]=find_lbl((N-1)*N+col);if(br2<0)return;fixed_cells[N-1][col]=true;bfs_tile(br2,bc2,N-1,col+1);fixed_cells[N-1][col]=false;if((int)out.size()>=T)return;fixed_cells[N-1][col]=fixed_cells[N-1][col+1]=true;move_empty(N-2,col);fixed_cells[N-1][col]=fixed_cells[N-1][col+1]=false;if((int)out.size()=T)return;int p0=(N-2)*N+(N-2),p1=(N-2)*N+(N-1),p2=(N-1)*N+(N-2);int a=board_label[N-2][N-2],b=board_label[N-2][N-1],c=board_label[N-1][N-2],d=board_label[N-1][N-1];if(a==p0&&b==p1&&c==p2&&d==-1)return;auto el=[&](int l)->int{if(l==p0)return 0;if(l==p1)return 1;if(l==p2)return 2;return 3;};auto enc=[](int v0,int v1,int v2,int v3){return v0*64+v1*16+v2*4+v3;};int gs=enc(0,1,2,3),ss=enc(el(a),el(b),el(c),el(d));if(ss==gs)return;static int par[256];static char mfr[256];fill(par,par+256,-2);par[ss]=-1;static int bq[256];int bqh=0,bqt=0;bq[bqt++]=ss;const int adj[4][2]={{1,2},{0,3},{0,3},{1,2}};const char amv[4][2]={{'R','D'},{'L','D'},{'U','R'},{'U','L'}};while(bqh>6)&3,(cur>>4)&3,(cur>>2)&3,cur&3};int ep=-1;for(int p=0;p<4;p++)if(v[p]==3){ep=p;break;}if(ep<0)continue;for(int k=0;k<2;k++){int np=adj[ep][k];char m=amv[ep][k];int nv[4]={v[0],v[1],v[2],v[3]};nv[ep]=nv[np];nv[np]=3;int nst=enc(nv[0],nv[1],nv[2],nv[3]);if(par[nst]==-2){par[nst]=cur;mfr[nst]=m;bq[bqt++]=nst;}}}if(par[gs]==-2)return;static char path[20];int plen=0;int cur=gs;while(cur!=ss){path[plen++]=mfr[cur];cur=par[cur];}for(int k=plen-1;k>=0;k--){if((int)out.size()>=T)break;do_move(path[k]);}}\nvoid solve(){for(int row=0;row<=N-3&&(int)out.size()=N||nc<0||nc>=N)continue;int sb[10][10];memcpy(sb,board,sizeof(board));int se=er,sf=ec;int tr2=er,tc2=ec;if(mv[d]=='U')tr2--;else if(mv[d]=='D')tr2++;else if(mv[d]=='L')tc2--;else tc2++;board[er][ec]=board[tr2][tc2];board[tr2][tc2]=0;er=tr2;ec=tc2;int sc=scoreBoard();memcpy(board,sb,sizeof(board));er=se;ec=sf;if(sc>bsc2){bsc2=sc;best=mv[d];}}if(!best)break;do_move(best);}}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);read_input();\n memset(avail,0,sizeof(avail));for(int i=0;i0)avail[board[i][j]]++;\n memset(tgt,-1,sizeof(tgt));memset(fixed_cells,0,sizeof(fixed_cells));memset(board_label,-1,sizeof(board_label));\n total_edges=0;uf_init();uf_ch.clear();g_ops=0;\n bool found=find_target(0);\n if(found){init_labels();fix_parity();solve();}\n if(scoreBoard()\nusing namespace std;\ntypedef long long ll;\ntypedef unsigned long long ull;\ntypedef pair puu;\nstruct PH{size_t operator()(const puu&p)const{size_t h=hash()(p.first);h^=hash()(p.second)+0x9e3779b9ULL+(h<<6)+(h>>2);return h;}};\nmt19937 rng(42);\nint N,K,a[11],stx[5501],sty[5501];\nstruct Line{ll px,py,qx,qy;};\nconst int MK=100;\nLine cur_lines[MK],best_lines[MK];\nint8_t sgn_data[5501][MK];\null slo[5501],shi[5501];\nunordered_mapgrps;\nint b_arr[12],cscore,best_score;\nstruct Change{int idx;puu old_sig,new_sig;int8_t new_sgn;};\nvectorpending;\nvector>dvec;\nbool is_dummy[MK];\nll ecross(const Line&l,ll x,ll y){return(l.qx-l.px)*(y-l.py)-(l.qy-l.py)*(x-l.px);}\nvoid upd(int oc,int nc){if(oc>=1&&oc<=10){cscore-=min(a[oc],b_arr[oc]);b_arr[oc]--;cscore+=min(a[oc],b_arr[oc]);}if(nc>=1&&nc<=10){cscore-=min(a[nc],b_arr[nc]);b_arr[nc]++;cscore+=min(a[nc],b_arr[nc]);}}\nvoid build(){grps.clear();grps.reserve(32768);grps.max_load_factor(0.3f);memset(b_arr,0,sizeof(b_arr));cscore=0;for(int i=0;i=0)?1:-1;sgn_data[i][j]=s;if(s==1){if(j<64)slo[i]|=(1ULL<second,it->second+1);it->second++;}}\nint try_ch(int j,const Line&nl){pending.clear();dvec.clear();for(int i=0;i=0)?1:-1;if(ns==sgn_data[i][j])continue;puu os{slo[i],shi[i]};ull nl2=slo[i],nh2=shi[i];if(j<64){if(ns==1)nl2|=(1ULL<second:0,nc=c+d;if(c>=1&&c<=10){nsc-=min(a[c],nb[c]);nb[c]--;nsc+=min(a[c],nb[c]);}if(nc>=1&&nc<=10){nsc-=min(a[nc],nb[nc]);nb[nc]++;nsc+=min(a[nc],nb[nc]);}}i=j2;}return nsc;}\nvoid do_ch(int j,const Line&nl){for(auto&ch:pending){{auto it=grps.find(ch.old_sig);upd(it->second,it->second-1);if(!--it->second)grps.erase(it);}slo[ch.idx]=ch.new_sig.first;shi[ch.idx]=ch.new_sig.second;sgn_data[ch.idx][j]=ch.new_sgn;{auto[it2,ins]=grps.emplace(ch.new_sig,0);upd(it2->second,it2->second+1);it2->second++;}}cur_lines[j]=nl;}\nLine rline(){double th=(rng()%314159)*(M_PI/314159.0);double r=(int)(rng()%18001)-9000;double cx=r*cos(th),cy=r*sin(th),sdx=-sin(th)*9000,sdy=cos(th)*9000;return{llround(cx+sdx),llround(cy+sdy),llround(cx-sdx),llround(cy-sdy)};}\nLine pline(const Line&l,int s){ll dx=(ll)(rng()%(2*s+1))-s,dy=(ll)(rng()%(2*s+1))-s;int t=rng()%3;if(t==0)return{l.px+dx,l.py+dy,l.qx,l.qy};if(t==1)return{l.px,l.py,l.qx+dx,l.qy+dy};return{l.px+dx,l.py+dy,l.qx-dx,l.qy-dy};}\nLine pline_perp(const Line&l,int s){ll ddx=l.qx-l.px,ddy=l.qy-l.py;double len=hypot((double)ddx,(double)ddy);if(len<1.0)return l;ll delta=(ll)(rng()%(2*s+1))-s;ll dx2=llround(delta*(-ddy)/len),dy2=llround(delta*ddx/len);return{l.px+dx2,l.py+dy2,l.qx+dx2,l.qy+dy2};}\nLine pline_rot(const Line&l,int mr){double mx=(l.px+l.qx)*0.5,my=(l.py+l.qy)*0.5;double hdx=(l.qx-l.px)*0.5,hdy=(l.qy-l.py)*0.5;double angle=((int)(rng()%(2*mr+1))-mr)*0.001;double ca=cos(angle),sa=sin(angle);ll ndx=llround(hdx*ca-hdy*sa),ndy=llround(hdx*sa+hdy*ca);return{llround(mx)-ndx,llround(my)-ndy,llround(mx)+ndx,llround(my)+ndy};}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>N>>K;for(int d=1;d<=10;d++)cin>>a[d];for(int i=0;i>stx[i]>>sty[i];\n // 25H + 25V coarser grid + 50 dummy lines above cake\n for(int i=0;i<25;i++){ll y=llround(-9000.0+18000.0*i/24.0);cur_lines[i]={-10000,y,10000,y};is_dummy[i]=false;}\n for(int i=0;i<25;i++){ll x=llround(-9000.0+18000.0*i/24.0);cur_lines[25+i]={x,-10000,x,10000};is_dummy[25+i]=false;}\n for(int i=50;i(chrono::steady_clock::now()-t0).count();\n if(e>2.90)break;\n T=max(0.05,15.0*pow(0.05/15.0,e/2.90));\n }\n int j=rng()%MK;Line nl;\n if(is_dummy[j]){\n nl=rline();\n }else{\n int sel=rng()%100;\n if(sel<22)nl=pline(cur_lines[j],30);\n else if(sel<38)nl=pline_perp(cur_lines[j],50);\n else if(sel<50)nl=pline_rot(cur_lines[j],10);\n else if(sel<68)nl=pline(cur_lines[j],300);\n else if(sel<82)nl=pline(cur_lines[j],2000);\n else nl=rline();\n }\n if(nl.px==nl.qx&&nl.py==nl.qy)continue;\n int ns=try_ch(j,nl);int ds=ns-cscore;bool acc=(ds>=0);\n if(!acc&&T>0.01)acc=((double)(rng()>>8)/(double)(1u<<24))best_score){best_score=cscore;memcpy(best_lines,cur_lines,sizeof(cur_lines));}\n }\n }\n cout<\nusing namespace std;\nconst int MAXN=65;\nint N,M,cc;\nbool dots[MAXN][MAXN],h_seg[MAXN][MAXN],v_seg[MAXN][MAXN],d1_seg[MAXN][MAXN],d2_seg[MAXN][MAXN],inPQ[MAXN][MAXN];\nvector row_dots[MAXN],col_dots[MAXN],diag_dots[130],ad_dots[130];\nstruct Op{int x1,y1,x2,y2,x3,y3,x4,y4;};\nvector ops,best_ops;\npriority_queue>> work_pq;\nlong long best_score=0;\nint init_M; pair init_list[400];\nmt19937 rng(0); int run_mode=0;\nvoid ins(vector&v,int x){v.insert(lower_bound(v.begin(),v.end(),x),x);}\nvoid addDot(int x,int y){dots[x][y]=true;ins(row_dots[y],x);ins(col_dots[x],y);ins(diag_dots[x-y+64],x);ins(ad_dots[x+y],x);}\nbool ec(int x1,int y1,int x2,int y2){\n if(x1==x2){for(int y=min(y1,y2);yx1)==(y2>y1)){int xm=min(x1,x2),ym=min(y1,y2);for(int t=0;tx1)?1:-1,dy=(y2>y1)?1:-1;for(int t=1;tx1)==(y2>y1)){int xm=min(x1,x2),ym=min(y1,y2);for(int t=0;t=N||y2<0||y2>=N||x3<0||x3>=N||y3<0||y3>=N||x4<0||x4>=N||y4<0||y4>=N)return false;\n if(!dots[x2][y2]||!dots[x3][y3]||!dots[x4][y4])return false;\n if(!en(nx,ny,x2,y2)||!en(x2,y2,x3,y3)||!en(x3,y3,x4,y4)||!en(x4,y4,nx,ny))return false;\n if(!ec(nx,ny,x2,y2)||!ec(x2,y2,x3,y3)||!ec(x3,y3,x4,y4)||!ec(x4,y4,nx,ny))return false;\n ops.push_back({nx,ny,x2,y2,x3,y3,x4,y4});addDot(nx,ny);de(nx,ny,x2,y2);de(x2,y2,x3,y3);de(x3,y3,x4,y4);de(x4,y4,nx,ny);return true;}\nbool fap(int nx,int ny){\n if(dots[nx][ny])return false;\n vector> cands;\n for(int x2:row_dots[ny]){if(x2==nx)continue;for(int y2:col_dots[nx]){if(y2==ny||!dots[x2][y2])continue;cands.emplace_back((abs(x2-nx)+abs(y2-ny))*2,x2,ny,x2,y2,nx,y2);}}\n for(int xa:diag_dots[nx-ny+64]){if(xa==nx)continue;int a=xa-nx;for(int xb:ad_dots[nx+ny]){if(xb==nx)continue;int b=xb-nx;int x3=nx+a+b,y3=ny+a-b;if(x3>=0&&x3=0&&y3(c)+=rng()%8;\n sort(cands.begin(),cands.end());\n }else{\n shuffle(cands.begin(),cands.end(),rng);\n }\n for(auto&[p,x2,y2,x3,y3,x4,y4]:cands)if(cando(nx,ny,x2,y2,x3,y3,x4,y4))return true;\n return false;}\nvoid addWork(int x,int y){if(x<0||x>=N||y<0||y>=N||dots[x][y]||inPQ[x][y])return;inPQ[x][y]=true;work_pq.push({(x-cc)*(x-cc)+(y-cc)*(y-cc)+1,{x,y}});}\nvoid afterPlace(int x,int y){\n for(int i=0;i>>();\n for(int i=0;i(chrono::steady_clock::now()-t0).count()>=lim)return;\n auto[w,pos]=work_pq.top();work_pq.pop();auto[x,y]=pos;inPQ[x][y]=false;\n if(dots[x][y])continue;if(fap(x,y))afterPlace(x,y);}}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>N>>M;cc=(N-1)/2;init_M=M;\n for(int i=0;i>init_list[i].first>>init_list[i].second;}\n vector>> pts;\n for(int x=0;x(chrono::steady_clock::now()-t0).count();};\n for(int run=0;el()<4380;run++){\n run_mode=run;\n if(run>=2)rng.seed((long long)run*31337+12345);\n resetRun();\n long long re=min(4380LL,el()+550LL);\n drainQ(re,t0);\n bool changed=true;\n while(changed&&el()=re)break;\n auto[x,y]=pos;if(dots[x][y])continue;\n if(fap(x,y)){changed=true;afterPlace(x,y);drainQ(re,t0);}\n }\n }\n long long sc=0;\n for(int x=0;xbest_score){best_score=sc;best_ops=ops;}\n }\n cout<\nusing namespace std;\ntypedef array,10> Grid;\n\nGrid applyTilt(Grid g, char dir) {\n if(dir=='L'){for(int i=0;i<10;i++){int p=0;for(int j=0;j<10;j++)if(g[i][j])g[i][p++]=g[i][j];for(;p<10;p++)g[i][p]=0;}}\n else if(dir=='R'){for(int i=0;i<10;i++){int p=9;for(int j=9;j>=0;j--)if(g[i][j])g[i][p--]=g[i][j];for(;p>=0;p--)g[i][p]=0;}}\n else if(dir=='F'){for(int j=0;j<10;j++){int p=0;for(int i=0;i<10;i++)if(g[i][j])g[p++][j]=g[i][j];for(;p<10;p++)g[p][j]=0;}}\n else{for(int j=0;j<10;j++){int p=9;for(int i=9;i>=0;i--)if(g[i][j])g[p--][j]=g[i][j];for(;p>=0;p--)g[p][j]=0;}}\n return g;\n}\n// Merged: connectivity (\u03a3ni\u00b2) + row/col purity in one pass\nlong long evalLeaf(const Grid& g){\n int rc[10][4]={},cc[10][4]={};\n bool vis[10][10]={};long long sum=0;int stk[100][2];\n const int dx[]={-1,1,0,0},dy[]={0,0,-1,1};\n for(int si=0;si<10;si++)for(int sj=0;sj<10;sj++){\n if(!g[si][sj])continue;\n rc[si][g[si][sj]]++;cc[sj][g[si][sj]]++;\n if(vis[si][sj])continue;\n int f=g[si][sj],sz=0,top=0;\n stk[top][0]=si;stk[top][1]=sj;top++;vis[si][sj]=true;\n while(top>0){--top;int x=stk[top][0],y=stk[top][1];sz++;\n for(int d=0;d<4;d++){int nx=x+dx[d],ny=y+dy[d];\n if(nx>=0&&nx<10&&ny>=0&&ny<10&&!vis[nx][ny]&&g[nx][ny]==f){vis[nx][ny]=true;stk[top][0]=nx;stk[top][1]=ny;top++;}}}\n sum+=(long long)sz*sz;}\n for(int i=0;i<10;i++)for(int f=1;f<=3;f++)\n sum+=(long long)(rc[i][f]*rc[i][f]+cc[i][f]*cc[i][f]);\n return sum;\n}\nGrid placeCandy(Grid g,int p,int flav){\n int cnt=0;for(int i=0;i<10;i++)for(int j=0;j<10;j++)if(!g[i][j]&&++cnt==p){g[i][j]=flav;return g;}return g;\n}\nconst char DIRS[]={'F','B','L','R'};\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n int fl[100];for(int t=0;t<100;t++)cin>>fl[t];\n Grid grid={};mt19937 rng(20230101);\n const int S=8;\n for(int t=0;t<100;t++){\n int p;cin>>p;grid=placeCandy(grid,p,fl[t]);\n char bestDir='F';\n if(t<99){\n int nc1=99-t,nc2=98-t;\n int s3[S],s_cnt=0;\n if(t+2<100){s_cnt=min(S,nc2);\n if(nc2<=S){for(int s=0;sbest){best=total;bestDir=d1;}}\n }\n cout<\n#include \nusing namespace std;\nusing namespace Eigen;\nint M, N; double eps;\ndouble normalCDF(double x){return 0.5*erfc(-x*M_SQRT1_2);}\nvector getDeg(const string& s,int n){vector d(n,0);int idx=0;for(int i=0;i getEig(const string& s,int n){MatrixXd A(n,n);A.setZero();int idx=0;for(int i=0;i sol(A,EigenvaluesOnly);vector ev(n);for(int i=0;iint{if(a>b)swap(a,b);return a*(2*n-a-1)/2+(b-a-1);};int cnt=0;for(int d=1;d> centers(M);\n for(int k=0;kbestScore){bestScore=score;optN=n;}\n }\n return optN;\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>M>>eps;N=computeOptimalN(M,eps);\n int ME=N*(N-1)/2;vector G(M);\n for(int k=0;k=20);\n int NS,FD;\n if(useEig){NS=min(500,NS_eig);FD=2*N;}\n else{long long opPS_deg=(long long)N*N;NS=max(30,min(1000,(int)(budget/max(1LL,(long long)M*opPS_deg))));FD=N;}\n vector> C(M,vector(FD,0.0));\n if(eps<1e-9){\n for(int k=0;k u(0.0,1.0);\n for(int k=0;k>h;\n vector hf(FD);auto dh=getDeg(h,N);for(int i=0;i\nusing namespace std;\ntypedef long long ll;typedef pair pli;\nconst ll INF=1e18;const int MXN=1005,MXM=3005,MXD=35,MAXCP=10;\nint N,M,D,K,EU[MXM],EV[MXM];ll EW[MXM];\nvector> G[MXN];ll gd[MXN][MXN];\ndouble imp[MXM];int aday[MXM];double ADJ[MXM][MXD];int cutD[MXM][MXD];\nvector ladj[MXM],cpairs[MXM],dayE[MXD];int dpos[MXM];ll dtmp2[MXN];\nuint64_t rs=0xdeadbeef123ULL;\nuint64_t rng(){rs^=rs<<13;rs^=rs>>7;rs^=rs<<17;return rs;}\nint ri(int n){return(int)(rng()%(unsigned)n);}double rd(){return(rng()>>11)*(1.0/(1ull<<53));}\nvoid dijk(int s){fill(gd[s]+1,gd[s]+N+1,INF);gd[s][s]=0;priority_queue,greater>pq;pq.push({0,s});while(!pq.empty()){auto[d,u]=pq.top();pq.pop();if(d>gd[s][u])continue;for(auto&[v,e]:G[u]){ll nd=d+EW[e];if(nd,greater>pq;pq.push({0,s});while(!pq.empty()){auto[dd,u]=pq.top();pq.pop();if(dd>d[u])continue;if(u==t)return d[t];for(auto&[v,e]:G[u]){if(e==sk)continue;ll nd=dd+EW[e];if(nd&srcs){double tot=0.0;for(int s:srcs){fill(dtmp2+1,dtmp2+N+1,INF);dtmp2[s]=0;priority_queue,greater>pq;pq.push({0,s});while(!pq.empty()){auto[dd,u]=pq.top();pq.pop();if(dd>dtmp2[u])continue;for(auto&[v,ei]:G[u]){if(aday[ei]==d)continue;ll nd=dd+EW[ei];if(ndgd[s][t])tot+=(double)(dtmp2[t]-gd[s][t]);}return tot/((double)srcs.size()*(N-1));}\nstruct BrFr{int u,pe,ix;};struct BrI{int e,sz;};int bdt[MXN],blv[MXN];vector bstk;\nvoid findBr(int sk,vector&br){fill(bdt+1,bdt+N+1,-1);int tm=0;bstk.clear();if((int)bstk.capacity()bdt[p.u])br.push_back({pe,sz});}}}}\nbool cvis[MXN];int cq[MXN];\nint main(){\n ios_base::sync_with_stdio(0);cin.tie(0);\n auto tst=chrono::steady_clock::now();\n cin>>N>>M>>D>>K;\n for(int i=0;i>EU[i]>>EV[i]>>EW[i];G[EU[i]].push_back({EV[i],i});G[EV[i]].push_back({EU[i],i});}\n for(int i=1;i<=N;i++){int x,y;cin>>x>>y;}\n for(int s=1;s<=N;s++)dijk(s);\n {vectorpar(N+1,-1),sv(N);vectorsz(N+1,1);iota(sv.begin(),sv.end(),1);for(int s=1;s<=N;s++){fill(par.begin(),par.end(),-1);fill(sz.begin(),sz.end(),1LL);sort(sv.begin(),sv.end(),[s](int a,int b){return gd[s][a]=0;i--){int v=sv[i];if(par[v]<0)continue;int p=(EU[par[v]]==v)?EV[par[v]]:EU[par[v]];sz[p]+=sz[v];}for(int v:sv){if(par[v]<0)continue;imp[par[v]]+=(double)sz[v];}}}\n for(int e=0;ebr;for(int e=0;emin(b.sz,N-b.sz);});for(auto&bi:br){if((int)cpairs[e].size()>=MAXCP)break;auto it=lower_bound(cpairs[e].begin(),cpairs[e].end(),bi.e);if(it==cpairs[e].end()||*it!=bi.e)cpairs[e].insert(it,bi.e);}}}\n for(int u=1;u<=N;u++){int dg=G[u].size();for(int i=0;ieo(M);iota(eo.begin(),eo.end(),0);sort(eo.begin(),eo.end(),[](int a,int b){return imp[a]>imp[b];});\n for(int e:eo){int best=-1;double bs=1e18;int bc=INT_MAX;\n for(int d=0;d=K)continue;int cuts=0;for(int f:cpairs[e])if(aday[f]==d)cuts++;double cf=0;for(int e2:ladj[e])if(aday[e2]==d)cf+=imp[e2];double sc=cf+1e-12*dc[d];if(cuts0)continue;\n double dl=imp[e1]*(ADJ[e1][d2]-ADJ[e1][d1])+imp[e2]*(ADJ[e2][d1]-ADJ[e2][d2])-2.*isAdj(e1,e2)*imp[e1]*imp[e2];\n sm+=fabs(dl);c++;}\n if(c>0)T=sm/c;if(T<1e-9)T=1.0;}\n double T0=T;\n // Phase 1: Proxy SA (1.5s)\n for(long long step=0;;step++){\n if(step%200000==0){double el=chrono::duration(chrono::steady_clock::now()-tst).count();if(el>1.5)break;T=T0*exp(-10.*el/1.5);}\n int d1=ri(D),d2=ri(D);if(d1==d2||dayE[d1].empty()||dayE[d2].empty())continue;\n int e1=dayE[d1][ri(dayE[d1].size())],e2=dayE[d2][ri(dayE[d2].size())];\n int ic=isCut(e1,e2)?1:0;int dlc=(cutD[e1][d2]-ic)+(cutD[e2][d1]-ic)-cutD[e1][d1]-cutD[e2][d2];if(dlc>0)continue;\n double dl=imp[e1]*(ADJ[e1][d2]-ADJ[e1][d1])+imp[e2]*(ADJ[e2][d1]-ADJ[e2][d2])-2.*isAdj(e1,e2)*imp[e1]*imp[e2];\n if(dl<=0||(T>1e-9&&rd() srcs;vector sfk(D);\n auto doSample=[&](){\n srcs.clear();setused;\n while((int)srcs.size()(chrono::steady_clock::now()-tst).count();if(el>5.2)break;\n int d1=ri(D);for(int k=0;k<3;k++){int d=ri(D);if(sfk[d]>sfk[d1])d1=d;}\n if(dayE[d1].empty())continue;\n int d2=-1;for(int k=0;k<4;k++){int d=ri(D);if(d!=d1&&!dayE[d].empty()&&(d2<0||sfk[d]0)continue;\n double old_f1=sfk[d1],old_f2=sfk[d2];\n aday[e1]=d2;aday[e2]=d1;\n double new_f1=diagFk(d1,srcs);double new_f2=diagFk(d2,srcs);\n aday[e1]=d1;aday[e2]=d2;\n double delta_act=(new_f1+new_f2)-(old_f1+old_f2);\n if(++eval_cnt%200==0)doSample();\n if(delta_act<0){\n for(int e:ladj[e1]){ADJ[e][d1]-=imp[e1];ADJ[e][d2]+=imp[e1];}for(int e:ladj[e2]){ADJ[e][d2]-=imp[e2];ADJ[e][d1]+=imp[e2];}\n for(int f:cpairs[e1]){cutD[f][d1]--;cutD[f][d2]++;}for(int f:cpairs[e2]){cutD[f][d2]--;cutD[f][d1]++;}\n {int p=dpos[e1],L=dayE[d1].back();dayE[d1][p]=L;dpos[L]=p;dayE[d1].pop_back();}\n {int p=dpos[e2],L=dayE[d2].back();dayE[d2][p]=L;dpos[L]=p;dayE[d2].pop_back();}\n dpos[e1]=dayE[d2].size();dayE[d2].push_back(e1);aday[e1]=d2;dpos[e2]=dayE[d1].size();dayE[d1].push_back(e2);aday[e2]=d1;\n sfk[d1]=new_f1;sfk[d2]=new_f2;\n }\n }\n }\n // Phase 3: Post-processing\n for(int d=0;d0){\n fill(cvis+1,cvis+N+1,false);int h=0,t=0;cvis[1]=true;cq[t++]=1;\n while(h=K)continue;double cost=0;for(int ef:ladj[e])if(aday[ef]==dd)cost+=imp[e]*imp[ef];if(bdd<0||cost=0){for(int ef:ladj[e]){ADJ[ef][d]-=imp[e];ADJ[ef][bdd]+=imp[e];}for(int f:cpairs[e]){cutD[f][d]--;cutD[f][bdd]++;}\n {int p=dpos[e],L=dayE[d].back();dayE[d][p]=L;dpos[L]=p;dayE[d].pop_back();}dpos[e]=dayE[bdd].size();dayE[bdd].push_back(e);aday[e]=bdd;fx=true;}}\n if(!fx)break;}}\n for(int i=0;i\nusing namespace std;\nint D;string Fs[2][14],Rs[2][14];int bid,B[2][2744];bool occ[2][2744];\nstruct Box{int x,y,z,a,b,c;};\nbool bf(int r,int x0,int y0,int z0,int a,int b,int c){for(int i=0;it0,vectort1){double sc=0;int r0=0,r1=0,i0=0,i1=0;while(true){if(!r0&&i0<(int)t0.size())r0=t0[i0++];if(!r1&&i1<(int)t1.size())r1=t1[i1++];if(!r0||!r1)break;int ml=min(r0,r1);sc+=1.0/ml;r0-=ml;r1-=ml;}sc+=r0;while(i0<(int)t0.size())sc+=t0[i0++];sc+=r1;while(i1<(int)t1.size())sc+=t1[i1++];return sc;}\ntemplate\nvoid runBestTP(vector>brv0,vector>brv1,const vector&F0,const vector&F1,auto fillFn){\n vectorl0,l1;for(auto[l,i]:brv0)l0.push_back(l);for(auto[l,i]:brv1)l1.push_back(l);\n double bsc=1e18;vector>rv0=brv0,rv1=brv1;mt19937 rng(42);\n auto tryOrd=[&](vector>r0,vector>r1){vectort0,t1;for(auto[l,i]:r0)t0.push_back(l);for(auto[l,i]:r1)t1.push_back(l);double sc=simTP(t0,t1);if(scb.first;});sort(r1.begin(),r1.end(),[=](auto&a,auto&b){return o1?a.firstb.first;});tryOrd(r0,r1);}\n for(int rep=0;rep<10;rep++){auto r0=brv0,r1=brv1;shuffle(r0.begin(),r0.end(),rng);shuffle(r1.begin(),r1.end(),rng);tryOrd(r0,r1);}\n struct SO{int idx,off;};dequer0d,r1d;for(auto[l,i]:rv0)r0d.push_back({i,0});for(auto[l,i]:rv1)r1d.push_back({i,0});\n while(!r0d.empty()&&!r1d.empty()){auto&[i0,o0]=r0d.front();auto&[i1,o1]=r1d.front();int ml=min(F0[i0].len-o0,F1[i1].len-o1);bid++;fillFn(0,F0[i0],bid,o0,ml);fillFn(1,F1[i1],bid,o1,ml);o0+=ml;o1+=ml;if(o0==F0[i0].len)r0d.pop_front();if(o1==F1[i1].len)r1d.pop_front();}\n while(!r0d.empty()){auto[i0,o0]=r0d.front();r0d.pop_front();bid++;fillFn(0,F0[i0],bid,o0,F0[i0].len-o0);}\n while(!r1d.empty()){auto[i1,o1]=r1d.front();r1d.pop_front();bid++;fillFn(1,F1[i1],bid,o1,F1[i1].len-o1);}\n}\nvectoreB(int arr){vectorv;uint16_t fz[14]={},rz[14]={};for(int z=0;zgRL(int arr,int ax){vectorL;if(ax==0){for(int y=0;y=0){L.push_back({s,y,z,x-s,0});s=-1;}}}}else if(ax==1){for(int x=0;x=0){L.push_back({x,s,z,y-s,1});s=-1;}}}}else{for(int x=0;x=0){L.push_back({x,y,s,z-s,2});s=-1;}}}}return L;}\ndouble mS(const vector&L0,const vector&L1){mapc0,c1;for(auto&l:L0)c0[l.len]++;for(auto&l:L1)c1[l.len]++;double sc=0;int v0=0,v1=0;for(auto&[l,c]:c0){int cl=c1.count(l)?c1[l]:0;sc+=min(c,cl)*1.0/l;v0+=(c-min(c,cl))*l;}for(auto&[l,c]:c1){int cl=c0.count(l)?c0[l]:0;if(c>cl)v1+=(c-cl)*l;}return sc+max(v0,v1);}\nvoid doBox(){auto bx0=eB(0),bx1=eB(1);typedef arrayKey;auto gk=[](const Box&b)->Key{Key k={b.a,b.b,b.c};sort(k.begin(),k.end());return k;};map>g0,g1;for(int i=0;i<(int)bx0.size();i++)g0[gk(bx0[i])].push_back(i);for(int i=0;i<(int)bx1.size();i++)g1[gk(bx1[i])].push_back(i);vector>grps;for(auto&[k,v]:g0)if(g1.count(k))grps.push_back({k[0]*k[1]*k[2],k});sort(grps.rbegin(),grps.rend());for(auto&[vol,key]:grps){auto&v0=g0[key];auto&v1=g1[key];int p1=0;for(int i0:v0){auto&B0=bx0[i0];if(!bf(0,B0.x,B0.y,B0.z,B0.a,B0.b,B0.c))continue;while(p1<(int)v1.size()&&!bf(1,bx1[v1[p1]].x,bx1[v1[p1]].y,bx1[v1[p1]].z,bx1[v1[p1]].a,bx1[v1[p1]].b,bx1[v1[p1]].c))p1++;if(p1>=(int)v1.size())break;auto&B1=bx1[v1[p1++]];bid++;fB(0,B0.x,B0.y,B0.z,B0.a,B0.b,B0.c,bid);fB(1,B1.x,B1.y,B1.z,B1.a,B1.b,B1.c,bid);}}\n int bax0=1,bax1=1;double bsc=1e18;for(int a0=0;a0<3;a0++){auto Lt0=gRL(0,a0);for(int a1=0;a1<3;a1++){auto Lt1=gRL(1,a1);double sc=mS(Lt0,Lt1);if(sc>gl0,gl1;for(int i=0;i<(int)L0.size();i++)gl0[L0[i].len].push_back(i);for(int i=0;i<(int)L1.size();i++)gl1[L1[i].len].push_back(i);vectorlu0(L0.size(),false),lu1(L1.size(),false);for(auto&[l,v0]:gl0){auto it=gl1.find(l);if(it==gl1.end())continue;auto&v1=it->second;int mc=min((int)v0.size(),(int)v1.size());for(int j=0;jtuple{return{s.x+(s.ax==0?off:0),s.y+(s.ax==1?off:0),s.z+(s.ax==2?off:0)};};auto[x0,y0,z0]=gp(L0[v0[j]],0);fL(0,x0,y0,z0,l,L0[v0[j]].ax,bid);auto[x1,y1,z1]=gp(L1[v1[j]],0);fL(1,x1,y1,z1,l,L1[v1[j]].ax,bid);lu0[v0[j]]=lu1[v1[j]]=true;}}\n vector>rv0,rv1;for(int i=0;i<(int)L0.size();i++)if(!lu0[i])rv0.push_back({L0[i].len,i});for(int i=0;i<(int)L1.size();i++)if(!lu1[i])rv1.push_back({L1[i].len,i});\n auto gp=[&](const Ln&s,int off)->tuple{return{s.x+(s.ax==0?off:0),s.y+(s.ax==1?off:0),s.z+(s.ax==2?off:0)};};auto fillLn=[&](int arr,const Ln&s,int id,int off,int len){auto[x,y,z]=gp(s,off);fL(arr,x,y,z,len,s.ax,id);};\n runBestTP(rv0,rv1,L0,L1,fillLn);}\nstruct Seg{int x,y,z,len,ax;};\nvectorbuildSegs(int arr,int ax){vectorc;if(ax==2)for(int x=0;x=0){c.push_back({x,y,zs,z-zs,2});zs=-1;}}}else if(ax==1)for(int x=0;x=0){c.push_back({x,ys,z,y-ys,1});ys=-1;}}}else for(int y=0;y=0){c.push_back({xs,y,z,x-xs,0});xs=-1;}}}return c;}\nvectorgreedyFill(vectorc){bool cx[14][14]={},cy[14][14]={};vectorsel;for(auto&s:c){bool u=false;for(int k=0;kmF(int arr,int ax){auto c=buildSegs(arr,ax);sort(c.begin(),c.end(),[](const Seg&a,const Seg&b){return a.len>b.len;});return greedyFill(c);}\nvectormFbiased(int arr,int ax,const multiset&prefer){auto c=buildSegs(arr,ax);sort(c.begin(),c.end(),[&](const Seg&a,const Seg&b){int pa=prefer.count(a.len),pb=prefer.count(b.len);if(pa!=pb)return pa>pb;return a.len>b.len;});return greedyFill(c);}\nvectormFspatial(int arr,int ax,int mode){auto c=buildSegs(arr,ax);sort(c.begin(),c.end(),[mode](const Seg&a,const Seg&b){if(a.len!=b.len)return a.len>b.len;if(mode==0){if(a.x!=b.x)return a.xmFbiasedSpatial(int arr,int ax,const multiset&prefer,int mode){auto c=buildSegs(arr,ax);sort(c.begin(),c.end(),[&](const Seg&a,const Seg&b){int pa=(int)prefer.count(a.len),pb=(int)prefer.count(b.len);if(pa!=pb)return pa>pb;if(a.len!=b.len)return a.len>b.len;if(mode==0){if(a.x!=b.x)return a.x&F0,const vector&F1){map>g0,g1;for(int i=0;i<(int)F0.size();i++)g0[F0[i].len].push_back(i);for(int i=0;i<(int)F1.size();i++)g1[F1[i].len].push_back(i);vectoru0(F0.size(),false),u1(F1.size(),false);for(auto&[l,v0]:g0){auto it=g1.find(l);if(it==g1.end())continue;auto&v1=it->second;int mc=min((int)v0.size(),(int)v1.size());for(int j=0;j>rv0,rv1;for(int i=0;i<(int)F0.size();i++)if(!u0[i])rv0.push_back({F0[i].len,i});for(int i=0;i<(int)F1.size();i++)if(!u1[i])rv1.push_back({F1[i].len,i});\n auto fillSeg=[&](int arr,const Seg&s,int id,int off,int len){fS(arr,s,id,off,len);};runBestTP(rv0,rv1,F0,F1,fillSeg);}\ndouble cScore(int mb){vectorv0(mb+1,0),v1(mb+1,0);for(int i=0;i0&&v1[k]>0)sc+=1.0/v0[k];else if(v0[k]>0)sc+=v0[k];else sc+=v1[k];}return sc;}\ndouble doMFboxed(const vector&F0,const vector&F1){\n uint16_t f0[14][14]={},f1[14][14]={};\n auto buildF=[&](uint16_t f[14][14],const vector&segs){for(auto&s:segs)for(int k=0;kvector{vectorv;for(int x0=0;x0bool{bool*lo=r?lo1:lo0;for(int i=0;iKey;auto gk=[](const Box&b)->Key{Key k={b.a,b.b,b.c};sort(k.begin(),k.end());return k;};\n map>gb0,gb1;for(int i=0;i<(int)bxs0.size();i++)gb0[gk(bxs0[i])].push_back(i);for(int i=0;i<(int)bxs1.size();i++)gb1[gk(bxs1[i])].push_back(i);\n vector>grps;for(auto&[k,v]:gb0)if(gb1.count(k))grps.push_back({k[0]*k[1]*k[2],k});sort(grps.rbegin(),grps.rend());\n for(auto&[vol,key]:grps){auto&v0=gb0[key];auto&v1=gb1[key];int p1=0;for(int i0:v0){if(!bfL(0,bxs0[i0]))continue;while(p1<(int)v1.size()&&!bfL(1,bxs1[v1[p1]]))p1++;if(p1>=(int)v1.size())break;bid++;fBL(0,bxs0[i0],bid);fBL(1,bxs1[v1[p1++]],bid);}}\n auto getR=[&](bool*lo,uint16_t f[14][14])->vector{vectorsegs;for(int x=0;x=0){segs.push_back({x,y,zs,z-zs,2});zs=-1;}}}return segs;};\n auto rem0=getR(lo0,f0),rem1=getR(lo1,f1);\n map>gr0,gr1;for(int i=0;i<(int)rem0.size();i++)gr0[rem0[i].len].push_back(i);for(int i=0;i<(int)rem1.size();i++)gr1[rem1[i].len].push_back(i);\n vectorur0(rem0.size(),false),ur1(rem1.size(),false);for(auto&[l,v0]:gr0){auto it=gr1.find(l);if(it==gr1.end())continue;auto&v1=it->second;int mc=min((int)v0.size(),(int)v1.size());for(int j=0;j>rv0,rv1;for(int i=0;i<(int)rem0.size();i++)if(!ur0[i])rv0.push_back({rem0[i].len,i});for(int i=0;i<(int)rem1.size();i++)if(!ur1[i])rv1.push_back({rem1[i].len,i});\n auto fillSeg=[&](int arr,const Seg&s,int id,int off,int len){fS(arr,s,id,off,len);};runBestTP(rv0,rv1,rem0,rem1,fillSeg);\n return cScore(bid);}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>D;for(int i=0;i<2;i++){for(int z=0;z>Fs[i][z];for(int z=0;z>Rs[i][z];}\n struct Res{int bid;int B[2][2744];};\n double best=1e18;Res bestR;bestR.bid=0;memset(bestR.B,0,sizeof(bestR.B));\n auto tryIt=[&](auto fn){memset(B,0,sizeof(B));bid=0;double s=fn();if(sL0,L1;for(auto&s:F0u)L0.insert(s.len);for(auto&s:F1u)L1.insert(s.len);\n auto F0b=mFbiased(0,a0,L1),F1b=mFbiased(1,a1,L0);\n tryIt([&,F0b,F1b]{doMF(F0b,F1b);return cScore(bid);});\n tryIt([&,F0b,F1b]{return doMFboxed(F0b,F1b);});\n multisetL0b,L1b;for(auto&s:F0b)L0b.insert(s.len);for(auto&s:F1b)L1b.insert(s.len);\n auto F0b2=mFbiased(0,a0,L1b),F1b2=mFbiased(1,a1,L0b);\n tryIt([&,F0b2,F1b2]{doMF(F0b2,F1b2);return cScore(bid);});\n tryIt([&,F0b2,F1b2]{return doMFboxed(F0b2,F1b2);});\n for(int mode=0;mode<2;mode++){\n auto F0s=mFspatial(0,a0,mode),F1s=mFspatial(1,a1,mode);\n tryIt([&,F0s,F1s]{doMF(F0s,F1s);return cScore(bid);});\n tryIt([&,F0s,F1s]{return doMFboxed(F0s,F1s);});\n auto F0bs=mFbiasedSpatial(0,a0,L1,mode),F1bs=mFbiasedSpatial(1,a1,L0,mode);\n tryIt([&,F0bs,F1bs]{return doMFboxed(F0bs,F1bs);});\n }\n }\n tryIt([&]{memset(occ,0,sizeof(occ));doBox();return cScore(bid);});\n bid=bestR.bid;memcpy(B,bestR.B,sizeof(B));\n cout<\nusing namespace std;\ntypedef long long ll;\n\nint main() {\n auto tStart = chrono::steady_clock::now();\n auto msElapsed = [&]() {\n return (int)chrono::duration_cast(chrono::steady_clock::now()-tStart).count();\n };\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int N,M,K; cin>>N>>M>>K;\n vector X(N),Y(N);\n for(int i=0;i>X[i]>>Y[i];\n vector EU(M),EV(M); vector EW(M);\n for(int j=0;j>EU[j]>>EV[j]>>EW[j];EU[j]--;EV[j]--;}\n vector A(K),B(K);\n for(int k=0;k>A[k]>>B[k];\n const ll MAXP=5000,MAXP2=MAXP*MAXP,INF=(ll)4e18;\n // D2[i][k] and D2T[k][i] (transposed, cache-efficient for fixed k, varying i)\n vector> D2(N,vector(K)),D2T(K,vector(N));\n for(int i=0;i>> adj(N);\n for(int j=0;jll{if(!d2)return 0;ll p=(ll)sqrt((double)d2);while(p*p> spD(N,vector(N,INF));\n vector> spE(N,vector(N,-1)),spPr(N,vector(N,-1));\n for(int s=0;s,vector>,greater<>> pq;pq.push({0,s});\n while(!pq.empty()){auto[d,v]=pq.top();pq.pop();if(d>spD[s][v])continue;\n for(auto&[u,j]:adj[v]){ll nd=d+EW[j];if(nd term)->vector{\n term[0]=true;vectorT;for(int i=0;iin(TN,false);vectorkey(TN,INF);vectorpar(TN,-1);key[0]=0;\n for(int it=0;it=INF)break;in[u]=true;\n for(int w=0;weo(M,false);\n for(int i=0;i&reach)->pair,ll>{\n vector>vR(N);vectorvMx(N,0);\n for(int k=0;kMAXP2)return{{},INF};\n vR[bv].push_back(k);vMx[bv]=max(vMx[bv],best);\n }\n vectorPv(N,0);for(int i=0;itp(N);\n for(int u=0;utp[u].d[0]){tp[u].d[3]=tp[u].d[2];tp[u].k[3]=tp[u].k[2];tp[u].d[2]=tp[u].d[1];tp[u].k[2]=tp[u].k[1];tp[u].d[1]=tp[u].d[0];tp[u].k[1]=tp[u].k[0];tp[u].d[0]=d;tp[u].k[0]=k;}\n else if(d>tp[u].d[1]){tp[u].d[3]=tp[u].d[2];tp[u].k[3]=tp[u].k[2];tp[u].d[2]=tp[u].d[1];tp[u].k[2]=tp[u].k[1];tp[u].d[1]=d;tp[u].k[1]=k;}\n else if(d>tp[u].d[2]){tp[u].d[3]=tp[u].d[2];tp[u].k[3]=tp[u].k[2];tp[u].d[2]=d;tp[u].k[2]=k;}\n else if(d>tp[u].d[3]){tp[u].d[3]=d;tp[u].k[3]=k;}\n }}\n ll bD=0;int bU=-1,bV=-1,bT=-1;\n for(int u=0;u=0){ll d1v=D2T[tp[u].k[1]][v];if(d1v<=MAXP2){ll nPu=pVal(tp[u].d[2]),nPv=pVal(max({vMx[v],d0v,d1v}));ll d=nPu*nPu+nPv*nPv-Pu2-Pv2;if(d=0){ll d1v=D2T[tp[u].k[1]][v],d2v=D2T[tp[u].k[2]][v];if(d1v<=MAXP2&&d2v<=MAXP2){ll nPu=pVal(tp[u].d[3]),nPv=pVal(max({vMx[v],d0v,d1v,d2v}));ll d=nPu*nPu+nPv*nPv-Pu2-Pv2;if(du&&f0&&tp[v].k[0]>=0){ll d0u=D2T[tp[v].k[0]][u];if(d0u<=MAXP2){ll nMxU=max(tp[u].d[1],d0u),nMxV=max(tp[v].d[1],d0v);ll nPu=pVal(nMxU),nPv=pVal(nMxV);ll d=nPu*nPu+nPv*nPv-Pu2-Pv2;if(dP(N,0);ll pc=0;for(int i=0;i&eo)->tuple,ll,bool>{\n vectorreach(N,false);queueq;q.push(0);reach[0]=true;\n while(!q.empty()){int v=q.front();q.pop();for(auto&[u,j]:adj[v])if(eo[j]&&!reach[u]){reach[u]=true;q.push(u);}}\n ll ec=0;for(int j=0;jmstPar(N,-1),mstPE(N,-1);vector>mstCh(N);\n {vectorvis(N,false);vectorkey(N,INF);key[0]=0;\n priority_queue,vector>,greater<>>pq;pq.push({0,0});\n while(!pq.empty()){auto[d,v]=pq.top();pq.pop();if(vis[v])continue;vis[v]=true;for(auto&[u,j]:adj[v])if(!vis[u]&&EW[j]act(N,true);vector>vRes(N);vectorvmx(N,0),Pv(N,0);\n for(int k=0;k>bAs;vector>bAf;\n for(int v=1;vtmp;vector>ta;bool ok=true;\n for(int k:vRes[v]){ll best=INF;int bu=-1;for(int u=0;uMAXP2){ok=false;break;}ta.push_back({k,bu});if(!tmp.count(bu))tmp[bu]=vmx[bu];tmp[bu]=max(tmp[bu],best);}\n if(!ok)continue;\n for(auto&[u,nd]:tmp){ll np=pVal(nd);delta+=np*np-Pv[u]*Pv[u];}\n if(delta=0){act[bV]=false;ec0-=EW[mstPE[bV]];pc0-=Pv[bV]*Pv[bV];Pv[bV]=0;vmx[bV]=0;vRes[bV].clear();\n for(auto&[k,u]:bAs)vRes[u].push_back(k);\n for(auto&[u,nd]:bAf){pc0-=Pv[u]*Pv[u];vmx[u]=nd;Pv[u]=pVal(nd);pc0+=Pv[u]*Pv[u];}imp2=true;}\n }\n ll bestCost=INF;vectorbestEO(M,false);vectorbestP(N,0);\n auto updateBest=[&](const vector&eo,const vector&P,ll cost){if(costeo(M,false);for(int v=1;vterm,int maxIter=20){\n term[0]=true;\n for(int sit=0;sitnt(N,false);nt[0]=true;for(int i=0;i0)nt[i]=true;\n if(nt==term)break;term=nt;\n }\n };\n {vectort(N,false);for(int i=0;i0)t[i]=true;runSteiner(t);}\n {vectort(N,true);runSteiner(t);}\n // Time-based systematic terminal set search\n auto getTerms=[&]()->vector{\n vectort(N,false);t[0]=true;for(int i=0;i0)t[i]=true;return t;\n };\n bool sysImp=true;\n while(sysImp&&msElapsed()<1850){\n sysImp=false;\n vectorcurT=getTerms();\n // Try adding each non-terminal\n for(int v=1;vt=curT;t[v]=true;\n auto eo=buildSteiner(t);auto[sp,sc,sf]=evalEO(eo);\n if(sf&&sct=curT;t[v]=false;\n auto eo=buildSteiner(t);auto[sp,sc,sf]=evalEO(eo);\n if(sf&&sc\nusing namespace std;\n\nconst int N = 30;\nint init_board[N][N], board[N][N];\n\nvoid do_heapify(mt19937* rng, int mode, vector>& ops) {\n memcpy(board, init_board, sizeof(board));\n ops.clear();\n int ys[N];\n for (int x = N-2; x >= 0; x--) {\n for (int y = 0; y <= x; y++) ys[y] = y;\n switch (mode) {\n case 1: // RL\n for (int l=0,r=x; l board[x][b]; });\n break;\n default: // Random\n if (rng) for (int i = x; i > 0; i--) swap(ys[i], ys[(*rng)()%(i+1)]);\n break;\n }\n for (int i = 0; i <= x; i++) {\n int y = ys[i], cx = x, cy = y;\n while (cx < N-1) {\n int ny = (board[cx+1][cy] <= board[cx+1][cy+1]) ? cy : cy+1;\n if (board[cx][cy] <= board[cx+1][ny]) break;\n swap(board[cx][cy], board[cx+1][ny]);\n ops.push_back({cx, cy, cx+1, ny});\n cy = ny; cx++;\n }\n }\n }\n}\n\nint main() {\n ios::sync_with_stdio(false); cin.tie(nullptr);\n for (int x = 0; x < N; x++) for (int y = 0; y <= x; y++) cin >> init_board[x][y];\n\n mt19937 rng(42);\n vector> best, v;\n best.reserve(5000); v.reserve(5000);\n\n do_heapify(nullptr, 0, best); // LR\n for (int mode = 1; mode <= 3; mode++) {\n do_heapify(nullptr, mode, v);\n if (v.size() < best.size()) swap(best, v);\n }\n for (int t = 0; t < 30000; t++) {\n do_heapify(&rng, 4, v);\n if (v.size() < best.size()) swap(best, v);\n }\n\n cout << best.size() << \"\\n\";\n for (auto& op : best)\n cout << op[0] << \" \" << op[1] << \" \" << op[2] << \" \" << op[3] << \"\\n\";\n}","toyota2023summer-final":"#include \nusing namespace std;\nconst int MAXD=9;\nint D,N,M,er,ec;\nbool obs[MAXD][MAXD],hasc[MAXD][MAXD];\nint cnum[MAXD][MAXD],sr[MAXD*MAXD],sc[MAXD*MAXD],pk[MAXD][MAXD];\nconst int DR[4]={-1,1,0,0},DC[4]={0,0,-1,1};\nbool in_(int r,int c){return(unsigned)r<(unsigned)D&&(unsigned)c<(unsigned)D;}\nvoid build_sigma(){\n int dist[MAXD][MAXD];memset(dist,-1,sizeof dist);\n queue>q;q.push({er,ec});dist[er][ec]=0;\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+DR[i],ny=y+DC[i];if(!in_(nx,ny)||dist[nx][ny]>=0||obs[nx][ny])continue;dist[nx][ny]=dist[x][y]+1;q.push({nx,ny});}}\n vector>pos;\n for(int r=0;r&a,const pair&b){if(dist[a.first][a.second]!=dist[b.first][b.second])return dist[a.first][a.second]1)ga[r][c]=true;if(pr!=-1&&gl[nr][nc]>=gd[r][c])ga[r][c]=true;}\n else if(!(nr==pr&&nc==pc))gl[r][c]=min(gl[r][c],gd[nr][nc]);}\n}\npairpick(int t){\n memset(gd,-1,sizeof gd);memset(gl,-1,sizeof gl);memset(ga,0,sizeof ga);gT=0;\n apdfs(er,ec,-1,-1);\n int ir=sr[t],ic=sc[t];\n if(gd[ir][ic]>=0&&!ga[ir][ic])return{ir,ic};\n pairbest={-1,-1};int bd=INT_MAX,brk=-1;bool gots=false;\n for(int r=0;rbrk)));\n if(better){best={r,c};bd=d;brk=rk;gots=s;}\n }\n return best;\n}\nvoid bfsr(bool st[MAXD][MAXD],bool reach[MAXD][MAXD]){\n static pairQ[MAXD*MAXD];memset(reach,0,MAXD*MAXD*sizeof(bool));\n int h=0,t=0;Q[t++]={er,ec};reach[er][ec]=true;\n while(h&v){int inv=0,n=v.size();for(int i=0;iv[j])inv++;return inv;}\nint sim_greedy_inv(bool hin[MAXD][MAXD],vector seq){\n bool h[MAXD][MAXD];memcpy(h,hin,sizeof h);\n while(true){\n bool reach[MAXD][MAXD];bfsr(h,reach);\n int bn=INT_MAX,br=-1,bc=-1;\n for(int r=0;r>transport(){\n bool h[MAXD][MAXD];memcpy(h,hasc,sizeof h);\n vector>ord;ord.reserve(M);\n vectorcommitted;\n for(int s=0;s>acc;\n for(int r=0;rbest_pos={mr,mc};int best_inv=-1;\n for(auto&[nx,rx,cx]:acc){\n if(nx==mn)continue;\n bool h2[MAXD][MAXD];memcpy(h2,h,sizeof h2);h2[rx][cx]=false;\n bool reach2[MAXD][MAXD];bfsr(h2,reach2);\n int gain=0;\n for(int r=0;rsg=committed;sg.push_back(mn);\n best_inv=sim_greedy_inv(hg,sg);\n }\n vectorsx=committed;sx.push_back(nx);\n int inv_x=sim_greedy_inv(h2,sx);\n if(inv_x>D>>N;memset(obs,false,sizeof obs);memset(hasc,false,sizeof hasc);memset(cnum,-1,sizeof cnum);\n er=0;ec=(D-1)/2;for(int i=0;i>r>>c;obs[r][c]=true;}\n build_sigma();\n for(int d=0;d>t;auto[r,c]=pick(t);hasc[r][c]=true;cnum[r][c]=t;cout<\nusing namespace std;using namespace chrono;\nint n,m,g[50][50],og[50][50];bool adj[102][102];\nint ac[102][102],cc[102],dp[102];\nconst int dr[]={0,0,1,-1},dc[]={1,-1,0,0};\nauto t0=steady_clock::now();\nbool tok(){return duration_cast(steady_clock::now()-t0).count()<1500;}\nint gc(int r,int c){return(r<0||r>=n||c<0||c>=n)?0:g[r][c];}\nvoid cajad(){memset(adj,0,sizeof(adj));for(int i=0;iq;for(int c=0;c<=m;c++)if(adj[c][0]){dp[c]=0;q.push(c);}dp[0]=0;while(!q.empty()){int u=q.front();q.pop();for(int v=1;v<=m;v++)if(adj[u][v]&&dp[v]>dp[u]+1){dp[v]=dp[u]+1;q.push(v);}}}\nvoid rcp(){memset(ac,0,sizeof(ac));memset(cc,0,sizeof(cc));for(int i=0;i>q;q.push({sr,sc});v[sr][sc]=1;int cnt=1;while(!q.empty()){auto[cr,cc2]=q.front();q.pop();for(int d=0;d<4;d++){int nr=cr+dr[d],nc=cc2+dc[d];if(nr>=0&&nr=0&&nc=0&&nr=0&&nc=2&&!cok(r,c,col))return 0;for(int d=0;d<4;d++){int nc=gc(r+dr[d],c+dc[d]);if(nc&&nc!=col&&ac[col][nc]<=1)return 0;}return 1;}\nvoid dtr(int r,int c){int col=g[r][c];bool s[102]={};for(int d=0;d<4;d++){int nc=gc(r+dr[d],c+dc[d]);if(nc!=col&&!s[nc]){ac[col][nc]--;s[nc]=1;}}g[r][c]=0;cc[col]--;cc[0]++;for(int d=0;d<4;d++){int nr=r+dr[d],nc=c+dc[d];if(nr<0||nr>=n||nc<0||nc>=n)continue;int ncol=g[nr][nc];if(!ncol)continue;bool hz=0;for(int d2=0;d2<4;d2++){int nr2=nr+dr[d2],nc2=nc+dc[d2];if(nr2==r&&nc2==c)continue;if(nr2<0||nr2>=n||nc2<0||nc2>=n){hz=1;break;}if(!g[nr2][nc2]){hz=1;break;}}if(!hz)ac[ncol][0]++;if(ncol==col)continue;bool sc2=0;for(int d2=0;d2<4;d2++){int nr2=nr+dr[d2],nc2=nc+dc[d2];if(nr2==r&&nc2==c)continue;if(nr2>=0&&nr2=0&&nc2=n||nc<0||nc>=n)continue;int ncol=g[nr][nc];if(!ncol)continue;if(ncol!=col){bool st=0;for(int d2=0;d2<4;d2++){int nr2=nr+dr[d2],nc2=nc+dc[d2];if(nr2==r&&nc2==c)continue;if(nr2>=0&&nr2=0&&nc2=0&&nr2=0&&nc2=2&&!cok(r,c,col))return 0;int best=-1,bd=dp[col]+1;for(int d=0;d<4;d++){int nr=r+dr[d],nc=c+dc[d];if(nr<0||nr>=n||nc<0||nc>=n)continue;int c2=g[nr][nc];if(!c2||c2==col||dp[c2]>dp[col])continue;bool ok=1;for(int d2=0;d2<4;d2++){int dc2=gc(r+dr[d2],c+dc[d2]);if(dc2&&dc2!=col&&dc2!=c2&&!adj[c2][dc2]){ok=0;break;}}if(!ok)continue;ok=1;for(int d2=0;d2<4;d2++){int dc2=gc(r+dr[d2],c+dc[d2]);if(dc2&&dc2!=col&&dc2!=c2&&ac[col][dc2]<=1){ok=0;break;}}if(!ok)continue;if(dp[c2]=0){co=best;return 1;}return 0;}\nint czero(){int c=0;for(int i=0;i&ord){rcp();gtrim();int pz=czero();while(tok()){rcp();for(int p=0;p<10;p++){bool a=0;for(int idx:ord){int i=idx/n,j=idx%n,col=g[i][j],co;if(cra(i,j,co)){dra(i,j,col,co);a=1;}}if(!a)break;}gtrim();int z=czero();if(z<=pz)break;pz=z;}}\nint mg[50][50],mac[102][102],mcc[102];\nbool wconn(int W){int sr=-1,sc_=-1,wc=0;for(int a=0;a>q;q.push({sr,sc_});v[sr][sc_]=1;int cnt=1;while(!q.empty()){auto[cr,c2]=q.front();q.pop();for(int d=0;d<4;d++){int nr=cr+dr[d],nc=c2+dc[d];if(nr>=0&&nr=0&&nc=n||nj<0||nj>=n)continue;\n int E=g[ni][nj];if(!E||!adj[E][0]||!adj[I][E])continue;\n bool bad=false;for(int d2=0;d2<4;d2++){int a2=ni+dr[d2],b2=nj+dc[d2];if(a2==i&&b2==j)continue;if(a2<0||a2>=n||b2<0||b2>=n||!g[a2][b2]){bad=true;break;}}\n if(!bad){\n int sz=czero();memcpy(mg,g,sizeof(g));memcpy(mac,ac,sizeof(ac));memcpy(mcc,cc,sizeof(cc));\n dra(ni,nj,E,I);dra(i,j,I,E);\n if(wconn(E)){rcp();bool vd=true;for(int a=1;a<=m&&vd;a++){if(adj[a][0]!=(ac[a][0]>0))vd=false;for(int b=1;b0))vd=false;}if(vd)for(int w=1;w<=m&&vd;w++)if(!wconn(w))vd=false;if(vd){gtrim();if(czero()>sz)continue;}}\n memcpy(g,mg,sizeof(g));memcpy(ac,mac,sizeof(ac));memcpy(cc,mcc,sizeof(cc));\n }\n for(int d12=0;d12<4;d12++){\n int r2=ni+dr[d12],c2=nj+dc[d12];if(r2<0||r2>=n||c2<0||c2>=n||(r2==i&&c2==j))continue;\n int E2=g[r2][c2];if(!E2||!adj[E2][0]||!adj[I][E2]||E2==I)continue;\n bool bad2=false;for(int d2=0;d2<4;d2++){int a2=r2+dr[d2],b2=c2+dc[d2];if(a2==ni&&b2==nj)continue;if(a2<0||a2>=n||b2<0||b2>=n||!g[a2][b2]){bad2=true;break;}}\n if(bad2)continue;\n int sz=czero();memcpy(mg,g,sizeof(g));memcpy(mac,ac,sizeof(ac));memcpy(mcc,cc,sizeof(cc));\n dra(ni,nj,E,I);dra(i,j,I,E);dra(r2,c2,E2,I);dra(ni,nj,I,E2);\n if(wconn(E)&&wconn(E2)){rcp();bool vd=true;for(int a=1;a<=m&&vd;a++){if(adj[a][0]!=(ac[a][0]>0))vd=false;for(int b=1;b0))vd=false;}if(vd)for(int w=1;w<=m&&vd;w++)if(!wconn(w))vd=false;if(vd){gtrim();if(czero()>sz)continue;}}\n memcpy(g,mg,sizeof(g));memcpy(ac,mac,sizeof(ac));memcpy(cc,mcc,sizeof(cc));\n }\n }\n }\n}\nstatic int bg[50][50];int bz=-1;\nvoid sv(){int z=czero();if(z>bz){bz=z;memcpy(bg,g,sizeof(g));}}\nvector centroid_last_ord(){\n vectorcx(102,0),cy(102,0);vectorcnt(102,0);\n for(int i=0;icidx(102,-1);vectorbd(102,1e18);\n for(int i=0;i,int>>keys;\n for(int i=0;iord;for(auto&[k,idx]:keys)ord.push_back(idx);\n return ord;\n}\nint main(){\n t0=steady_clock::now();ios_base::sync_with_stdio(0);cin.tie(0);\n cin>>n>>m;for(int i=0;i>g[i][j];og[i][j]=g[i][j];}\n cajad();cdep();mt19937 rng(42);\n for(int trial=0;trial==0||tok();trial++){\n memcpy(g,og,sizeof(g));\n vectorord(n*n);iota(ord.begin(),ord.end(),0);\n if(trial==1)reverse(ord.begin(),ord.end());\n else if(trial==2){for(int j2=0;j2abs(b/n-cx)+abs(b%n-cy);});}\n else if(trial==4){int cx=n/2,cy=n/2;sort(ord.begin(),ord.end(),[&](int a,int b){return abs(a/n-cx)+abs(a%n-cy)\nusing namespace std;\nint N, D, Q, q_used = 0;\nchar bq(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; q_used++;\n char c; cin >> c; return c;\n}\nint slm;\nvector ms(vector a) {\n if ((int)a.size() <= 1 || q_used >= slm) return a;\n int m = a.size() / 2;\n auto L = ms(vector(a.begin(), a.begin() + m));\n auto R = ms(vector(a.begin() + m, a.end()));\n vector r; int i = 0, j = 0;\n while (i < (int)L.size() && j < (int)R.size()) {\n if (q_used >= slm) break;\n if (bq({L[i]}, {R[j]}) != '>') r.push_back(L[i++]);\n else r.push_back(R[j++]);\n }\n while (i < (int)L.size()) r.push_back(L[i++]);\n while (j < (int)R.size()) r.push_back(R[j++]);\n return r;\n}\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> D >> Q;\n auto t0 = chrono::high_resolution_clock::now();\n auto el = [&]() { return chrono::duration(chrono::high_resolution_clock::now() - t0).count(); };\n slm = Q / 2;\n vector ini(N); iota(ini.begin(), ini.end(), 0);\n vector ord = ms(ini);\n vector pos(N);\n for (int i = 0; i < N; i++) pos[ord[i]] = i;\n int est_end = Q * 4 / 5;\n vector w(N, 1.0), ps(N + 1, 0.0);\n w[ord[0]] = 1.0; ps[1] = 1.0;\n for (int i = 1; i < N; i++) {\n if (q_used >= est_end) { w[ord[i]] = w[ord[i-1]]; ps[i+1] = ps[i] + w[ord[i]]; continue; }\n int lo = 0, hi = i;\n while (lo < hi && q_used < est_end) {\n int mid = (lo + hi) / 2;\n if (bq({ord[i]}, vector(ord.begin(), ord.begin() + mid + 1)) == '>') lo = mid + 1;\n else hi = mid;\n }\n double wlo = ps[lo], whi = (lo < i) ? ps[lo + 1] : ps[i] * 2.0;\n w[ord[i]] = max(w[ord[i-1]], (wlo + whi) / 2.0);\n ps[i+1] = ps[i] + w[ord[i]];\n }\n vector oi(N); iota(oi.begin(), oi.end(), 0);\n sort(oi.begin(), oi.end(), [&](int a, int b) { return fabs(w[a]-w[b]) > 1e-12 ? w[a] > w[b] : pos[a] > pos[b]; });\n vector gw(D, 0.0); vector asgn(N, 0);\n for (int x : oi) { int g = (int)(min_element(gw.begin(), gw.end()) - gw.begin()); asgn[x] = g; gw[g] += w[x]; }\n double total = 0; for (double x : gw) total += x;\n double mean = total / D;\n for (int p = 0; p < 5000 && el() < 1.5; p++) {\n bool imp = false;\n for (int x = 0; x < N; x++) {\n int g0 = asgn[x]; int bg = g0; double bd = 0, d0 = gw[g0] - mean;\n for (int g = 0; g < D; g++) {\n if (g == g0) continue;\n double d1 = gw[g] - mean;\n double dc = d0*d0 + d1*d1 - (d0-w[x])*(d0-w[x]) - (d1+w[x])*(d1+w[x]);\n if (dc > bd) { bd = dc; bg = g; }\n }\n if (bg != g0) { gw[g0] -= w[x]; gw[bg] += w[x]; asgn[x] = bg; imp = true; }\n }\n for (int i = 0; i < N && el() < 1.45; i++) for (int j = i+1; j < N; j++) {\n if (asgn[i] == asgn[j]) continue;\n int g1 = asgn[i], g2 = asgn[j];\n double d1 = gw[g1]-mean, d2 = gw[g2]-mean, d1n = d1-w[i]+w[j], d2n = d2+w[i]-w[j];\n if (d1*d1 + d2*d2 > d1n*d1n + d2n*d2n + 1e-9) {\n gw[g1] += w[j]-w[i]; gw[g2] += w[i]-w[j]; asgn[i] = g2; asgn[j] = g1; imp = true;\n }\n }\n if (!imp) break;\n }\n vector> gi(D);\n for (int x = 0; x < N; x++) gi[asgn[x]].push_back(x);\n for (int g = 0; g < D; g++) sort(gi[g].begin(), gi[g].end(), [&](int a, int b){ return pos[a] < pos[b]; });\n auto cpos = [&](int a, int b){ return pos[a] < pos[b]; };\n // Phase 5a: cheap with verify\n bool phase5a_made_moves = false;\n int p5a_end = q_used + min(Q * 3 / 10, 300);\n int no5a = 0;\n while (q_used + 2 <= Q && q_used < p5a_end && el() < 1.85) {\n int gh = (int)(max_element(gw.begin(), gw.end()) - gw.begin());\n int gl = (int)(min_element(gw.begin(), gw.end()) - gw.begin());\n if (gw[gh] <= gw[gl] + 1e-9 || gi[gh].empty() || gi[gl].empty()) break;\n char cmp = bq(gi[gh], gi[gl]);\n if (cmp == '=') { gw[gh] = gw[gl] = (gw[gh]+gw[gl])/2; continue; }\n if (cmp == '<') { swap(gh, gl); swap(gw[gh], gw[gl]); }\n auto& hv = gi[gh]; auto& lt = gi[gl];\n if ((int)hv.size() <= 1) continue;\n bool seq = false;\n int lo = 0, hi = (int)hv.size() - 1;\n while (lo < hi && q_used + 1 <= Q && el() < 1.8) {\n int mid = (lo + hi) / 2;\n vector L2, R2 = lt;\n for (int k = 0; k < (int)hv.size(); k++) if (k != mid) L2.push_back(hv[k]);\n R2.push_back(hv[mid]);\n char r = bq(L2, R2);\n if (r == '=') { lo = hi = mid; seq = true; break; }\n else if (r == '>') lo = mid + 1;\n else hi = mid;\n }\n lo = min(lo, (int)hv.size() - 1);\n if (lo > 0) {\n double da = fabs((gw[gh]-w[hv[lo]])-(gw[gl]+w[hv[lo]]));\n double db = fabs((gw[gh]-w[hv[lo-1]])-(gw[gl]+w[hv[lo-1]]));\n if (db < da) lo--;\n }\n bool made = seq;\n if (!seq && q_used + 1 <= Q) {\n vector vL, vR = lt;\n for (int k = 0; k < (int)hv.size(); k++) if (k != lo) vL.push_back(hv[k]);\n vR.push_back(hv[lo]);\n if (!vL.empty()) {\n char v = bq(vL, vR);\n if (v == '>' || v == '=') made = true;\n else if (v == '<' && lo > 0 && q_used + 1 <= Q) {\n vector vL2, vR2 = lt;\n for (int k = 0; k < (int)hv.size(); k++) if (k != lo-1) vL2.push_back(hv[k]);\n vR2.push_back(hv[lo-1]);\n char v2 = bq(vL2, vR2);\n if (v2 == '>' || v2 == '=') { lo--; made = true; }\n }\n }\n }\n if (made) {\n no5a = 0; phase5a_made_moves = true;\n int mv = hv[lo]; asgn[mv] = gl; gw[gh] -= w[mv]; gw[gl] += w[mv];\n hv.erase(hv.begin() + lo);\n lt.insert(lower_bound(lt.begin(), lt.end(), mv, cpos), mv);\n } else { if (++no5a >= 3) break; }\n }\n // Phase 5b: rank-list approach (initial tournament once, then cheap bubble updates)\n if (phase5a_made_moves) {\n // Build initial rank sorted by estimated gw\n vector grank;\n for (int g = 0; g < D; g++) if (!gi[g].empty()) grank.push_back(g);\n sort(grank.begin(), grank.end(), [&](int a, int b){ return gw[a] > gw[b]; });\n // Find actual max with tournament (D-1 queries)\n if ((int)grank.size() >= 2 && q_used + (int)grank.size() <= Q) {\n int mxg = grank[0];\n for (int i = 1; i < (int)grank.size() && q_used < Q; i++)\n if (!gi[grank[i]].empty() && bq(gi[mxg], gi[grank[i]]) == '<') mxg = grank[i];\n auto it = find(grank.begin(), grank.end(), mxg);\n if (it != grank.begin()) { rotate(grank.begin(), it, it+1); }\n // Find actual min (D-2 queries)\n int mng = -1;\n for (int i = (int)grank.size()-1; i >= 1 && q_used < Q; i--) {\n if (gi[grank[i]].empty()) continue;\n if (mng == -1) { mng = grank[i]; continue; }\n if (bq(gi[mng], gi[grank[i]]) == '>') mng = grank[i];\n }\n if (mng != -1) {\n auto it2 = find(grank.begin(), grank.end(), mng);\n if (it2 != grank.end()-1) { rotate(it2, it2+1, grank.end()); }\n }\n }\n int no_im = 0, eq_str = 0;\n while ((int)grank.size() >= 2 && q_used + 8 <= Q && el() < 1.9) {\n int gh = grank[0], gl = grank.back();\n if (gi[gh].empty()) { grank.erase(grank.begin()); continue; }\n if (gi[gl].empty()) { grank.pop_back(); continue; }\n char cmp = bq(gi[gh], gi[gl]);\n if (cmp == '=') { if (++eq_str >= 3) break; continue; }\n eq_str = 0;\n if (cmp == '<') { swap(grank.front(), grank.back()); gh = grank[0]; gl = grank.back(); }\n auto& hv = gi[gh]; auto& lt = gi[gl];\n if ((int)hv.size() <= 1) { grank.erase(grank.begin()); continue; }\n bool se = false;\n int lo = 0, hi = (int)hv.size()-1;\n while (lo < hi && q_used + 1 <= Q && el() < 1.87) {\n int mid = (lo+hi)/2;\n vector L2, R2 = lt;\n for (int k = 0; k < (int)hv.size(); k++) if (k!=mid) L2.push_back(hv[k]);\n R2.push_back(hv[mid]);\n char r = bq(L2, R2);\n if (r=='=') { lo=hi=mid; se=true; break; }\n else if (r=='>') lo=mid+1; else hi=mid;\n }\n lo = min(lo, (int)hv.size()-1);\n bool mm = se;\n if (!se && q_used+1<=Q) {\n vector vL, vR=lt;\n for (int k=0;k<(int)hv.size();k++) if(k!=lo) vL.push_back(hv[k]);\n vR.push_back(hv[lo]);\n if (!vL.empty()) {\n char v=bq(vL,vR);\n if (v=='>'||v=='=') mm=true;\n else if (v=='<'&&lo>0&&q_used+1<=Q) {\n vector vL2,vR2=lt;\n for (int k=0;k<(int)hv.size();k++) if(k!=lo-1) vL2.push_back(hv[k]);\n vR2.push_back(hv[lo-1]);\n char v2=bq(vL2,vR2);\n if(v2=='>'||v2=='='){lo--;mm=true;}\n }\n }\n }\n bool usw=false; int syi=0;\n if (!se&&!lt.empty()) {\n int ll=(int)(log2((double)lt.size())+2);\n if (q_used+ll+1<=Q&&el()<1.87) {\n int y0=0,y1=(int)lt.size()-1; bool s2=false;\n while(y0L2,R2;\n for(int k=0;k<(int)hv.size();k++) if(k!=lo) L2.push_back(hv[k]);\n for(int k=0;k<(int)lt.size();k++) if(k!=ym) R2.push_back(lt[k]);\n L2.push_back(lt[ym]); R2.push_back(hv[lo]);\n if(L2.empty()||R2.empty()) break;\n char r=bq(L2,R2);\n if(r=='='){y0=y1=ym;s2=true;break;}\n else if(r=='>') y0=ym+1; else y1=ym;\n }\n if(s2){usw=true;syi=min(y0,(int)lt.size()-1);}\n }\n }\n auto do_bubble=[&](){\n for(int i=0;i+1<(int)grank.size()&&q_used+1<=Q;i++){\n if(gi[grank[i]].empty()||gi[grank[i+1]].empty()) break;\n if(bq(gi[grank[i]],gi[grank[i+1]])=='<') swap(grank[i],grank[i+1]); else break;}\n for(int i=(int)grank.size()-1;i>0&&q_used+1<=Q;i--){\n if(gi[grank[i]].empty()||gi[grank[i-1]].empty()) break;\n if(bq(gi[grank[i]],gi[grank[i-1]])=='>') swap(grank[i],grank[i-1]); else break;}\n };\n if(usw){\n int xmv=hv[lo],ymv=lt[syi];\n asgn[xmv]=gl;asgn[ymv]=gh;\n gw[gh]+=w[ymv]-w[xmv];gw[gl]+=w[xmv]-w[ymv];\n hv.erase(hv.begin()+lo);lt.erase(lt.begin()+syi);\n hv.insert(lower_bound(hv.begin(),hv.end(),ymv,cpos),ymv);\n lt.insert(lower_bound(lt.begin(),lt.end(),xmv,cpos),xmv);\n no_im=0; do_bubble();\n } else if(mm){\n int mv=hv[lo];asgn[mv]=gl;gw[gh]-=w[mv];gw[gl]+=w[mv];\n hv.erase(hv.begin()+lo);\n lt.insert(lower_bound(lt.begin(),lt.end(),mv,cpos),mv);\n bool undo=false;\n if(!se&&q_used+1<=Q&&!hv.empty()&&!lt.empty()){\n char post=bq(gi[gh],gi[gl]);\n if(post=='<'){\n undo=true;\n asgn[mv]=gh;gw[gh]+=w[mv];gw[gl]-=w[mv];\n auto it=lower_bound(lt.begin(),lt.end(),mv,cpos);\n if(it!=lt.end()&&*it==mv) lt.erase(it);\n hv.insert(lower_bound(hv.begin(),hv.end(),mv,cpos),mv);\n }\n }\n if(!undo){no_im=0; do_bubble();}\n else{if(++no_im>=3) break;}\n } else{if(++no_im>=3) break;}\n }\n }\n while(q_used\nusing namespace std;\nint n, m;\nlong long run_algo(int mode, long long noise, vector> stacks, vector stk, vector pidx, vector sm, vector>& ops, mt19937_64& rng) {\n bool psfx = (mode <= 1), pat = (mode==1||mode==3);\n ops.clear(); long long energy = 0;\n auto recomp = [&](int t){ sm[t]=stacks[t].empty()?n+1:*min_element(stacks[t].begin(),stacks[t].end()); };\n for (int v = 1; v <= n; v++) {\n int s = stk[v], j = pidx[v];\n while ((int)stacks[s].size() > j+1) {\n int re=(int)stacks[s].size()-1, rs=re;\n while (rs>j+1&&stacks[s][rs-1]>stacks[s][rs]) rs--;\n int fu1=stacks[s][rs], ars=rs, bt=-1;\n if (psfx) {\n for (int sp=rs; sp<=re&&bt==-1; sp++) {\n int u1c=stacks[s][sp]; long long bs=LLONG_MIN; int bk=-1;\n for (int t=0;tu1c&&mt>u1c){ long long sc=(long long)n-tt; if(noise>0)sc+=(long long)(rng()%(2*noise+1))-noise; if(sc>bs){bs=sc;bk=t;} } }\n if(bk!=-1){ars=sp;bt=bk;}\n }\n }\n if (bt==-1) {\n long long best=LLONG_MIN;\n for (int t=0;tfu1)sc=(mt>fu1)?3LL*n*n+(n-tt):n*n+mt; else sc=mt-(long long)n*n; }\n else{ if(emp)sc=(long long)n; else if(tt>fu1)sc=2LL*n*n+(n-tt); else sc=tt-(long long)n*n; }\n if(noise>0)sc+=(long long)(rng()%(2*noise+1))-noise;\n if(sc>best){best=sc;bt=t;} }\n }\n energy+=(re-ars+1)+1; ops.push_back({stacks[s][ars],bt+1});\n int nb=(int)stacks[bt].size(), oz=(int)stacks[s].size();\n for(int p=ars;p>n>>m; int h=n/m;\n vector> is(m,vector(h)); vector ist(n+1),ip(n+1),ism(m,n+1);\n for(int i=0;i>is[i][j];ist[is[i][j]]=i;ip[is[i][j]]=j;} ism[i]=*min_element(is[i].begin(),is[i].end()); }\n long long be=LLONG_MAX; vector> bops; mt19937_64 rng(0);\n for(int mode=0;mode<4;mode++){ mt19937_64 d(0); vector> ops; long long e=run_algo(mode,0,is,ist,ip,ism,ops,d); if(e> ops; long long e=run_algo(mode,2000,is,ist,ip,ism,ops,rng);\n if(e\nusing namespace std;\nconst int MAXN=41,MAXC=1601,BUD=100000;\nint N,n;bool hw[MAXN][MAXN],vw[MAXN][MAXN];int dv[MAXN][MAXN];\nconst int DI[]={0,1,0,-1},DJ[]={1,0,-1,0};const char DC[]=\"RDLU\";\nint C(int i,int j){return i*N+j;}int RI(int c){return c/N;}int RJ(int c){return c%N;}\nbool OK(int i,int j,int d){int ni=i+DI[d],nj=j+DJ[d];if(ni<0||ni>=N||nj<0||nj>=N)return false;if(d==0)return!vw[i][j];if(d==1)return!hw[i][j];if(d==2)return!vw[i][nj];return!hw[ni][j];}\nshort AP[MAXC][MAXC];int AF[MAXC][MAXC];\nvoid bfs(int s){memset(AP[s],0xFF,n*sizeof(short));int fs[MAXC];AP[s][s]=0;fs[s]=s;static int q[MAXC];int h=0,tail=0;q[tail++]=s;while(h>N;n=N*N;\n for(int i=0;i>s;for(int j=0;j>s;for(int j=0;j>dv[i][j];\n for(int s=0;s lv(n,0);int pos=0,t=0;\n {vector vis(n,false);vis[0]=true;vector> stk;stk.reserve(n);stk.push_back({0,0});\n while(!stk.empty()){int u=stk.back().first;int&nd=stk.back().second;bool found=false;\n while(nd<4){int d=nd++;if(OK(RI(u),RJ(u),d)){int v=C(RI(u)+DI[d],RJ(u)+DJ[d]);if(!vis[v]){route+=DC[d];t++;pos=v;lv[v]=t;vis[v]=true;stk.push_back({v,0});found=true;break;}}}\n if(!found){stk.pop_back();if(!stk.empty()){int par=stk.back().first;for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==par){route+=DC[d];t++;pos=par;lv[par]=t;break;}}}};}\n for(int c=0;c=20);\n if(!rrt&&t+(int)AP[pos][committed]+(int)D_home[committed]+2>BUD)rrt=true;\n if(rrt){\n const short*Ap=AP[pos];int best=-1;float bu=0.0f;\n for(int c=0;cBUD)continue;\n // Age-at-arrival: estimate dirtiness when we actually arrive\n float u=sqd[c]*(float)(t+dc-lv[c]+1)/sqrtf((float)dc+1.0f);\n if(u>bu){bu=u;best=c;}}\n committed=best;sr=0;if(committed<0)break;}\n int nx=AF[pos][committed];bool moved=false;\n for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==nx){route+=DC[d];pos=nx;t++;sr++;lv[pos]=t;moved=true;break;}\n if(!moved)break;}\n while(pos!=0){int nx=AF[pos][0];for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==nx){route+=DC[d];pos=nx;t++;break;}}\n cout<\nusing namespace std;\nint N,M,si,sj;\nvector targets;\nvector> charPos[26];\nint ovM[200][200],tCI[200][200],EV[200][200];\nfloat amd[26][26],tC[200][200];\nconst int SCALE=100,OV_W=350;\nvoid computeAll(){\n for(int i=0;i=1;k--){bool ok=true;for(int l=0;l&p){int s=0;for(int i=1;i<(int)p.size();i++)s+=EV[p[i-1]][p[i]];return s;}\nvector greedyP(int s){vector used(M,false);vector p;p.reserve(M);p.push_back(s);used[s]=true;while((int)p.size()bcs){bcs=EV[last][j];best=j;}p.push_back(best);used[best]=true;}return p;}\nint swapCG(const vector&p,int i,int j){int m=p.size(),a=p[i],b=p[j],cg=0;if(i>0)cg+=EV[p[i-1]][b]-EV[p[i-1]][a];if(j0)cg+=EV[p[j-1]][a]-EV[p[j-1]][b];}return cg;}\nbool swapOpt(vector&p){int m=p.size(),bg=0,bi=-1,bj=-1;for(int i=0;ibg){bg=g;bi=i;bj=j;}}if(bi==-1)return false;swap(p[bi],p[bj]);return true;}\nbool orOpt(vector&p){int m=p.size(),bg=0,bk=-1,bp=-1;for(int k=0;k rest;rest.reserve(m-1);for(int i=0;i0)?EV[p[k-1]][x]:0,ro=(k0&&k0)?EV[rest[q-1]][x]:0,nr=(q<(int)rest.size())?EV[x][rest[q]]:0;int nb=(q>0&&q<(int)rest.size())?EV[rest[q-1]][rest[q]]:0;int g=(nl+nr-nb)-rc;if(g>bg){bg=g;bk=k;bp=q;}}}if(bk==-1)return false;int x=p[bk];vector rest;rest.reserve(m-1);for(int i=0;i&p){int m=p.size();if(m<2)return false;vector cd(m-1),cp(m,0);for(int k=0;k0)g+=EV[p[i-1]][p[j]]-EV[p[i-1]][p[i]];if(jbg){bg=g;bi=i;bj=j;}}if(bi==-1)return false;reverse(p.begin()+bi,p.begin()+bj+1);return true;}\nvoid localS(vector&p,int maxP=1000){bool imp=true;int pass=0;while(imp&&pass&p,mt19937&rng){int m=p.size();if(m<4)return;uniform_int_distribution d(1,m-1);int a,b,c;do{a=d(rng);b=d(rng);c=d(rng);}while(a==b||b==c||a==c);if(a>b)swap(a,b);if(b>c)swap(b,c);if(a>b)swap(a,b);vector np;np.reserve(m);for(int i=0;i&p){string s=targets[p[0]];for(int i=1;i<(int)p.size();i++)s+=targets[p[i]].substr(ovM[p[i-1]][p[i]]);return s;}\npair>,int> dpSolve(const string&s){\n int L=s.size(),G=N*N;const int INF=1e9;vector dp((L+1)*G,INF),prv((L+1)*G,-1);dp[si*N+sj]=0;\n for(int i=0;i> path(L);int pos=bp;for(int i=L;i>=1;i--){path[i-1]={pos/N,pos%N};pos=prv[i*G+pos];}\n return{path,bc};\n}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n auto t0=chrono::steady_clock::now();\n auto ms=[&](){return chrono::duration_cast(chrono::steady_clock::now()-t0).count();};\n cin>>N>>M>>si>>sj;\n for(int i=0;i>row;for(int j=0;j>targets[i];\n computeAll();\n vector>> cands;\n for(int s=0;s best;vector> bestPath;int bestT=INT_MAX;\n for(int k=0;k\n#include \n#include \n#include \n#include \n#include \nusing namespace std;\ntypedef pair pii;\nint main(){\n int N,M,MAX_OPS,ops=0;double eps,coef;\n scanf(\"%d%d%lf\",&N,&M,&eps);MAX_OPS=2*N*N;coef=1.0-2.0*eps;\n struct Oil{int hi,hj;vectorcells,pos;vectorrp,cp;};\n vectorF(M);\n for(int k=0;k>prob(M);\n for(int k=0;k0?sz:1,sz>0?1.0/sz:1.0);}\n vector>drld(N,vector(N,-1));\n vectorrobs(N,0),cobs(N,0);int nrr=0,nrc=0;\n auto qdiv=[&](const vector&c)->double{ops++;printf(\"q %d\",(int)c.size());for(auto&p:c)printf(\" %d %d\",p.first,p.second);printf(\"\\n\");fflush(stdout);int v;scanf(\"%d\",&v);return(double)v;};\n auto qdrl=[&](int i,int j)->int{ops++;printf(\"q 1 %d %d\\n\",i,j);fflush(stdout);int v;scanf(\"%d\",&v);drld[i][j]=v;return v;};\n auto qans=[&](const vector&oil)->bool{ops++;printf(\"a %d\",(int)oil.size());for(auto&p:oil)printf(\" %d %d\",p.first,p.second);printf(\"\\n\");fflush(stdout);int r;scanf(\"%d\",&r);return r==1;};\n auto run_mf=[&](int nit){\n if(!nrr&&!nrc)return;\n double vr=max(1e-9,(double)nrr*N*eps*(1-eps)),vc=max(1e-9,(double)nrc*N*eps*(1-eps));\n vectortmr(N,0),tmc(N,0);\n for(int k=0;kkmr(N,0),kmc(N,0);\n for(int p=0;p>drow(N,vector(F[k].hi+1,0)),dcol(N,vector(F[k].hj+1,0));\n for(int i=0;iop2=prob[k],ll(np,0.0);double mx=-1e300;\n for(int p=0;pmx)mx=lp;}\n double s=0;for(int p=0;p1e-15)for(int p=0;p1e-15)for(double&pp:prob[k])pp/=s;else fill(prob[k].begin(),prob[k].end(),1.0/max(1,(int)prob[k].size()));}\n }\n };\n auto get_oil=[&]()->vector>{\n vector>noc(N,vector(N,1.0));\n for(int k=0;k>cvk(N,vector(N,0.0));int np=(int)F[k].pos.size();for(int p=0;p>op(N,vector(N,0));for(int i=0;i>&op,double thr=0.5)->vector{\n vectorr;for(int i=0;i0||(drld[i][j]<0&&op[i][j]>thr))r.push_back({i,j});return r;\n };\n auto shape_q=[&](int k)->bool{\n if(ops>=MAX_OPS-5)return false;\n int np=(int)F[k].pos.size();if(!np)return false;\n int p1=0;for(int p=1;pprob[k][p1])p1=p;\n if(prob[k][p1]>0.98)return false;\n int p2=-1;for(int p=0;pprob[k][p2]))p2=p;\n int di1=F[k].pos[p1].first,dj1=F[k].pos[p1].second;\n setSs;\n if(p2>=0){setc2;int di2=F[k].pos[p2].first,dj2=F[k].pos[p2].second;for(auto&c:F[k].cells)c2.insert({di2+c.first,dj2+c.second});for(auto&c:F[k].cells){pii cc={di1+c.first,dj1+c.second};if(cc.first>=0&&cc.first=0&&cc.second=0&&cc.first=0&&cc.secondS(Ss.begin(),Ss.end());\n vectorSm(N*N,0);for(auto&p:S)Sm[p.first*N+p.second]=1;\n vectorovl(np,0);\n for(int p=0;p=0&&i=0&&j=0&&i=0&&jll2(np);\n for(int p=0;pmx2)mx2=ll2[p];}\n if(mx2>-1e290){double s=0;for(int p=0;pmx2-500)?exp(ll2[p]-mx2):0.0;s+=prob[k][p];}if(s>1e-15)for(int p=0;pdouble{double H=0;for(double p:prob[k])if(p>1e-12)H-=p*log(p);return H;};\n // SA: find best joint assignment minimizing row/col residuals\n auto find_best=[&](int n_restarts,int nit)->vector{\n if(!nrr&&!nrc){vectorst(M);for(int k=0;kprob[k][p1])p1=p;st[k]=p1;}return st;}\n double vr=max(1e-9,(double)nrr*N*eps*(1-eps)),vc=max(1e-9,(double)nrc*N*eps*(1-eps));\n auto cE=[&](const vector&er,const vector&ec)->double{\n double E=0;for(int i=0;i>vps(M);\n for(int k=0;kur(0,1);\n vectorgbest(M,0);double gbest_E=1e300;\n for(int restart=0;restartstate(M);\n if(restart==0){for(int k=0;kprob[k][p1])p1=p;state[k]=p1;}}\n else{for(int k=0;k=r2){state[k]=vp[pi];break;}}}}\n // Validate: ensure initial state is valid\n for(int k=0;ker(N,0),ec(N,0);\n for(int k=0;kbest=state;double best_E=cur_E;\n for(int it=0;it&state)->vector{\n setoil_set;\n for(int k=0;k0)oil_set.insert({i,j});\n return vector(oil_set.begin(),oil_set.end());\n };\n // Phase 1: Row/col queries\n int nr=(eps>=0.15)?3:(eps>=0.08)?2:1;\n for(int rep=0;repc;for(int j=0;jc;for(int i=0;ibe){be=h;bk=k;}}if(be<0.05)break;if(!shape_q(bk))break;run_mf(10);}}\n apply_hard();run_mf(100);\n // Phase 3: SA + first guess\n {auto bs=find_best(5,150000);auto g=sa_guess(bs);if(ops=0)continue;double u=min(op[i][j],1.0-op[i][j]);if(u>bu){bu=u;bi=i;bj=j;}}\n if(bi<0||bu<0.1)break;\n qdrl(bi,bj);\n if(drld[bi][bj]==0){for(int k=0;k1e-15)for(double&pp:prob[k])pp/=s;else fill(prob[k].begin(),prob[k].end(),1.0/max(1,(int)prob[k].size()));}}\n run_mf(5);op=get_oil();\n }\n apply_hard();run_mf(20);\n auto bs=find_best(3,70000);auto g=sa_guess(bs);\n if(ops\nusing namespace std;\ntypedef long long ll;\ntypedef tuple T3;\nint W,D,N;\nvector>a;\nstruct CS{\nint s0,st,nc,cw;\nint r(int d,int k)const{return a[d][s0+k*st];}\nvectorch(const vector&days)const{\n vectorh(nc,1);\n auto be=[&](int k,int cur)->ll{ll b=0;for(int d:days){int df=r(d,k)-cur*cw;if(df>0)b+=(ll)min(cw,df);}return b;};\n priority_queuepq;\n for(int k=0;k0)pq.push({b,k,1});}\n for(int rem=W-nc;rem>0&&!pq.empty();){auto[b,kk,cu]=pq.top();pq.pop();if(b<=0)break;h[kk]++;rem--;ll nb=be(kk,h[kk]);if(nb>0)pq.push({nb,kk,h[kk]});}\n sort(h.begin(),h.end());\n {int s=0;for(int x:h)s+=x;if(s&h)const{ll c=0;for(int k=0;k0)c+=(ll)df*100;}return c;}\nsetgb(const vector&arr)const{setS;int y=0;for(int i=0;i+1<(int)arr.size();i++){y+=arr[i];S.insert(y);}return S;}\nll bd(const set&A,const set&B)const{ll c=0;for(int x:A)if(!B.count(x))c++;for(int x:B)if(!A.count(x))c++;return c*(ll)cw;}\nvectorag(const vector&h,const set&t)const{\n vectortg(t.begin(),t.end());multisetav(h.begin(),h.end());\n vectorarr;int S=0,j=0,nt=(int)tg.size();\n while(!av.empty()){while(j=tg[j])j++;if(j>=nt){for(int x:av)arr.push_back(x);break;}\n int nd=tg[j]-S;auto it=av.find(nd);\n if(it!=av.end()){arr.push_back(nd);S+=nd;av.erase(it);j++;}\n else{auto ub=av.upper_bound(nd);\n if(ub!=av.begin()){--ub;arr.push_back(*ub);S+=*ub;av.erase(ub);while(j=tg[j])j++;}\n else{it=av.begin();arr.push_back(*it);S+=*it;av.erase(it);while(j=tg[j])j++;}\n }\n }return arr;\n}\nvectorhc(vectorarr,const set&t)const{\n if(t.empty()||(int)arr.size()<=1)return arr;\n int n2=arr.size();vectorps(n2+1,0);for(int i=0;i0){swap(arr[i],arr[j]);for(int k=i+1;k<=j;k++)ps[k]+=dl;im=true;}\n }}return arr;\n}\npair>>solve()const{\n vector>C;vectorai(D);iota(ai.begin(),ai.end(),0);\n C.push_back(ch(ai));\n for(int d=0;d>SS(NC);for(int L=0;L>AR(D,vector(NC));for(int d=0;d>pcg(NC,vector(NC,0));\n for(int L1=0;L1>pcgt(NC,vector(NC,0));\n for(int L1=0;L1zr(NC,0LL);\n const ll INF=2e18;\n vector>dp(D,vector(NC,INF));vector>frm(D,vector(NC,-1));\n for(int L=0;Ldpseq(D);dpseq[D-1]=bL;for(int d=D-2;d>=0;d--)dpseq[d]=frm[d+1][dpseq[d+1]];\n // Fast local search: O(1) per eval using pcg table lookups\n auto dls=[&](vectors)->vector{\n vectordc(D);\n for(int d=0;d0&&s[d]!=s[d-1])dc[d]+=pcg[s[d-1]][s[d]];}\n for(int it=0;it<200;it++){bool any=false;\n for(int d=0;d0)?pcg[s[d-1]].data():zr.data();\n const ll*rt=(d+10&&s[d]!=s[d-1]?pcg[s[d-1]][s[d]]:0LL);\n if(d+1&s)->pair>>{\n vector>arrs(D);ll cost=0;arrs[0]=C[s[0]];cost+=AR[0][s[0]];setcur=gb(arrs[0]);\n for(int d=1;dns=gb(arrs[d]);cost+=AR[d][s[d]]+bd(cur,ns);cur=ns;}}\n return{cost,arrs};\n };\n auto[c1,a1]=fs(dls(dpseq));\n vectorgseq(D);{int L0=0;for(int L=0;Lapseq(D);for(int d=0;dfseq(D,0);\n auto[c4,a4]=fs(dls(fseq));\n ll bc2=min({c1,c2,c3,c4});\n if(bc2==c1)return{c1,a1};else if(bc2==c2)return{c2,a2};else if(bc2==c3)return{c3,a3};else return{c4,a4};\n}\n};\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>W>>D>>N;a.resize(D,vector(N));\n for(int d=0;d>a[d][k];\n ll best=2e18;int bK=1;\n vector>>>bcr;\n for(int K=1;K<=N;K++){\n if(N%K!=0||W%K!=0)continue;\n int npc=N/K,cw=W/K;\n if(npc==1){\n ll tc=0;vector>>>cr(K);\n for(int c=0;c0)cc+=(ll)df*100;}\n cr[c]={cc,vector>(D,vector(1,W))};tc+=cc;}\n if(tc10)continue;\n vector>>>cr(K);ll tc=0;\n for(int c=0;c>rects(N);\n for(int c=0;cy(npc+1);y[0]=0;for(int j=0;j>strips(npc);for(int j=0;j\nusing namespace std;\nusing namespace chrono;\nconstexpr long long MOD=998244353;\nint N,M,K;long long sv[20][3][3],b[9][9],cur_score;\ninline long long add_mod(long long a,long long c){long long s=a+c;return s>=MOD?s-MOD:s;}\ninline long long sub_mod(long long a,long long c){return a>=c?a-c:a-c+MOD;}\nvoid apply_s(int m,int p,int q){for(int i=0;i<3;i++)for(int j=0;j<3;j++){long long&c=b[p+i][q+j];long long nv=add_mod(c,sv[m][i][j]);cur_score+=nv-c;c=nv;}}\nvoid undo_s(int m,int p,int q){for(int i=0;i<3;i++)for(int j=0;j<3;j++){long long&c=b[p+i][q+j];long long nv=sub_mod(c,sv[m][i][j]);cur_score+=nv-c;c=nv;}}\nstruct Op{int m,p,q;};\nconst int TK=15;\nlong long gdtv[3][3],gdts,gdtbest;int gdbs[9],gdcs[9],gdord[20],gdfl;bool gdto;steady_clock::time_point gddl;\nvoid tile_dfs(int dep,int mi){\n if(gdto)return;\n if(dep==9){if(++gdfl%200000==0&&steady_clock::now()>=gddl){gdto=true;return;}if(gdts>gdtbest){gdtbest=gdts;for(int d=0;d<9;d++)gdbs[d]=gdord[gdcs[d]];}return;}\n long long ub=gdts;for(int i=0;i<3;i++)for(int j=0;j<3;j++)ub+=(MOD-1)-gdtv[i][j];if(ub<=gdtbest)return;\n for(int idx=mi;idx>N>>M>>K;cur_score=0;\n for(int i=0;i>b[i][j];b[i][j]%=MOD;cur_score+=b[i][j];}\n for(int m=0;m>sv[m][i][j];\n auto t0=steady_clock::now();const long long TL_US=1850000;\n vectorops;ops.reserve(K);\n const int tpos[9][2]={{0,0},{0,3},{0,6},{3,0},{3,3},{3,6},{6,0},{6,3},{6,6}};\n gdfl=0;gdto=false;gddl=t0+milliseconds(1300);\n for(int tile=0;tile<9;tile++){\n int p=tpos[tile][0],q=tpos[tile][1];long long itv[3][3];long long its=0;\n for(int i=0;i<3;i++)for(int j=0;j<3;j++){itv[i][j]=b[p+i][q+j];its+=itv[i][j];}\n long long gn[20];int ord[20];iota(ord,ord+20,0);\n for(int m=0;mgn[b_];});\n long long grtv[3][3];memcpy(grtv,itv,sizeof(itv));long long grts=its;int grs[9];\n for(int d=0;d<9;d++){long long bg=0;int bm=0;for(int m=0;mbg){bg=g;bm=m;}}grs[d]=bm;for(int i=0;i<3;i++)for(int j=0;j<3;j++){long long nv=add_mod(grtv[i][j],sv[bm][i][j]);grts+=nv-grtv[i][j];grtv[i][j]=nv;}}\n memcpy(gdtv,itv,sizeof(itv));gdts=its;gdtbest=grts;for(int d=0;d<9;d++)gdbs[d]=grs[d];for(int m=0;m<20;m++)gdord[m]=ord[m];\n tile_dfs(0,0);\n int best_s[9];memcpy(best_s,gdbs,sizeof(gdbs));long long best_ts=gdtbest;\n bool imp=true;\n while(imp){imp=false;for(int d=0;d<9;d++){int om=best_s[d];for(int m=0;mbest_ts){best_ts=ts;memcpy(best_s,tmp,sizeof(tmp));imp=true;}}}}\n // 2-opt refinement\n bool imp2=true;\n while(imp2){\n imp2=false;long long b2ts=best_ts;int bd1=-1,bd2=-1,bm1=-1,bm2=-1;\n for(int d1=0;d1<9;d1++)for(int d2=d1+1;d2<9;d2++)for(int m1=0;m1b2ts){b2ts=ts;bd1=d1;bd2=d2;bm1=m1;bm2=m2;}\n }\n if(bd1>=0){best_ts=b2ts;best_s[bd1]=bm1;best_s[bd2]=bm2;imp2=true;}\n }\n for(int d=0;d<9;d++){apply_s(best_s[d],p,q);ops.push_back({best_s[d],p,q});}\n }\n long long best_score=cur_score;vectorbest_ops=ops;\n mt19937 rng(42);const int POS=N-2;\n auto rand_op=[&]()->Op{return{(int)(rng()%M),(int)(rng()%POS),(int)(rng()%POS)};};\n double T_start=1e8;\n if(!ops.empty()){long long sumd=0;int cnt=0;for(int i=0;i<3000;i++){int L=ops.size();if(!L)break;int idx=rng()%L;Op oo=ops[idx],no=rand_op();long long s0=cur_score;undo_s(oo.m,oo.p,oo.q);apply_s(no.m,no.p,no.q);long long d=cur_score-s0;sumd+=(d<0?-d:d);cnt++;undo_s(no.m,no.p,no.q);apply_s(oo.m,oo.p,oo.q);}if(cnt>0)T_start=max(1.0,(double)sumd/cnt);}\n double T=T_start,T_end=max(T_start*1e-7,1.0);\n for(long long it=0;;it++){\n if(it%50000==0){long long el=duration_cast(steady_clock::now()-t0).count();if(el>=TL_US)break;T=T_start*pow(T_end/T_start,(double)el/TL_US);}\n int L=ops.size();Op n1=rand_op(),o1{},o2{},n2{};int i1=-1,i2=-1,mt;\n if(L==0){mt=0;}else{int r=rng()%10;if(L==K)mt=(r<2)?1:(r<7)?2:3;else mt=(r<2)?0:(r<3)?1:(r<7)?2:3;if(mt==3&&L<2)mt=2;}\n if(mt==1||mt==2){i1=rng()%L;o1=ops[i1];}\n if(mt==3){i1=rng()%L;do{i2=rng()%L;}while(i2==i1);o1=ops[i1];o2=ops[i2];n2=rand_op();}\n long long s0=cur_score;\n switch(mt){case 0:apply_s(n1.m,n1.p,n1.q);break;case 1:undo_s(o1.m,o1.p,o1.q);break;case 2:undo_s(o1.m,o1.p,o1.q);apply_s(n1.m,n1.p,n1.q);break;case 3:undo_s(o1.m,o1.p,o1.q);undo_s(o2.m,o2.p,o2.q);apply_s(n1.m,n1.p,n1.q);apply_s(n2.m,n2.p,n2.q);break;}\n long long delta=cur_score-s0;bool acc=(delta>=0)||(T>0.5&&(double)(rng()%1000000)best_score){best_score=cur_score;best_ops=ops;}}\n else{switch(mt){case 0:undo_s(n1.m,n1.p,n1.q);break;case 1:apply_s(o1.m,o1.p,o1.q);break;case 2:undo_s(n1.m,n1.p,n1.q);apply_s(o1.m,o1.p,o1.q);break;case 3:undo_s(n2.m,n2.p,n2.q);undo_s(n1.m,n1.p,n1.q);apply_s(o2.m,o2.p,o2.q);apply_s(o1.m,o1.p,o1.q);break;}}\n }\n cout<\nusing namespace std;\nconst int N=5;\nint A[N][N],posR[N*N],posP[N*N],grid[N][N];\nint craneR,craneC;bool craneHolding;int craneContainer;\nint recvSent[N],recvPickedUp[N],dispatchCount[N];bool done_[N*N];\nmap> bufPos;set> usedBufs;\nstring result;\nvoid sRecv(){for(int r=0;rtr)turn_('U');else if(craneC freeBuf(int tR=-1){\n if(tR>=0)for(int c=N-2;c>=1;c--){auto p=make_pair(tR,c);if(!usedBufs.count(p)&&grid[tR][c]==-1)return p;}\n for(int c=N-2;c>=1;c--)for(int r=0;rblPos)return false;\n for(int pos=disp;pos planOrd(){\n const int ND=N+1;int DB=1;for(int i=0;id,int r,int c){int s=0;for(int i=0;i&d,int&r,int&c){c=s%N;s/=N;r=s%N;s/=N;for(int i=N-1;i>=0;i--){d[i]=s%ND;s/=ND;}};\n vectordist(NS,INT_MAX/2),pS(NS,-1),pG(NS,-1);\n priority_queue,vector>,greater<>>pq;\n arrayd0{};int s0=enc(d0,0,0);dist[s0]=0;pq.push({0,s0});\n while(!pq.empty()){\n auto[w,s]=pq.top();pq.pop();if(w>dist[s])continue;\n arrayd;int r,c;dec(s,d,r,c);\n for(int g=0;g=N)continue;int k=N*g+d[g],sR=posR[k];\n int tc=abs(r-sR)+abs(c)+abs(sR-g)+(N-1)+2+posP[k]*12;\n auto nd=d;nd[g]++;int ns=enc(nd,g,N-1);\n if(dist[s]+tcgD;gD.fill(N);int best=-1,bd=INT_MAX;\n for(int r=0;rord;if(best!=-1)for(int s=best;pS[s]!=-1;s=pS[s])ord.push_back(pG[s]);\n reverse(ord.begin(),ord.end());return ord;\n}\nvoid solve(){\n for(int r=0;r=0){deliver_(bSR,bSC,bBuf,!bBuf,bK/N);continue;}\n int bG_chain=-1,bD_chain=INT_MAX,bG_buf=-1,bD_buf=INT_MAX;\n for(int g=0;g=0)?bG_chain:bG_buf;\n if(bG>=0)clearBlocker_(posR[nNext(bG)]);\n }\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n int n;cin>>n;for(int r=0;r>A[r][p];\n solve();cout<\nusing namespace std;\nint N,h[20][20],origH[20][20],curR,curC,curLoad;\nvector ops;long long totalCost;\nvoid doLoad(int d){if(d<=0)return;totalCost+=d;ops.push_back(\"+\"+to_string(d));h[curR][curC]-=d;curLoad+=d;}\nvoid doUnload(int d){d=min(d,curLoad);if(d<=0)return;totalCost+=d;ops.push_back(\"-\"+to_string(d));h[curR][curC]+=d;curLoad-=d;}\nvoid moveStep(char dir,int dr,int dc){totalCost+=100LL+curLoad;curR+=dr;curC+=dc;ops.push_back(string(1,dir));if(h[curR][curC]>0)doLoad(h[curR][curC]);else if(h[curR][curC]<0&&curLoad>0)doUnload(min(curLoad,-h[curR][curC]));}\nvoid moveTo(int tr,int tc){\n if(curR==tr&&curC==tc)return;\n int nrow=abs(tr-curR),ncol=abs(tc-curC),rs=curR0?'D':'U',rs,0);while(curC!=tc)moveStep(cs>0?'R':'L',0,cs);return;}\n bool ld=(curLoad>0);\n auto cv=[&](int r,int c)->int{int ri=curR+r*rs,ci=curC+c*cs;return ld?abs(h[ri][ci]):max(0,h[ri][ci]);};\n int dp[21][21]={};bool fr[21][21]={};\n for(int r=1;r<=nrow;r++){dp[r][0]=dp[r-1][0]+cv(r,0);fr[r][0]=1;}\n for(int c=1;c<=ncol;c++)dp[0][c]=dp[0][c-1]+cv(0,c);\n for(int r=1;r<=nrow;r++)for(int c=1;c<=ncol;c++){int a=dp[r-1][c]+cv(r,c),b=dp[r][c-1]+cv(r,c);if(a>=b){dp[r][c]=a;fr[r][c]=1;}else dp[r][c]=b;}\n string path;int r=nrow,c=ncol;\n while(r||c){if(!r){path+='c';c--;}else if(!c){path+='r';r--;}else if(fr[r][c]){path+='r';r--;}else{path+='c';c--;}}\n reverse(path.begin(),path.end());\n for(char ch:path)if(ch=='r')moveStep(rs>0?'D':'U',rs,0);else moveStep(cs>0?'R':'L',0,cs);\n}\nbool allZero(){for(int i=0;i0)doLoad(h[0][0]);\n while(!allZero()&&(int)ops.size()<95000){\n auto md=[&](int i,int j){return abs(i-curR)+abs(j-curC);};\n int nD=INT_MAX,di=-1,dj=-1;double bDS=-1;int sdi=-1,sdj=-1;\n for(int i=0;i0){double sc=(double)min(curLoad,-h[i][j])/(d+1);if(sc>bDS){bDS=sc;sdi=i;sdj=j;}}}\n int dI=(sd&&sdi>=0)?sdi:di,dJ=(sd&&sdj>=0)?sdj:dj;\n if(curLoad==0){\n double bs=-1;int bi=-1,bj=-1;\n for(int i=0;i0){double sc=(double)h[i][j]/(md(i,j)+1);if(sc>bs){bs=sc;bi=i;bj=j;}}\n if(bi<0)break;moveTo(bi,bj);if(h[bi][bj]>0)doLoad(h[bi][bj]);\n }else{\n int fsi=-1,fsj=-1;\n if(threshold==-1){\n double bss=-1,bds=-1;int ssi=-1,ssj=-1;\n for(int i=0;i0){double sc=(double)h[i][j]*100/((double)(d+1)*max(curLoad,1));if(sc>bss){bss=sc;ssi=i;ssj=j;}}if(h[i][j]<0){double sc=(double)min(curLoad,-h[i][j])/(d+1);if(sc>bds)bds=sc;}}\n if(bss>bds&&ssi>=0){fsi=ssi;fsj=ssj;}\n }else{\n double bfs=-1;\n for(int i=0;i=(long long)nD*threshold)continue;double sc=nls?1.0/(d+1):(double)h[i][j]/(d+1);if(sc>bfs){bfs=sc;fsi=i;fsj=j;}}\n }\n if(fsi>=0){moveTo(fsi,fsj);if(h[fsi][fsj]>0)doLoad(h[fsi][fsj]);}\n else if(dI>=0){moveTo(dI,dJ);if(h[dI][dJ]<0&&curLoad>0)doUnload(min(curLoad,-h[dI][dJ]));}\n else break;\n }\n }\n for(int i=0;i> cells;\n for(int i=0;ivis(n,false);int cr=0,cc=0;\n for(int s=0;s0)doLoad(h[r][c]);else if(h[r][c]<0&&curLoad>0)doUnload(min(curLoad,-h[r][c]));\n }\n while(!allZero()&&(int)ops.size()<95000){\n auto md=[&](int i,int j){return abs(i-curR)+abs(j-curC);};\n int nD=INT_MAX,di=-1,dj=-1;\n for(int i=0;i0){double sc=(double)h[i][j]/(md(i,j)+1);if(sc>bs){bs=sc;bi=i;bj=j;}}if(bi<0)break;moveTo(bi,bj);if(h[bi][bj]>0)doLoad(h[bi][bj]);}\n else{double bfs=-1;int fsi=-1,fsj=-1;for(int i=0;i=(long long)nD*fb)continue;double sc=(double)h[i][j]/(d+1);if(sc>bfs){bfs=sc;fsi=i;fsj=j;}}\n if(fsi>=0){moveTo(fsi,fsj);if(h[fsi][fsj]>0)doLoad(h[fsi][fsj]);}else if(di>=0){moveTo(di,dj);if(h[di][dj]<0&&curLoad>0)doUnload(min(curLoad,-h[di][dj]));}else break;}\n }\n for(int i=0;i>N;for(int i=0;i>h[i][j];origH[i][j]=h[i][j];}\n long long best=LLONG_MAX;vectorbestOps;\n auto go=[&](auto f){for(int i=0;i>{{-1,0,0},{-1,1,0},{0,0,0},{0,1,0},{30,0,0},{50,0,0},{70,0,0},{80,0,0},{90,0,0},{100,0,0},{110,0,0},{120,0,0},{130,0,0},{150,0,0},{175,0,0},{200,0,0},{250,0,0},{300,0,0},{400,0,0},{500,0,0},{750,0,0},{1000,0,0},{2000,0,0},{80,1,0},{100,1,0},{120,1,0},{150,1,0},{200,1,0},{300,1,0},{80,0,1},{100,0,1},{120,0,1},{150,0,1}})\n go([&]{run(t,sd,nls);});\n for(int fb:{80,100,150})go([&]{runTSP(fb);});\n for(auto&op:bestOps)cout<\nusing namespace std;\nint main(){\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int N,M,T; cin>>N>>M>>T;\n const int SC=2*N*(N-1),nn=N*N;\n vector> X(SC,vector(M));\n for(int i=0;i>X[i][j];\n mt19937 rng(42);\n vector> nbr(nn); vector ndeg(nn,0);\n for(int p=0;p0)nbr[p][ndeg[p]++]=p-N;if(r0)nbr[p][ndeg[p]++]=p-1;if(c vals(SC,0);\n for(int k=0;k ins(SC,false); vector sel;\n for(int l=0;lX[bk][l])bk=k;if(!ins[bk]){ins[bk]=true;sel.push_back(bk);}}\n {vector ord(SC);iota(ord.begin(),ord.end(),0);sort(ord.begin(),ord.end(),[&](int a,int b){return vals[a]>vals[b];});for(int k:ord){if((int)sel.size()>=nn)break;if(!ins[k]){ins[k]=true;sel.push_back(k);}}}\n vector pst(nn*nn);\n for(int i=0;i psum(nn,0);\n for(int i=0;i&g,int p)->int{int v=0;for(int d=0;d&g)->int{int s=0;for(int p=0;p g)->vector{bool imp=true;while(imp){imp=false;for(int a=0;abef)imp=true;else swap(g[a],g[b]);}}return g;};\n auto grinit=[&]()->vector{vector g(nn,-1);vector used(nn,false);for(int pos=0;pos0)cv+=pst[s*nn+g[pos-N]];if(c>0)cv+=pst[s*nn+g[pos-1]];int64_t ev=(int64_t)cv*1000000LL+psum[s];if(ev>bv){bv=ev;bs=s;}}g[pos]=bs;used[bs]=true;}return g;};\n int gbest=-1; vector bg;\n for(int rest=0;rest<3;rest++){\n double rt0=chrono::duration(chrono::steady_clock::now()-ts).count();\n if(rt0>=0.185) break;\n double tl=(0.185-rt0)/(3-rest),tend=rt0+tl;\n vector g(nn); double T0;\n if(rest==0){g=grinit();T0=200.0;}else{iota(g.begin(),g.end(),0);shuffle(g.begin(),g.end(),rng);T0=1000.0;}\n int cur=totsc(g),lb=cur; vector lg=g; double temp=T0;\n for(int it=0;;it++){\n if((it&0x7FF)==0){double now=chrono::duration(chrono::steady_clock::now()-ts).count();if(now>=tend)break;temp=T0*pow(0.1/T0,(now-rt0)/tl);}\n int p1=rng()%nn,p2=rng()%nn; if(p1==p2)continue;\n int bef=ctrb(g,p1)+ctrb(g,p2); swap(g[p1],g[p2]); int aft=ctrb(g,p1)+ctrb(g,p2); int d=aft-bef;\n if(d>=0||(rng()%1000000)<(int)(1e6*exp((double)d/temp))){cur+=d;if(cur>lb){lb=cur;lg=g;}}else swap(g[p1],g[p2]);\n }\n lg=locsrch(lg); int sc=totsc(lg); if(sc>gbest){gbest=sc;bg=lg;}\n }\n for(int i=0;i>X[i][j];\n }\n return 0;\n}","ahc038":"#include \nusing namespace std;\nint N,M,V;\nconst int DR[]={0,1,0,-1},DC[]={1,0,-1,0};\nint rx,ry,nfp,Vp,rfp=-1;\nint fpd[4],hld[4];\nstruct Del{int sr,sc,tr,tc;bool done;};\nvectorP;int np;\nvector>g;\nmap,int>sm;\nvectorops;\nbool navto(int tr,int tc,int pk,int td){\n while((rx!=tr||ry!=tc||fpd[pk]!=td)&&(int)ops.size()<99990){\n char mv='.';\n if(rx!=tr||ry!=tc){if(rxtr)mv='U';else if(ry=N||fc<0||fc>=N)continue;\n if(hld[k]<0){if(k==rfp)continue;auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}}\n else{int di=hld[k];if(P[di].tr==fr&&P[di].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di].done=true;hld[k]=-1;op[Vp+1+k]='P';}}\n }\n ops.push_back(op);\n }\n return rx==tr&&ry==tc&&fpd[pk]==td;\n}\nint pickfp(int di,int r,int c){\n sm.erase({r,c});\n int bk=-1,br=-1,bc=-1,bdir=-1,bv=INT_MAX;\n for(int k=0;k=0)continue;\n for(int d=0;d<4;d++){\n int ar=r-DR[d],ac=c-DC[d];if(ar<0||ar>=N||ac<0||ac>=N)continue;\n int md=abs(rx-ar)+abs(ry-ac),rot=min((d-fpd[k]+4)%4,(fpd[k]-d+4)%4),v=max(md,rot);\n if(v=99990){sm[{r,c}]=di;return -1;}\n string op(2*Vp,'.');bool picked=false;\n for(int k=0;k=N||fc<0||fc>=N)continue;\n if(k==bk&&fr==r&&fc==c&&g[r][c]==1&&hld[k]<0){hld[k]=di;g[r][c]=0;op[Vp+1+k]='P';picked=true;}\n else if(hld[k]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}}\n else if(hld[k]>=0){int di2=hld[k];if(P[di2].tr==fr&&P[di2].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di2].done=true;hld[k]=-1;op[Vp+1+k]='P';}}\n }\n ops.push_back(op);if(!picked){sm[{r,c}]=di;return -1;}return bk;\n}\nbool dropfp(int k,int di){\n if(hld[k]!=di)return true;\n int r=P[di].tr,c=P[di].tc;\n int bdir=-1,bar=-1,bac=-1,bv=INT_MAX;\n for(int d=0;d<4;d++){\n int ar=r-DR[d],ac=c-DC[d];if(ar<0||ar>=N||ac<0||ac>=N)continue;\n int md=abs(rx-ar)+abs(ry-ac),rot=min((d-fpd[k]+4)%4,(fpd[k]-d+4)%4),v=max(md,rot);\n if(v=99990)return false;\n string op(2*Vp,'.');bool ok=false;\n for(int k2=0;k2=N||fc<0||fc>=N)continue;\n if(k2==k&&fr==r&&fc==c&&g[r][c]==0&&hld[k2]==di){g[r][c]=1;P[di].done=true;hld[k2]=-1;op[Vp+1+k2]='P';ok=true;}\n else if(hld[k2]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k2]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k2]='P';}}\n else if(hld[k2]>=0){int di2=hld[k2];if(P[di2].tr==fr&&P[di2].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di2].done=true;hld[k2]=-1;op[Vp+1+k2]='P';}}\n }\n ops.push_back(op);return ok;\n}\nbool cbh(int bk){\n if(hld[bk]<0)return false;int di=hld[bk];\n pairtmp={-1,-1};\n {set>ts;for(auto&d:P)if(!d.done)ts.insert({d.tr,d.tc});\n int bdist=INT_MAX;\n for(int i=0;i>N>>M>>V;\n vectorsg(N),tg(N);for(auto&s:sg)cin>>s;for(auto&s:tg)cin>>s;\n vector>S,T;g.assign(N,vector(N,0));\n for(int i=0;imt(m,-1);\n {vectorsu(m,false),tu(m,false);\n for(int i=0;i=N||fc<0||fc>=N)continue;if(hld[k]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}}else{int di=hld[k];if(P[di].tr==fr&&P[di].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di].done=true;hld[k]=-1;op[Vp+1+k]='P';}}}};\n if(nfp>=2){string op(2*Vp,'.');if(nfp>=2){op[2]='R';fpd[1]=1;}if(nfp>=3){op[3]='R';fpd[2]=1;}if(nfp>=4){op[4]='L';fpd[3]=3;}och(op);ops.push_back(op);}\n if(nfp>=3){string op(2*Vp,'.');op[3]='R';fpd[2]=2;och(op);ops.push_back(op);}\n vectortsp(np);\n if(np>0){\n {vectorused(np,false);int cr=0,cc=0;for(int s=0;sint{if(b<0||b>=np)return 0;int r0=(a<0||a>=np)?0:P[tsp[a]].tr,c0=(a<0||a>=np)?0:P[tsp[a]].tc;return abs(r0-P[tsp[b]].sr)+abs(c0-P[tsp[b]].sc);};\n {bool imp=true;while(imp){imp=false;for(int i=0;i=0){imp=true;int val=tsp[bi];if(bj>bi){tsp.erase(tsp.begin()+bi);tsp.insert(tsp.begin()+bj,val);}else{tsp.erase(tsp.begin()+bi);tsp.insert(tsp.begin()+bj+1,val);}}}}\n }\n vectortsp_rank(np,np);for(int s=0;s>dr;\n for(int k=0;kperm(n);iota(perm.begin(),perm.end(),0);\n vectorbest=perm;int bc=INT_MAX;\n do{int cost=0,cr=rx,cc=ry;for(int i:perm){int r=P[dr[i].second].tr,c=P[dr[i].second].tc;cost+=abs(cr-r)+abs(cc-c);cr=r;cc=c;}if(cost=0){\n int k=pickfp(fi,P[fi].sr,P[fi].sc);\n if(k>=0){\n for(int ex=0;ex=0){if(cbh(k))prog=true;break;}\n if(!prog){int ci=-1,bd=INT_MAX;for(auto&[src,di]:sm){int d=abs(rx-src.first)+abs(ry-src.second);if(d=0){int k=pickfp(ci,P[ci].sr,P[ci].sc);if(k>=0&&cbh(k))prog=true;}}}\n if(prog)stall=0;\n else{stall++;if(stall>300)break;\n string op(2*Vp,'.');for(int k=0;k=N||fc<0||fc>=N)continue;if(hld[k]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}}else{int di=hld[k];if(P[di].tr==fr&&P[di].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di].done=true;hld[k]=-1;op[Vp+1+k]='P';}}}ops.push_back(op);}\n }\n for(auto&op:ops)cout<\nusing namespace std;\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n using Clock=chrono::steady_clock;auto t0=Clock::now();\n auto elMs=[&](){return(long long)chrono::duration_cast(Clock::now()-t0).count();};\n int N;cin>>N;int M=2*N;\n vectorX(M),Y(M),W(M);\n for(int i=0;i>X[i]>>Y[i];W[i]=(ix2)swap(x1,x2);if(y1>y2)swap(y1,y2);\n cout<<4<<\"\\n\"<bx(M),by(M);\n {vectoridx(M);iota(idx.begin(),idx.end(),0);\n sort(idx.begin(),idx.end(),[&](int a,int b){return X[a]&f,int lo,int hi)->pair{\n int cur=0,cs=-1,mx=0,blo=-1,bhi=-1;bool ir=false;\n for(int i=0,n=(int)f.size();i=lo&&f[i].other<=hi)gs+=f[i].w;i++;}\n if(!ir){if(gs>0){cs=xv;cur=gs;ir=true;if(cur>mx){mx=cur;blo=cs;bhi=xv;}}}\n else{cur+=gs;if(cur>mx){mx=cur;blo=cs;bhi=xv;}if(cur<0){cur=0;ir=false;}}}\n return{blo,bhi};};\n auto evalRect=[&](int x1,int x2,int y1,int y2){int s=0;\n for(int i=0;i=x1&&X[i]<=x2&&Y[i]>=y1&&Y[i]<=y2)s+=W[i];return s;};\n auto coordDescent=[&](int x1,int x2,int y1,int y2)->tuple{\n x1=max(0,min(CMAX,x1));x2=max(0,min(CMAX,x2));y1=max(0,min(CMAX,y1));y2=max(0,min(CMAX,y2));\n if(x1>x2)swap(x1,x2);if(y1>y2)swap(y1,y2);\n int px1=-1,px2=-1,py1=-1,py2=-1;\n for(int it=0;it<20;it++){if(x1==px1&&x2==px2&&y1==py1&&y2==py2)break;\n px1=x1;px2=x2;py1=y1;py2=y2;\n auto[nx1,nx2]=kadane(bx,y1,y2);if(nx1>=0){x1=nx1;x2=nx2;}\n auto[ny1,ny2]=kadane(by,x1,x2);if(ny1>=0){y1=ny1;y2=ny2;}}\n return make_tuple(evalRect(x1,x2,y1,y2),x1,x2,y1,y2);};\n const int G=200,step=CMAX/G;\n vector>grid(G,vector(G,0));\n for(int i=0;ics(G,0);\n for(int gx2=gx1;gx2mx){mx=cur;ms=cst;me=gy;}if(cur<0){cur=0;cst=gy+1;}}\n if(me>=0&&mx>bgs){bgs=mx;bgx1=gx1;bgx2=gx2;bgy1=ms;bgy2=me;}}}\n int ix1=bgx1*step,ix2=min((bgx2+1)*step,CMAX),iy1=bgy1*step,iy2=min((bgy2+1)*step,CMAX);\n int gscore=-1,rx1=0,rx2=1,ry1=0,ry2=1;\n auto tryRun=[&](int x1,int x2,int y1,int y2){\n auto[s,a,b,c,d]=coordDescent(x1,x2,y1,y2);\n if(s>gscore){gscore=s;rx1=a;rx2=b;ry1=c;ry2=d;}};\n tryRun(ix1,ix2,iy1,iy2);tryRun(0,CMAX,0,CMAX);\n {long long cx=0,cy=0;for(int i=0;i1700)break;\n int seed=rng()%N;int cx=X[seed],cy=Y[seed];int half;\n switch(rng()%4){case 0:half=200+rng()%800;break;case 1:half=1000+rng()%9000;break;\n case 2:half=10000+rng()%20000;break;default:half=30000+rng()%20000;break;}\n tryRun(cx-half,cx+half,cy-half,cy+half);}\n auto findArm=[&](const vector>&fish,int clo,int chi)->tuple{\n vectorxs;\n for(auto&[s,c,w]:fish)if(c>=clo&&c<=chi)xs.push_back(c);\n sort(xs.begin(),xs.end());xs.erase(unique(xs.begin(),xs.end()),xs.end());\n if(xs.empty())return{0,-1,-1,0};\n int kx=(int)xs.size();vectorcum(kx,0);int bsc=0,bc1=-1,bc2=-1,bsw=0;\n for(int i=0,n=(int)fish.size();i(fish[i]);\n while(i(fish[i])==csw){auto&[s2,c,w]=fish[i];++i;\n if(c>=clo&&c<=chi)cum[(int)(lower_bound(xs.begin(),xs.end(),c)-xs.begin())]+=w;}\n int cur=0,cs2=-1,mx=0,blo=-1,bhi=-1;bool ir=false;\n for(int j=0;j0){cs2=xs[j];cur=gs;ir=true;if(cur>mx){mx=cur;blo=cs2;bhi=xs[j];}}}\n else{cur+=gs;if(cur>mx){mx=cur;blo=cs2;bhi=xs[j];}if(cur<0){cur=0;ir=false;}}}\n if(mx>bsc){bsc=mx;bc1=blo;bc2=bhi;bsw=csw;}}\n return{bsc,bc1,bc2,bsw};};\n vector>ft,fb,fr,fl;\n for(int i=0;iry2&&X[i]>=rx1&&X[i]<=rx2)ft.emplace_back(Y[i],X[i],W[i]);\n if(Y[i]=rx1&&X[i]<=rx2)fb.emplace_back(-Y[i],X[i],W[i]);\n if(X[i]>rx2&&Y[i]>=ry1&&Y[i]<=ry2)fr.emplace_back(X[i],Y[i],W[i]);\n if(X[i]=ry1&&Y[i]<=ry2)fl.emplace_back(-X[i],Y[i],W[i]);}\n sort(ft.begin(),ft.end());sort(fb.begin(),fb.end());sort(fr.begin(),fr.end());sort(fl.begin(),fl.end());\n auto[ts,tax1,tax2,tay2]=findArm(ft,rx1,rx2);\n auto[bms,bax1,bax2,neg_bay]=findArm(fb,rx1,rx2);int bay1=-neg_bay;\n auto[rms,ray1,ray2,rax2]=findArm(fr,ry1,ry2);\n auto[ls,lay1,lay2,neg_lax]=findArm(fl,ry1,ry2);int lax1=-neg_lax;\n bool ht=ts>0&&tax1>=rx1&&tax2<=rx2&&tax1ry2;\n bool hb=bms>0&&bax1>=rx1&&bax2<=rx2&&bax10&&ray1>=ry1&&ray2<=ry2&&ray1rx2;\n bool hl=ls>0&&lay1>=ry1&&lay2<=ry2&&lay1budget){\n vector>ae;\n if(ht&&ct>0)ae.push_back({(double)ts/ct,0});\n if(hb&&cb>0)ae.push_back({(double)bms/cb,1});\n if(hr&&cr_>0)ae.push_back({(double)rms/cr_,2});\n if(hl&&cl>0)ae.push_back({(double)ls/cl,3});\n sort(ae.begin(),ae.end());\n for(auto&[e,idx]:ae){if(total_cost<=budget)break;\n if(idx==0){ht=false;total_cost-=ct;}else if(idx==1){hb=false;total_cost-=cb;}\n else if(idx==2){hr=false;total_cost-=cr_;}else{hl=false;total_cost-=cl;}}}\n struct AI{int c1,c2,sw,score,side;};\n vectorall_arms;\n if(ht)all_arms.push_back({tax1,tax2,tay2,ts,0});\n if(hb)all_arms.push_back({bax1,bax2,-bay1,bms,1});\n if(hr)all_arms.push_back({ray1,ray2,rax2,rms,2});\n if(hl)all_arms.push_back({lay1,lay2,-lax1,ls,3});\n int used_budget=total_cost,used_vtx=4*(int)all_arms.size();\n auto armCostFn=[&](const AI&a)->int{\n if(a.side==0)return 2*(a.sw-ry2);if(a.side==1)return 2*(ry1+a.sw);\n if(a.side==2)return 2*(a.sw-rx2);return 2*(rx1+a.sw);};\n vectorsub_cands;\n function>&,int,int,int,int)>far;\n far=[&](const vector>&fish,int clo,int chi,int side,int dep){\n if(clo>chi||dep<=0||elMs()>1920)return;\n auto[sc,c1,c2,sw]=findArm(fish,clo,chi);\n if(sc<=0||c1<0||c1>=c2)return;\n sub_cands.push_back({c1,c2,sw,sc,side});\n far(fish,clo,c1-1,side,dep-1);far(fish,c2+1,chi,side,dep-1);};\n // Depth=3 for richer sub-arm search\n if(ht){far(ft,rx1,tax1-1,0,3);far(ft,tax2+1,rx2,0,3);}\n if(hb){far(fb,rx1,bax1-1,1,3);far(fb,bax2+1,rx2,1,3);}\n if(hr){far(fr,ry1,ray1-1,2,3);far(fr,ray2+1,ry2,2,3);}\n if(hl){far(fl,ry1,lay1-1,3,3);far(fl,lay2+1,ry2,3,3);}\n sort(sub_cands.begin(),sub_cands.end(),[](const AI&a,const AI&b){return a.score>b.score;});\n for(auto&sc:sub_cands){int c=armCostFn(sc);\n if(c<=0||used_budget+c>budget||used_vtx+4>996)continue;\n all_arms.push_back(sc);used_budget+=c;used_vtx+=4;}\n auto outR=[&](int x1,int x2,int y1,int y2){\n if(x1>=x2){if(x2=y2){if(y2=1)outR(rx1,rx2,ry1,ry2);return 0;}\n vectorta,ba,ra,la;\n for(auto&a:all_arms){if(a.side==0)ta.push_back(a);else if(a.side==1)ba.push_back(a);\n else if(a.side==2)ra.push_back(a);else la.push_back(a);}\n sort(ba.begin(),ba.end(),[](const AI&a,const AI&b){return a.c1b.c2;});\n sort(la.begin(),la.end(),[](const AI&a,const AI&b){return a.c2>b.c2;});\n vector>v;\n v.push_back({rx1,ry1});\n {int cx=rx1;for(auto&a:ba){int b1=-a.sw;if(a.c1>cx)v.push_back({a.c1,ry1});\n v.push_back({a.c1,b1});v.push_back({a.c2,b1});v.push_back({a.c2,ry1});cx=a.c2;}}\n v.push_back({rx2,ry1});\n {int cy=ry1;for(auto&a:ra){if(a.c1>cy)v.push_back({rx2,a.c1});\n v.push_back({a.sw,a.c1});v.push_back({a.sw,a.c2});v.push_back({rx2,a.c2});cy=a.c2;}}\n v.push_back({rx2,ry2});\n {int cx=rx2;for(auto&a:ta){if(a.c2>res;\n for(auto&p:v){if(res.empty()||res.back()!=p)res.push_back(p);}\n while(res.size()>1&&res.front()==res.back())res.pop_back();\n if((int)res.size()<4){outR(rx1,rx2,ry1,ry2);return 0;}\n {set>vs(res.begin(),res.end());\n if((int)vs.size()!=(int)res.size()){outR(rx1,rx2,ry1,ry2);return 0;}}\n cout<<(int)res.size()<<\"\\n\";\n for(auto&[x,y]:res)cout<\nusing namespace std;\ntypedef long long ll;\n\nint N, T;\nvector W, H;\ndouble sW, sH, mxW, mxH, totA;\n\nstruct Op { int p, r; char d; int b; };\n\npair simulate(const vector& ops) {\n vector x0(N,0),y0(N,0),x1(N,0),y1(N,0);\n vector pl(N,false);\n for (const auto& o : ops) {\n int p = o.p;\n ll w = max(1LL, llround(o.r ? H[p] : W[p]));\n ll h = max(1LL, llround(o.r ? W[p] : H[p]));\n if (o.d == 'U') {\n ll xl = o.b >= 0 ? x1[o.b] : 0LL;\n ll yt = 0;\n for (int i = 0; i < N; i++)\n if (pl[i] && x0[i] < xl+w && x1[i] > xl)\n yt = max(yt, y1[i]);\n x0[p]=xl; y0[p]=yt; x1[p]=xl+w; y1[p]=yt+h;\n } else {\n ll yt = o.b >= 0 ? y1[o.b] : 0LL;\n ll xl = 0;\n for (int i = 0; i < N; i++)\n if (pl[i] && y0[i] < yt+h && y1[i] > yt)\n xl = max(xl, x1[i]);\n x0[p]=xl; y0[p]=yt; x1[p]=xl+w; y1[p]=yt+h;\n }\n pl[p] = true;\n }\n ll rW=0, rH=0;\n for (int i = 0; i < N; i++)\n if (pl[i]) { rW=max(rW,x1[i]); rH=max(rH,y1[i]); }\n return {rW, rH};\n}\n\n// col=false: shelf packing (rows); col=true: column packing\n// For col=false, line0 uses U, rest use L\n// For col=true, line0 uses L, rest use U\nvector make_pack(const vector& rot, double tgt, bool col) {\n vector ops; ops.reserve(N);\n int cl = -1; double cm = 0;\n vector lr; vector lc;\n int p0 = -1;\n for (int i = 0; i < N; i++) {\n double m = col ? (rot[i] ? W[i] : H[i]) : (rot[i] ? H[i] : W[i]);\n double c = col ? (rot[i] ? H[i] : W[i]) : (rot[i] ? W[i] : H[i]);\n if (cl < 0 || cm + m > tgt) {\n cl++; cm = m;\n lr.push_back(i); lc.push_back(c);\n if (cl == 0) {\n ops.push_back({i, rot[i], col?'L':'U', -1});\n p0 = i;\n } else {\n ops.push_back({i, rot[i], col?'U':'L', lr[cl-1]});\n }\n } else {\n cm += m;\n if (c > lc[cl]) { lc[cl]=c; lr[cl]=i; }\n if (cl == 0) {\n ops.push_back({i, rot[i], col?'L':'U', p0});\n p0 = i;\n } else {\n ops.push_back({i, rot[i], col?'U':'L', lr[cl-1]});\n }\n }\n }\n return ops;\n}\n\ndouble calc_score(const vector& rot, double tgt, bool col) {\n auto [a,b] = simulate(make_pack(rot, tgt, col));\n return (double)(a+b);\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n\n double sigma;\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 sW=sH=mxW=mxH=totA=0;\n for (int i = 0; i < N; i++) {\n sW+=W[i]; sH+=H[i];\n mxW=max(mxW,W[i]); mxH=max(mxH,H[i]);\n totA+=W[i]*H[i];\n }\n\n const double BUDGET = 2600.0;\n auto t0 = chrono::steady_clock::now();\n auto now = [&]() {\n return chrono::duration(chrono::steady_clock::now()-t0).count();\n };\n\n vector g_rot;\n double g_tgt=0, g_score=1e18;\n bool g_col=false;\n\n for (int t = 0; t < T; t++) {\n double ts = now();\n double per = max(1.0, (BUDGET - ts) / (T - t));\n double dl = ts + per * 0.95;\n\n mt19937 rng(t * 1234567891u ^ 987654321u);\n uniform_real_distribution uni(0,1);\n\n bool col;\n double lo, hi, tgt;\n vector rot(N);\n\n if (t < (T+1)/2) {\n col = (t & 1);\n lo = col ? mxH : mxW;\n hi = col ? sH : sW;\n tgt = max(lo, min(hi, sqrt(totA)));\n // Init rotation: minimize cross-dim\n for (int i = 0; i < N; i++)\n rot[i] = col ? (H[i] br=rot;\n double bt=tgt;\n bool bc=col;\n double bs=cur;\n\n double Th = cur*0.05+1.0;\n double Tl = max(1.0, cur*1e-5);\n\n // Simulated Annealing\n for (int it=0; ; it++) {\n if ((it&63)==0 && now()>=dl) break;\n double frac = max(0.0, min(1.0, (now()-ts)/per));\n double Tc = max(Tl, Th * pow(Tl/Th, frac));\n\n int mv = rng()%10, fi=-1;\n double ot=tgt;\n bool oc=col;\n double olo=lo, ohi=hi;\n\n if (mv < 7) {\n fi = rng()%N;\n rot[fi] ^= 1;\n } else if (mv < 9) {\n tgt = max(lo, min(hi, tgt * exp((uni(rng)*2-1)*0.35)));\n } else {\n col ^= 1;\n lo = col ? mxH : mxW;\n hi = col ? sH : sW;\n tgt = max(lo, min(hi, ot));\n }\n\n double ns = calc_score(rot, tgt, col);\n double d = ns - cur;\n if (d <= 0 || uni(rng) < exp(-d/Tc)) {\n cur = ns;\n if (ns < bs) { bs=ns; br=rot; bt=tgt; bc=col; }\n } else {\n if (fi >= 0) rot[fi] ^= 1;\n else if (mv < 9) tgt = ot;\n else { col=oc; lo=olo; hi=ohi; tgt=ot; }\n }\n }\n\n // Final greedy passes\n for (int pass=0; pass<3; pass++) {\n bool imp=false;\n for (int i=0; i> Wf >> Hf;\n }\n\n return 0;\n}","ahc041":"#include \nusing namespace std;\ntypedef long long ll;\nint N,M,H,A[1000];\nvectorG[1000];\nint par[1000],dep[1000],ssm[1000],mdn[1000];\nvectorch[1000];\nvoid dfs_init(int v){ssm[v]=A[v];mdn[v]=0;for(int c:ch[v]){dfs_init(c);ssm[v]+=ssm[c];mdn[v]=max(mdn[v],mdn[c]+1);}}\nvoid push_dep(int v,int d){dep[v]=d;for(int c:ch[v])push_dep(c,d+1);}\nbool in_sub(int w,int v){for(;w!=-1;w=par[w])if(w==v)return true;return false;}\nvoid pull_ssm(int v){for(;v!=-1;v=par[v]){int s=A[v];for(int c:ch[v])s+=ssm[c];ssm[v]=s;}}\nvoid pull_mdn(int v){for(;v!=-1;v=par[v]){int m=0;for(int c:ch[v])m=max(m,mdn[c]+1);mdn[v]=m;}}\nvoid do_move(int v,int np){int op=par[v];if(op!=-1){auto&c=ch[op];c.erase(find(c.begin(),c.end(),v));}par[v]=np;if(np!=-1){ch[np].push_back(v);push_dep(v,dep[np]+1);}else push_dep(v,0);if(op!=-1){pull_ssm(op);pull_mdn(op);}if(np!=-1){pull_ssm(np);pull_mdn(np);}}\nvoid rebuild(){for(int i=0;iq;q.push(v);while(!q.empty()){int u=q.front();q.pop();for(int c:ch[u]){dep[c]=dep[u]+1;q.push(c);}}}for(int v=0;vp(N);iota(p.begin(),p.end(),0);if(iter==0)sort(p.begin(),p.end(),[](int a,int b){return A[a]>A[b];});else shuffle(p.begin(),p.end(),rng);for(int v:p){int lim=H-1-mdn[v];if(lim<0)continue;int bp=par[v];ll bg=0;for(int w:G[v]){if(dep[w]>lim||in_sub(w,v))continue;ll g=(ll)(dep[w]+1-dep[v])*ssm[v];if(g>bg){bg=g;bp=w;}}if(bg>0){do_move(v,bp);ok=true;}}if(!ok)break;}}\nvoid build_bfs(vector&ord){fill(par,par+N,-1);fill(dep,dep+N,0);for(int i=0;ivis(N,false);for(int s:ord){if(vis[s])continue;queueq;q.push(s);vis[s]=true;while(!q.empty()){int v=q.front();q.pop();if(dep[v]>=H)continue;for(int u:G[v])if(!vis[u]){vis[u]=true;par[u]=v;dep[u]=dep[v]+1;ch[v].push_back(u);q.push(u);}}}for(int v=0;v=H)return;int lim=H-1-mdn[v];int bp=par[v];ll bg=0;for(int w:G[v]){if(dep[w]>lim||in_sub(w,v))continue;ll g=(ll)(dep[w]+1-dep[v])*ssm[v];if(g>bg){bg=g;bp=w;}}if(bg>0){do_move(v,bp);cur+=bg;}}\nint main(){\n ios::sync_with_stdio(false);cin.tie(0);\n cin>>N>>M>>H;for(int i=0;i>A[i];\n for(int i=0;i>u>>v;G[u].push_back(v);G[v].push_back(u);}\n for(int i=0;i>x>>y;}\n auto t0=chrono::steady_clock::now();\n mt19937 rng(42);\n ll best_sc=-1;vectorbest_par(N);\n for(int trial=0;;trial++){\n if(chrono::duration(chrono::steady_clock::now()-t0).count()>0.3)break;\n vectorord(N);iota(ord.begin(),ord.end(),0);\n if(trial==0)sort(ord.begin(),ord.end(),[](int a,int b){return A[a]best_sc){best_sc=sc;copy(par,par+N,best_par.begin());}\n }\n copy(best_par.begin(),best_par.end(),par);rebuild();ll cur=best_sc;\n uniform_real_distributionuni(0,1);\n auto ts=chrono::steady_clock::now();\n double sa_t=max(0.05,1.82-chrono::duration(ts-t0).count());\n double T=1000.0;\n for(long long step=0;;step++){\n if(step%10000==0){double t=chrono::duration(chrono::steady_clock::now()-ts).count();if(t>=sa_t)break;T=1000.0*pow(0.001,t/sa_t);}\n int v=rng()%N;int lim=H-1-mdn[v];if(lim<0)continue;\n if(G[v].empty())continue;int w=G[v][rng()%G[v].size()];\n if(w==par[v]||dep[w]>lim||in_sub(w,v))continue;\n ll gain=(ll)(dep[w]+1-dep[v])*ssm[v];\n if(gain>0||(T>0.01&&uni(rng)0)greedy_one(v,cur);\n if(cur>best_sc){best_sc=cur;copy(par,par+N,best_par.begin());}\n }\n }\n copy(best_par.begin(),best_par.end(),par);rebuild();\n run_greedy(rng);{ll sc=compute_score();if(sc>best_sc)copy(par,par+N,best_par.begin());}\n for(int v=0;v\nusing namespace std;\nint N,M,OR_[42],OC_[42],ctop_[21],cbot_[21],rleft_[21],rright_[21];\nint gcost(int d,int dep){return(d==0||d==2)?2*(dep+1):2*(N-dep);}\nint odep(int k,int d){return(d<=1)?OR_[k]:OC_[k];}\nint ad_[42],ax_[42];\nvectorgv[4][21];\nvoid ins(int d,int ax,int v){auto&vec=gv[d][ax];vec.insert(lower_bound(vec.begin(),vec.end(),v),v);}\nvoid del(int d,int ax,int v){auto&vec=gv[d][ax];vec.erase(lower_bound(vec.begin(),vec.end(),v));}\nint gcv(int d,int ax){if(gv[d][ax].empty())return 0;return gcost(d,(d==0||d==2)?gv[d][ax].back():gv[d][ax].front());}\nbool vgrp(int k,int d,int ax){int r=OR_[k],c=OC_[k],kd=(d<=1)?r:c;if(d==0)return ax==c&&kdcbot_[ax];if(d==2)return ax==r&&kdrright_[ax];}\nint tc(){int t=0;for(int d=0;d<4;d++)for(int i=0;ico[21],ro[21];\nvoid ls(){bool imp=true;while(imp){imp=false;int bg=0,bt=-1,bk=-1,ba=-1,bb=-1,bd=-1,bx=-1;for(int k=0;kbg){bg=gg;bt=1;bk=k;bd=d;bx=ax;}};if(rcbot_[c])t(1,c);if(crright_[r])t(3,r);}for(int j=0;jbg){bg=gg;bt=2;ba=a;bb=b;bd=d;bx=ax;}};t(0,j);t(1,j);}}for(int i=0;ibg){bg=gg;bt=2;ba=a;bb=b;bd=d;bx=ax;}};t(2,i);t(3,i);}}if(bg>0){if(bt==1)mv1(bk,bd,bx);else mv2(ba,bb,bd,bx);imp=true;}}}\nint main(){ios_base::sync_with_stdio(false);cin.tie(NULL);cin>>N;vectorbrd(N);for(int i=0;i>brd[i];M=0;for(int i=0;i>opts;if(rcbot_[c])opts.push_back({1,c});if(crright_[r])opts.push_back({3,r});int gd,gax;if(trial==0){int bcc=INT_MAX;gd=-1;gax=-1;for(auto[d,ax]:opts){int cc=gcost(d,odep(ki,d));if(cc\nusing namespace std;\nconst int MAXN=100;\nint N,L,T[MAXN],a[MAXN],b[MAXN],cv[MAXN],fv[MAXN],flow[MAXN];\nvoid computeFlow(){fill(flow,flow+N,0);for(int i=0;i0&&!vis[j])return false;return true;}\nbool checkBwd(){if(T[0]==0)return true;static int rl[MAXN][2*MAXN],rc[MAXN];static bool vis[MAXN];int q[MAXN],qh=0,qt=0;fill(rc,rc+N,0);for(int i=0;i0&&!vis[j])return false;return true;}\nvoid fixFwdConn(){for(int pass=0;pass0&&!vis[j]){u=j;break;}if(u<0)break;long long bd=(long long)4e18;int bi=-1;bool bA=false;for(int i=0;i0)?((long long)(abs(flow[oa]-w-T[oa])-abs(flow[oa]-T[oa]))+(long long)(abs(flow[u]+w-T[u])-abs(flow[u]-T[u]))):0LL;if(d0)?((long long)(abs(flow[ob]-w-T[ob])-abs(flow[ob]-T[ob]))+(long long)(abs(flow[u]+w-T[u])-abs(flow[u]-T[u]))):0LL;if(d0){flow[a[bi]]-=cv[bi];flow[u]+=cv[bi];}a[bi]=u;}else{if(fv[bi]>0){flow[b[bi]]-=fv[bi];flow[u]+=fv[bi];}b[bi]=u;}}}\nvoid fixBwdConn(){if(T[0]==0)return;for(int pass=0;pass0&&!vis[j]){u=j;break;}if(u<0)break;long long bd=(long long)4e18;int bk=-1;bool bA=false;for(int k=0;k0)?((long long)(abs(flow[oa]-w-T[oa])-abs(flow[oa]-T[oa]))+(long long)(abs(flow[k]+w-T[k])-abs(flow[k]-T[k]))):0LL;if(d0)?((long long)(abs(flow[ob]-w-T[ob])-abs(flow[ob]-T[ob]))+(long long)(abs(flow[k]+w-T[k])-abs(flow[k]-T[k]))):0LL;if(d0){flow[a[u]]-=cv[u];flow[bk]+=cv[u];}a[u]=bk;}else{if(fv[u]>0){flow[b[u]]-=fv[u];flow[bk]+=fv[u];}b[u]=bk;}}}\nvoid flowSearch(){long long ce=flowErr();bool imp=true;while(imp){imp=false;for(int i=0;i0)?((long long)(abs(flow[old]-w-T[old])-abs(flow[old]-T[old]))+(long long)(abs(flow[j]+w-T[j])-abs(flow[j]-T[j]))):0LL;if(d=0){if(w>0){flow[old]-=w;flow[bj]+=w;}ce+=bd;if(t2)b[i]=bj;else a[i]=bj;imp=true;}}}}\nlong long simulateFull(int co[],int od[],int ed[]){int cnt[MAXN]={},vc[MAXN]={};fill(od,od+N,0);fill(ed,ed+N,0);int cur=0;cnt[0]=vc[0]=1;for(int w=2;w<=L;w++){if(vc[cur]&1){od[cur]++;cur=a[cur];}else{ed[cur]++;cur=b[cur];}cnt[cur]++;vc[cur]++;}long long e=0;for(int j=0;j>N>>L;for(int i=0;i>T[i];\n for(int i=0;i>items;\n for(int i=0;i0)rem[0]--;\n priority_queue>pq;for(int j=0;j(chrono::steady_clock::now()-t0).count();};\n struct Cand{long long d;int i,t,j;bool operator<(const Cand&o)const{return dcands;cands.reserve(20001);\n int noImp=0;\n while(el()<1750000LL){\n cands.clear();\n for(int i=0;i0){int oj=a[i];for(int j=0;j0){int oj=b[i];for(int j=0;j0)partial_sort(cands.begin(),cands.begin()+K,cands.end());\n bool found=false;\n for(int k=0;k=15){\n // Enhanced ILS perturbation: random changes + re-optimization\n bool pittBetter=false;\n for(int ptry=0;ptry<3&&!pittBetter;ptry++){\n copy(ba,ba+N,a);copy(bb,bb+N,b);\n for(int p=0;p<8;p++){int i=rng()%N,t=rng()%2,j=(int)(rng()%N);if(t)b[i]=j;else a[i]=j;}\n computeFlow();flowSearch();fixFwdConn();\n long long err=simulate();\n if(err\nusing namespace std;\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int N,M,Q,L,W; cin>>N>>M>>Q>>L>>W;\n vectorG(M);for(int&g:G)cin>>g;\n vectorcx(N),cy(N);\n for(int i=0;i>lx>>rx>>ly>>ry;cx[i]=(lx+rx)/2.0;cy[i]=(ly+ry)/2.0;}\n auto ed2=[&](int a,int b)->double{double dx=cx[a]-cx[b],dy=cy[a]-cy[b];return dx*dx+dy*dy;};\n vectormpar(N,-1);vectormkey(N,0);\n {vectorvis(N,false);vectorkey(N,1e18);key[0]=0;\n for(int it=0;it>mch(N);for(int v=1;vpost,preord;\n {stack>s;s.push({0,0});while(!s.empty()){auto&[v,ci]=s.top();if(ci<(int)mch[v].size())s.push({mch[v][ci++],0});else{post.push_back(v);s.pop();}}}\n {stacks;s.push(0);while(!s.empty()){int v=s.top();s.pop();preord.push_back(v);for(int i=(int)mch[v].size()-1;i>=0;i--)s.push(mch[v][i]);}}\n vectoresz(N,1);for(int v:post)for(int c:mch[v])esz[v]+=esz[c];\n vector>elist;for(int v=1;v());\n multisetremG(G.begin(),G.end());map>szg;for(int i=0;iscut(N,false),asgn(N,false);vector>groups(M);\n for(auto&[w,v]:elist){if(asgn[v])continue;int s=esz[v];if(s<=0||!remG.count(s))continue;\n remG.erase(remG.find(s));int u=mpar[v];while(u!=-1&&!scut[u]){esz[u]-=s;u=mpar[u];}scut[v]=true;\n int gid=szg[s].front();szg[s].pop();queueq;q.push(v);\n while(!q.empty()){int nu=q.front();q.pop();if(asgn[nu])continue;groups[gid].push_back(nu);asgn[nu]=true;for(int c:mch[nu])if(!asgn[c])q.push(c);}}\n {vectorrem;for(int v:preord)if(!asgn[v])rem.push_back(v);\n int pos=0;for(int i=0;i>sc(M);\n for(int i=0;icx[v[rxi]])rxi=k;\n if(cy[v[k]]cy[v[ryi]])ryi=k;}\n avgx/=g;avgy/=g;double cd=1e18;\n for(int k=0;kvector{\n vectorused(g,false);vectorp;p.reserve(g);p.push_back(v[s0]);used[s0]=true;\n for(int k=1;k&p)->double{double l=0;for(int k=1;k&p){\n for(int it=0;it<30;it++){bool imp=false;\n for(int a=0;astarts={lxi,rxi,lyi,ryi,ceni};\n sort(starts.begin(),starts.end());starts.erase(unique(starts.begin(),starts.end()),starts.end());\n double bestl=1e18;\n for(int s:starts){auto p=nn(s);topt(p);double l=plen(p);if(lp(v);topt(p);double l=plen(p);if(l=4){\n for(int it=0;it<10;it++){\n double bg=1e-9;int ba=-1,bj=-1;\n for(int a=1;abg){bg=rg-ic;ba=a;bj=j;}}}\n if(ba<0)break;\n int moved=sc[i][ba];\n if(bjbj;k--)sc[i][k]=sc[i][k-1];sc[i][bj]=moved;}\n else{for(int k=ba;k>>>ae(M);\n auto dq=[&](const vector&qc,int gi){if((int)qc.size()<2||qrem<=0)return;qrem--;\n cout<<\"? \"<>a>>b;ae[gi].push_back({ed2(a,b),{a,b}});}};\n auto nw=[&](int g)->int{if(g<=1)return 0;if(g<=L)return 1;return(g-2)/(L-1)+1;};\n int tmand=0;for(int i=0;i=g);if(last&&en-st(sc[i].begin()+st,sc[i].begin()+en),i);if(last)break;st+=L-1;}}\n {vectorlg;for(int i=0;iL)lg.push_back(i);\n if(!lg.empty()&&xtra>0)for(int qi=0;qi0;qi++){int gi=lg[qi%(int)lg.size()];int g=G[gi];\n int stride=max(1,g/L),off=(qi/(int)lg.size())%stride;\n vectorwin;for(int k=off;k=2)dq(win,gi);}}\n vectorpar(N);auto fu=[&](int x)->int{while(par[x]!=x){par[x]=par[par[x]];x=par[x];}return x;};\n vector>>ans(M);\n for(int i=0;i0)cout<<\" \";cout<\nusing namespace std;\nconst int N=20;bool grid[N][N];\nconst int DR[]={-1,1,0,0},DC[]={0,0,-1,1};\ninline bool inB(int r,int c){return(unsigned)r<(unsigned)N&&(unsigned)c<(unsigned)N;}\n// O(1) slide: assumes grid always empty (invariant maintained throughout)\ninline void slE(int r,int c,int d,int er,int ec,int &sr,int &sc){\n switch(d){\n case 0:sr=(ec==c&&er>=0&&err&&er=0&&ecc&&ec> fp1(int r0,int c0,int tr,int tc){\n memset(d1,-1,sizeof(d1));int S=(r0*N+c0)*441,G=(tr*N+tc)*441;if(S==G)return{};\n d1[S]=0;int qh=0,qt=0;q1[qt++]=S;\n while(qh> res;int r=r0,c=c0;while(r!=tr){res.push_back({'M',r> path;for(int cur=G;cur!=S;cur=p1[cur])path.push_back({\"MSA\"[a1[cur]>>2],\"UDLR\"[a1[cur]&3]});reverse(path.begin(),path.end());return path;}\nconst int NS2=N*N*2*21*21;static int d2[NS2],p2[NS2],q2[NS2];static uint8_t a2[NS2];\nvector> fp2(int r0,int c0,int t1r,int t1c,int t2r,int t2c){\n memset(d2,-1,sizeof(d2));auto E=[](int r,int c,int v,int er,int ec){return (r*N+c)*2*441+v*441+(er+1)*21+(ec+1);};\n int S=E(r0,c0,0,-1,-1),G=E(t2r,t2c,1,-1,-1);d2[S]=0;int qh=0,qt=0;q2[qt++]=S;\n while(qh> path;for(int cur=G;cur!=S;cur=p2[cur])path.push_back({\"MSA\"[a2[cur]>>2],\"UDLR\"[a2[cur]&3]});reverse(path.begin(),path.end());return path;}\nconst int NS3=N*N*3*21*21;static int d3[NS3],p3[NS3],q3[NS3];static uint8_t a3[NS3];\nvector> fp3(int r0,int c0,int t1r,int t1c,int t2r,int t2c,int t3r,int t3c){\n memset(d3,-1,sizeof(d3));auto E=[](int r,int c,int ph,int er,int ec){return (r*N+c)*3*441+ph*441+(er+1)*21+(ec+1);};\n int S=E(r0,c0,0,-1,-1),G=E(t3r,t3c,2,-1,-1);d3[S]=0;int qh=0,qt=0;q3[qt++]=S;\n while(qh> path;for(int cur=G;cur!=S;cur=p3[cur])path.push_back({\"MSA\"[a3[cur]>>2],\"UDLR\"[a3[cur]&3]});reverse(path.begin(),path.end());return path;}\nconst int NS4=N*N*4*21*21;static int d4[NS4],p4[NS4],q4[NS4];static uint8_t a4[NS4];\nvector> fp4(int r0,int c0,int t1r,int t1c,int t2r,int t2c,int t3r,int t3c,int t4r,int t4c){\n memset(d4,-1,sizeof(d4));auto E=[](int r,int c,int ph,int er,int ec){return (r*N+c)*4*441+ph*441+(er+1)*21+(ec+1);};\n int S=E(r0,c0,0,-1,-1),G=E(t4r,t4c,3,-1,-1);d4[S]=0;int qh=0,qt=0;q4[qt++]=S;\n while(qh> path;for(int cur=G;cur!=S;cur=p4[cur])path.push_back({\"MSA\"[a4[cur]>>2],\"UDLR\"[a4[cur]&3]});reverse(path.begin(),path.end());return path;}\nint cr,cc,eebr=-1,eebc=-1;\nvoid execPath(const vector>&path){\n for(auto[a,d]:path){cout<>Nin>>M;vector> pts(M);\n for(int i=0;i>pts[i].first>>pts[i].second;\n memset(grid,0,sizeof(grid));cr=pts[0].first;cc=pts[0].second;eebr=eebc=-1;\n int k=1;\n while(k\nusing namespace std;\nconst int MAXN=205;\nint n,px[MAXN],py[MAXN];long long pr[MAXN];\ndouble score_pi(double si,long long ri){if(si<=0)return 0;double r=(si<=(double)ri)?si/ri:(double)ri/si;return 1-(1-r)*(1-r);}\nstruct Split{int x1,y1,x2,y2,dir,sp,lo,hi;vectorL,R;};\nvectorsplits;int rx1[MAXN],ry1[MAXN],rx2[MAXN],ry2[MAXN];\nvoid recompute(){for(int i=0;icomp,int x1,int y1,int x2,int y2){\n int nc=(int)comp.size();if(nc==1)return;\n long long tr=0;for(int i:comp)tr+=pr[i];long long H=y2-y1,W=x2-x1;\n vectorbx(comp),by(comp);\n sort(bx.begin(),bx.end(),[](int a,int b){return px[a]cands;\n auto ss=[](long long AL,long long RL,int nL,long long AR,long long RR,int nR){double a=(RL<=0||AL>=RL)?(double)nL:nL*(1-pow(1-(double)AL/RL,2));double b=(RR<=0||AR>=RR)?(double)nR:nR*(1-pow(1-(double)AR/RR,2));return a+b;};\n {long long pf=0;for(int k=1;k=px[bx[k]])continue;int lo=max(px[bx[k-1]]+1,x1+1),hi=min(px[bx[k]],x2-1);if(lo>hi)continue;int sp=(int)round(x1+(double)W*pf/tr);sp=max(lo,min(hi,sp));cands.push_back({ss((long long)(sp-x1)*H,pf,k,(long long)(x2-sp)*H,tr-pf,nc-k),0,k,sp,lo,hi});}}\n {long long pf=0;for(int k=1;k=py[by[k]])continue;int lo=max(py[by[k-1]]+1,y1+1),hi=min(py[by[k]],y2-1);if(lo>hi)continue;int sp=(int)round(y1+(double)H*pf/tr);sp=max(lo,min(hi,sp));cands.push_back({ss((long long)(sp-y1)*W,pf,k,(long long)(y2-sp)*W,tr-pf,nc-k),1,k,sp,lo,hi});}}\n if(cands.empty())return;\n sort(cands.begin(),cands.end(),[](const Cand&a,const Cand&b){return a.sc>b.sc;});\n int ch=0;\n if(p_rand>0&&(int)cands.size()>1){int K=min((int)cands.size(),5);if(uniform_real_distribution(0,1)(rng)=s.hi)continue;int bsp=s.sp;double bs=evalAt(s,s.sp);int lo=s.lo,hi=s.hi;while(hi-lo>=3){int m1=lo+(hi-lo)/3,m2=hi-(hi-lo)/3;double s1=evalAt(s,m1),s2=evalAt(s,m2);if(s1bs){bs=sc;bsp=sp;}}if(bsp!=s.sp){s.sp=bsp;recompute();imp=true;}}return imp;}\ndouble computeScore(){double t=0;for(int i=0;i>n;for(int i=0;i>px[i]>>py[i]>>pr[i];\n vectorall(n);iota(all.begin(),all.end(),0);\n auto t0=chrono::steady_clock::now();\n auto msf=[&](){return(int)chrono::duration_cast(chrono::steady_clock::now()-t0).count();};\n const double prs[]={0.0,0.1,0.2,0.3,0.4,0.5};\n double best=-1;int bx1[MAXN],by1[MAXN],bx2[MAXN],by2[MAXN];\n auto save=[&](){for(int i=0;isaved;};\n vectorph1data;ph1data.reserve(600);\n for(int trial=0;msf()<2200;trial++){\n uint32_t seed=(uint32_t)(trial*7919+12345);double pr=prs[trial==0?0:1+(trial-1)%5];\n splits.clear();rng.seed(seed);p_rand=pr;\n doBuild(all,0,0,10000,10000);recompute();\n for(int p=0;p<2&&msf()<2200;p++)if(!lsPass())break;\n double q=computeScore();ph1data.push_back({q,splits});\n if(q>best){best=q;save();}\n }\n sort(ph1data.begin(),ph1data.end(),[](const TrialData&a,const TrialData&b){return a.score>b.score;});\n for(auto&td:ph1data){\n if(msf()>4500)break;\n splits=td.saved;recompute();\n while(msf()<4500)if(!lsPass())break;\n double sc=computeScore();if(sc>best){best=sc;save();}\n }\n for(int extra=0;msf()<4500;extra++){\n uint32_t seed=(uint32_t)(extra*54321+987654321);double pr=prs[1+extra%5];\n splits.clear();rng.seed(seed);p_rand=pr;\n doBuild(all,0,0,10000,10000);recompute();\n while(msf()<4500)if(!lsPass())break;\n double sc=computeScore();if(sc>best){best=sc;save();}\n }\n // Initial post-processing\n int fa_a[MAXN],fa_b[MAXN],fa_c[MAXN],fa_d[MAXN];\n for(int i=0;i(long long)ri){for(int w=1;w<=W&&!done;w++){long long h0=ri/w;for(int dh=0;dh<=1;dh++){long long hh=h0+dh;if(hh<1||hh>(long long)H)continue;long long area=(long long)w*hh;double ratio=(area<=(long long)ri)?(double)area/ri:(double)ri/area;if(ratio>br){br=ratio;bw=w;bh=(int)hh;if(br>=1-1e-9){done=true;break;}}}}}\n int a=max(x1,xi+1-bw),b=max(y1,yi+1-bh);\n fa_a[i]=a;fa_b[i]=b;fa_c[i]=a+bw;fa_d[i]=b+bh;\n }\n // Expansion: grow deficit companies into free space\n for(int pass=0;pass<20;pass++){\n bool changed=false;\n vectorord(n);iota(ord.begin(),ord.end(),0);\n sort(ord.begin(),ord.end(),[&](int a,int b){return max(0LL,pr[a]-(long long)(fa_c[a]-fa_a[a])*(fa_d[a]-fa_b[a]))>max(0LL,pr[b]-(long long)(fa_c[b]-fa_a[b])*(fa_d[b]-fa_b[b]));});\n for(int ii:ord){\n long long ri=pr[ii];int xi=px[ii],yi=py[ii];\n int a0=fa_a[ii],b0=fa_b[ii],c0=fa_c[ii],d0=fa_d[ii];\n long long si=(long long)(c0-a0)*(d0-b0);if(si>=(long long)ri)continue;\n // Width expansion (keep height)\n int cur_h=d0-b0,amin=0,cmax=10000;\n for(int j=0;j=c0)cmax=min(cmax,fa_a[j]);if(fa_c[j]<=a0)amin=max(amin,fa_c[j]);}}\n amin=min(amin,xi);cmax=max(cmax,xi+1);\n double bst_rw=score_pi((double)si,ri);int bst_bw=c0-a0,bst_aw=a0;\n for(int bw=bst_bw;bw<=cmax-amin;bw++){long long area=(long long)bw*cur_h;double r=(area<=(long long)ri)?(double)area/ri:(double)ri/area;if(r>bst_rw+1e-12){bst_rw=r;bst_bw=bw;bst_aw=max(amin,xi+1-bw);bst_aw=min(bst_aw,cmax-bw);bst_aw=max(bst_aw,amin);}if(area>=(long long)ri)break;}\n if(bst_bw!=c0-a0||bst_aw!=a0){fa_a[ii]=bst_aw;fa_c[ii]=bst_aw+bst_bw;changed=true;}\n // Height expansion (keep updated width)\n int a1=fa_a[ii],c1=fa_c[ii];si=(long long)(c1-a1)*(d0-b0);if(si>=(long long)ri)continue;\n int cur_w=c1-a1,bmin=0,dmax=10000;\n for(int j=0;j=d0)dmax=min(dmax,fa_b[j]);if(fa_d[j]<=b0)bmin=max(bmin,fa_d[j]);}}\n bmin=min(bmin,yi);dmax=max(dmax,yi+1);\n double bst_rh=score_pi((double)si,ri);int bst_bh=d0-b0,bst_b=b0;\n for(int bh=bst_bh;bh<=dmax-bmin;bh++){long long area=(long long)cur_w*bh;double r=(area<=(long long)ri)?(double)area/ri:(double)ri/area;if(r>bst_rh+1e-12){bst_rh=r;bst_bh=bh;bst_b=max(bmin,yi+1-bh);bst_b=min(bst_b,dmax-bh);bst_b=max(bst_b,bmin);}if(area>=(long long)ri)break;}\n if(bst_bh!=d0-b0||bst_b!=b0){fa_b[ii]=bst_b;fa_d[ii]=bst_b+bst_bh;changed=true;}\n }\n if(!changed)break;\n }\n for(int i=0;i\nusing namespace std;\ntypedef chrono::steady_clock Clock;\nconst int N=50,MAXM=N*N+1;\nint si,sj,M,tid[N][N],pval[N][N];\nconst int dx[]={-1,1,0,0},dy[]={0,0,-1,1};\nconst char dc[]={'U','D','L','R'};\nmt19937 rng;\nbool tu[MAXM],btu[MAXM];\nint pi_[MAXM],pj_[MAXM],pt_[MAXM],bpi[MAXM],bpj[MAXM],bpt[MAXM];\nchar pmv[MAXM],bpmv[MAXM];\nint plen,blen;long long cscore,bscore;int ci,cj;\nint g_seen[MAXM]={};int g_ts=0;\nvoid save_best(){if(cscore<=bscore)return;bscore=cscore;blen=plen;memcpy(btu,tu,M);memcpy(bpi,pi_,plen*4);memcpy(bpj,pj_,plen*4);memcpy(bpt,pt_,plen*4);if(plen>1)memcpy(bpmv,pmv,plen-1);}\nvoid restore_best(){cscore=bscore;plen=blen;memcpy(tu,btu,M);memcpy(pi_,bpi,plen*4);memcpy(pj_,bpj,plen*4);memcpy(pt_,bpt,plen*4);if(plen>1)memcpy(pmv,bpmv,plen-1);ci=pi_[plen-1];cj=pj_[plen-1];}\nvoid walk_init(){fill(tu,tu+M,false);plen=1;ci=si;cj=sj;pi_[0]=si;pj_[0]=sj;pt_[0]=tid[si][sj];tu[tid[si][sj]]=true;cscore=pval[si][sj];}\nbool walk_step(double a,double b,double g,double g2,double g3){\n int bd=-1;double bh=-1e18;bool g3pos=(g3>0);\n for(int d=0;d<4;d++){\n int ni=ci+dx[d],nj=cj+dy[d];\n if((unsigned)ni>=(unsigned)N||(unsigned)nj>=(unsigned)N)continue;\n int t=tid[ni][nj];if(tu[t])continue;\n tu[t]=true;++g_ts;g_seen[t]=g_ts;\n int cnt=0;double nv=0,nv2=0,nv3=0;\n for(int d2=0;d2<4;d2++){\n int nni=ni+dx[d2],nnj=nj+dy[d2];\n if((unsigned)nni>=(unsigned)N||(unsigned)nnj>=(unsigned)N)continue;\n int t2=tid[nni][nnj];if(tu[t2]||g_seen[t2]==g_ts)continue;\n g_seen[t2]=g_ts;cnt++;nv+=pval[nni][nnj];\n for(int d3=0;d3<4;d3++){\n int n3i=nni+dx[d3],n3j=nnj+dy[d3];\n if((unsigned)n3i>=(unsigned)N||(unsigned)n3j>=(unsigned)N)continue;\n int t3=tid[n3i][n3j];if(tu[t3]||g_seen[t3]==g_ts)continue;\n g_seen[t3]=g_ts;nv2+=pval[n3i][n3j];\n if(g3pos){for(int d4=0;d4<4;d4++){\n int n4i=n3i+dx[d4],n4j=n3j+dy[d4];\n if((unsigned)n4i>=(unsigned)N||(unsigned)n4j>=(unsigned)N)continue;\n int t4=tid[n4i][n4j];if(tu[t4]||g_seen[t4]==g_ts)continue;\n g_seen[t4]=g_ts;nv3+=pval[n4i][n4j];\n }}\n }\n }\n tu[t]=false;\n double h=a*pval[ni][nj]+g*nv+g2*nv2+g3*nv3-b*cnt+(cnt==0?-1e6:0.0)\n +uniform_real_distribution(-0.5,0.5)(rng);\n if(h>bh){bh=h;bd=d;}\n }\n if(bd==-1)return false;\n int ni=ci+dx[bd],nj=cj+dy[bd];\n tu[tid[ni][nj]]=true;cscore+=pval[ni][nj];pmv[plen-1]=dc[bd];\n pi_[plen]=ni;pj_[plen]=nj;pt_[plen]=tid[ni][nj];plen++;ci=ni;cj=nj;return true;\n}\nvoid walk_extend(double a,double b,double g,double g2,double g3){while(walk_step(a,b,g,g2,g3));}\nvoid walk_undo(int s){s=min(s,plen-1);while(s-->0){plen--;tu[pt_[plen]]=false;cscore-=pval[pi_[plen]][pj_[plen]];}ci=pi_[plen-1];cj=pj_[plen-1];}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n rng.seed(chrono::steady_clock::now().time_since_epoch().count());\n cin>>si>>sj;\n for(int i=0;i>tid[i][j];\n for(int i=0;i>pval[i][j];\n M=0;for(int i=0;i=phase2);\n double a=uniform_real_distribution(0.5,2.0)(rng);\n double b=uniform_real_distribution(0,25)(rng);\n double g=uniform_real_distribution(0,1.0)(rng);\n double g2,g3;\n if(!p2){g2=uniform_real_distribution(0,0.1)(rng);g3=0.0;}\n else{g2=uniform_real_distribution(0,0.15)(rng);g3=(rng()%3==0)?0.0:uniform_real_distribution(0,0.02)(rng);}\n if(iter%4==0||blen<=1){walk_init();}\n else{restore_best();int mb=blen-1,back,r=rng()%10;\n if(r<5)back=uniform_int_distribution(1,max(1,mb/10))(rng);\n else if(r<8)back=uniform_int_distribution(max(1,mb/10),max(1,mb/3))(rng);\n else back=uniform_int_distribution(max(1,mb/3),mb)(rng);\n walk_undo(back);}\n walk_extend(a,b,g,g2,g3);save_best();\n }\n cout<\nusing namespace std;\nconst int N=30;\nconst double DELTA_VAR=1e6,INIT_SIG2R=1e8,INIT_SIG2E=1e7,MIN_SIG2=1e4;\nconst double UCB_A=0.03;\ndouble mu_row[N],sig2_row[N],mu_col[N],sig2_col[N];\ndouble mu_h[N][N-1],sig2_h[N][N-1],mu_v[N-1][N],sig2_v[N-1][N];\nbool obs_h[N][N-1],obs_v[N-1][N];\nstring dijkstra(int sr,int sc,int tr,int tc){\n static double wu_h[N][N-1],wu_v[N-1][N],dist[N*N];\n static int par[N*N];static char pdir[N*N];\n for(int i=0;i,vector>,greater<>> pq;\n int src=sr*N+sc,dst=tr*N+tc;dist[src]=0;pq.push({0.0,src});\n while(!pq.empty()){\n auto[d,u]=pq.top();pq.pop();\n if(d>dist[u]+1e-9)continue;if(u==dst)break;\n int r=u/N,c=u%N;\n auto go=[&](int nr,int nc,char dir,double w){int nv=nr*N+nc;double nd=d+w;if(nd0)go(r-1,c,'U',wu_v[r-1][c]);\n if(r0)go(r,c-1,'L',wu_h[r][c-1]);\n if(c>sr>>sc>>tr>>tc;\n string path=dijkstra(sr,sc,tr,tc);cout<>obs;\n double noise_var=(double)obs*obs/300.0;\n int kh[N]={},lv[N]={};\n struct E{bool is_h;int i,j;};vector edges;\n int r=sr,c=sc;\n for(char ch:path){\n if(ch=='U'){edges.push_back({false,r-1,c});lv[c]++;r--;}\n else if(ch=='D'){edges.push_back({false,r,c});lv[c]++;r++;}\n else if(ch=='L'){edges.push_back({true,r,c-1});kh[r]++;c--;}\n else{edges.push_back({true,r,c});kh[r]++;c++;}\n }\n double pred_r=0,pvar_r=0;\n for(int i=0;i0){pred_r+=kh[i]*mu_row[i];pvar_r+=(double)kh[i]*kh[i]*sig2_row[i]+kh[i]*DELTA_VAR;}\n for(int j=0;j0){pred_r+=lv[j]*mu_col[j];pvar_r+=(double)lv[j]*lv[j]*sig2_col[j]+lv[j]*DELTA_VAR;}\n double tvr=pvar_r+noise_var,resr=(double)obs-pred_r;\n for(int i=0;i0){double K=sig2_row[i]*kh[i]/tvr;mu_row[i]=clamp(mu_row[i]+K*resr,1000.0,9000.0);sig2_row[i]=max(sig2_row[i]*(1.0-K*kh[i]),MIN_SIG2);}\n for(int j=0;j0){double K=sig2_col[j]*lv[j]/tvr;mu_col[j]=clamp(mu_col[j]+K*resr,1000.0,9000.0);sig2_col[j]=max(sig2_col[j]*(1.0-K*lv[j]),MIN_SIG2);}\n for(auto& e:edges){\n if(e.is_h&&!obs_h[e.i][e.j]){obs_h[e.i][e.j]=true;mu_h[e.i][e.j]=mu_row[e.i];sig2_h[e.i][e.j]=INIT_SIG2E;}\n else if(!e.is_h&&!obs_v[e.i][e.j]){obs_v[e.i][e.j]=true;mu_v[e.i][e.j]=mu_col[e.j];sig2_v[e.i][e.j]=INIT_SIG2E;}\n }\n double pred_e=0,pvar_e=0;\n for(auto& e:edges){pred_e+=(e.is_h?mu_h[e.i][e.j]:mu_v[e.i][e.j]);pvar_e+=(e.is_h?sig2_h[e.i][e.j]:sig2_v[e.i][e.j]);}\n double tve=pvar_e+noise_var,rese=(double)obs-pred_e;\n for(auto& e:edges){\n double& mu=e.is_h?mu_h[e.i][e.j]:mu_v[e.i][e.j];\n double& s2=e.is_h?sig2_h[e.i][e.j]:sig2_v[e.i][e.j];\n double K=s2/tve;mu=clamp(mu+K*rese,1000.0,9000.0);s2=max(s2*(1.0-K),MIN_SIG2);\n }\n }\n return 0;\n}","ahc004":"#include \nusing namespace std;\nconst int N=20,MAXM=800,MAXL=12;\nint M,bs,score;\nint8_t grid[N][N],bg[N][N],h_mm[N][MAXM][N],v_mm[N][MAXM][N];\nint match_count[MAXM],slen[MAXM];\nint8_t S[MAXM][MAXL],char_pos[MAXM][8][MAXL],char_pos_cnt[MAXM][8];\nuint8_t char_appears[MAXM];\nint unsat_arr[MAXM],unsat_cnt,unsat_pos[MAXM];\nvoid unsat_remove(int k){int pos=unsat_pos[k];if(pos<0)return;int last=unsat_arr[--unsat_cnt];unsat_arr[pos]=last;unsat_pos[last]=pos;unsat_pos[k]=-1;}\nvoid unsat_add(int k){if(unsat_pos[k]>=0)return;unsat_pos[k]=unsat_cnt;unsat_arr[unsat_cnt++]=k;}\nvoid apply_cell(int r,int c,int oc,int nc){\n uint8_t mask=(1u<0&&nm==0){unsat_add(k);score--;}else if(om==0&&nm>0){unsat_remove(k);score++;}}grid[r][c]=nc;}\nint compute_delta(int r,int c,int oc,int nc){\n uint8_t mask=(1u<0)-(match_count[k]>0);}return d;}\nvoid recompute(){score=0;unsat_cnt=0;fill(unsat_pos,unsat_pos+M,-1);\n for(int r=0;r0)score++;else unsat_add(k);}}\nvoid safe_refresh(){\n int votes[N][N][8];memset(votes,0,sizeof(votes));\n for(int k=0;k=7?slen[k]-4:slen[k]-5));if(bm>rthr)continue;\n for(int p=0;pbv){bv=votes[r][c][ch];bc=ch;}\n if(bv>0&&grid[r][c]!=bc){int d=compute_delta(r,c,grid[r][c],bc);\n if(d>0){apply_cell(r,c,grid[r][c],bc);if(score>bs){bs=score;memcpy(bg,grid,sizeof(grid));}}}}}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n int n;cin>>n>>M;\n for(int k=0;k>s;slen[k]=s.size();char_appears[k]=0;memset(char_pos_cnt[k],0,8);\n for(int p=0;p0){double el=chrono::duration(chrono::steady_clock::now()-t0).count();\n if(el>=0.15||score>=M*2/5)break;\n int k=unsat_arr[rng()%(uint32_t)unsat_cnt];int bm=INT_MAX,br=0,bj=0,bd=0;\n for(int r=0;rbs){bs=score;memcpy(bg,grid,sizeof(grid));}}\n if(score!=bs){memcpy(grid,bg,sizeof(grid));recompute();}}\n double sa0=chrono::duration(chrono::steady_clock::now()-t0).count();\n double sad=max(0.1,TL-sa0);\n double phase1_end=sa0+sad*0.50,phase2_end=sa0+sad*0.75;\n bool p1t=false,p1d=false,p2t=false,p2d=false;\n int bs_last_upd=0;double T=5.0,phase3_T_start=1.5;\n for(int iter=0;;iter++){\n if((iter&0xFFF)==0){\n double el=chrono::duration(chrono::steady_clock::now()-t0).count();\n if(el>=TL)break;\n if(!p1t&&el>=phase1_end){p1t=true;\n if(bs=phase2_end){p2t=true;\n if(bs=100000){p2d=true;bs_last_upd=iter;\n memcpy(grid,bg,sizeof(grid));recompute();\n if(bs0&&(iter%100000)==0&&bspb)bs_last_upd=iter;}\n bool guided=false;int r,c,nc,oc;\n if(unsat_cnt>0&&rng()%(uint32_t)M<(uint32_t)unsat_cnt){\n int k=unsat_arr[rng()%(uint32_t)unsat_cnt];int bm=INT_MAX,br=0,bj=0,bd=0;\n for(int rr=0;rr=7?slen[k]-4:slen[k]-5));\n if(bm>=1&&bm<=thr)for(int p=0;p=0||(double)rng()bs){bs=score;memcpy(bg,grid,sizeof(grid));bs_last_upd=iter;}}\n }\n for(int i=0;i\nusing namespace std;\nint N,si,sj;vector grid;\nbool isRoad(int r,int c){return r>=0&&r=0&&c,vector> dijkstra(int src){\n vector d(N*N,INF),p(N*N,-1);priority_queue,vector>,greater<>> pq;\n d[src]=0;pq.push({0,src});const int DR[]={-1,1,0,0},DC[]={0,0,-1,1};\n while(!pq.empty()){auto[dd,u]=pq.top();pq.pop();if(dd>d[u])continue;int r=u/N,c=u%N;for(int i=0;i<4;i++){int nr=r+DR[i],nc=c+DC[i];if(!isRoad(nr,nc))continue;int v=nr*N+nc,nd=dd+(grid[nr][nc]-'0');if(nd(chrono::steady_clock::now()-t0).count();};\n cin>>N>>si>>sj;grid.resize(N);for(int i=0;i>grid[i];\n vector roads;vector rIdx(N*N,-1);\n for(int r=0;r> vis(R);\n for(int i=0;i=0&&isRoad(r,c-d);d++)vis[i].push_back(rIdx[r*N+(c-d)]);\n for(int d=1;r+d=0&&isRoad(r-d,c);d++)vis[i].push_back(rIdx[(r-d)*N+c]);}\n vector cov(R,false);int uncov=R;\n vector cnt(R);for(int i=0;i> pqsc;for(int i=0;i sents;\n while(uncov>0){int best=-1;while(!pqsc.empty()){auto[cv,id]=pqsc.top();pqsc.pop();if(cv==cnt[id]){best=id;break;}}if(best<0)break;sents.push_back(roads[best]);for(int j:vis[best])if(!cov[j]){cov[j]=true;uncov--;for(int k:vis[j]){cnt[k]--;pqsc.push({cnt[k],k});}}}\n int stSq=si*N+sj;{auto it=find(sents.begin(),sents.end(),stSq);if(it==sents.end())sents.insert(sents.begin(),stSq);else swap(*it,sents[0]);}\n int S=sents.size();\n {vector cc(R,0);for(int sq:sents)for(int j:vis[rIdx[sq]])cc[j]++;bool ch=true;while(ch){ch=false;for(int i=S-1;i>=1;i--){if(sents[i]<0)continue;int idx=rIdx[sents[i]];bool red=true;for(int j:vis[idx])if(cc[j]<=1){red=false;break;}if(red){for(int j:vis[idx])cc[j]--;sents[i]=-1;ch=true;}}}sents.erase(remove(sents.begin(),sents.end(),-1),sents.end());S=sents.size();}\n vector> aD(S),aP(S);for(int i=0;i> dm(S,vector(S,INF));for(int i=0;i tour;\n auto do2opt=[&](){int sz=tour.size();for(bool imp=true;imp;){imp=false;for(int i=0;ibool{int sz=tour.size();int bg=0,bi=-1,bj=-1;for(int i=1;ibg){bg=rmv-ins;bi=i;bj=j;}}}if(bi!=-1){int nd=tour[bi];tour.erase(tour.begin()+bi);int ip=(bjbool{int sz=tour.size();if(sz<5)return false;int bg=0,bi=-1,bj=-1;for(int i=1;ibg){bg=rmv-ins;bi=i;bj=j;}}}if(bi!=-1){int ci=tour[bi],ni=tour[bi+1];tour.erase(tour.begin()+bi,tour.begin()+bi+2);int ip=(bjbool{int sz=tour.size();if(sz<6)return false;int bg=0,bi=-1,bj=-1;for(int i=1;ibg){bg=rmv-ins;bi=i;bj=j;}}}if(bi!=-1){int ci=tour[bi],ni=tour[bi+1],ni2=tour[bi+2];tour.erase(tour.begin()+bi,tour.begin()+bi+3);int ip=(bj& t)->bool{\n vector cv(R,false);int sz=t.size();\n for(int i=0;i=0)for(int j:vis[si2])cv[j]=true;\n for(int c=toSq;c!=srcSq;c=aP[fi][c]){int ci=rIdx[c];if(ci>=0)for(int j:vis[ci])cv[j]=true;}}\n for(int j=0;j bestTour;\n auto trySave=[&](){runLS();int c=tourCost();if(c tv(S,false);tour={0};tv[0]=true;for(int s=1;s inT(S,false);inT[0]=true;while((int)tour.size() inT(S,false);inT[0]=true;while((int)tour.size()fd){fd=minD;fn=node;}}int sz=tour.size(),bp=-1,bi2=INF;for(int pos=0;pos rem;for(int i=1;i=sz)p3=sz-1;if(b>=p3)b=p3-1;if(a>=b)a=b-1;if(a<1)a=1;vector nt;nt.reserve(sz);for(int i=0;i=1&&ms()<2600;ti--){\n auto nt=tour;nt.erase(nt.begin()+ti);\n if(checkCovers(nt)){tour=nt;removed=true;break;}\n }\n if(!removed)break;\n }\n // Coverage-preserving local search\n {auto cp2opt=[&]()->bool{int sz=tour.size();for(int i=0;ibool{int sz=tour.size();for(int i=1;i0){auto nt=tour;nt.erase(nt.begin()+i);int ip=(jbool{int sz=tour.size();if(sz<5)return false;for(int i=1;i0){auto nt=tour;nt.erase(nt.begin()+i,nt.begin()+i+2);int ip=(j path;for(int c=tSq;c!=sSq;c=aP[fi][c])path.push_back(c);\n reverse(path.begin(),path.end());\n int pp=sSq;for(int nx:path){int pr=pp/N,pc=pp%N,nr=nx/N,nc=nx%N;if(nrpr)res+='D';else if(nc\nusing namespace std;\nint N,M,K,R;\nvector> d,succs,preds;\nvector task_st,task_pre,task_w,worker_t,task_sd;\nvector> sk,et;\nvector> lb;\nvector>> obs;\nvector cp;\nint cur_day;double prior_sk;\nvoid upd_et(int w){for(int i=0;i0)ww+=df;}et[i][w]=ww<0.5?1.0:ww;}}\nvoid calc_cp(){cp.assign(N,0.0);for(int i=N-1;i>=0;i--){if(task_st[i]==2)continue;double mn;if(task_st[i]==1){double rem=task_sd[i]+et[i][task_w[i]]-cur_day;mn=max(1.0,rem);}else{mn=et[i][0];for(int j=1;j0)wh+=df;}double tgt=to==1?0.0:(double)to,err=wh-tgt;loss+=err*err;for(int k=0;ksk[w][k])delta[k]+=err;else if(err<-0.5&&d[ti][k]>0)delta[k]+=0.3*err;}}bool ch=false;for(int k=0;k>N>>M>>K>>R;d.assign(N,vector(K));for(int i=0;i>d[i][k];\n succs.assign(N,{});preds.assign(N,{});task_pre.assign(N,0);\n for(int r=0;r>u>>v;u--;v--;succs[u].push_back(v);preds[v].push_back(u);task_pre[v]++;}\n task_st.assign(N,0);task_w.assign(N,-1);worker_t.assign(M,-1);task_sd.assign(N,0);\n prior_sk=40.0/sqrt((double)K);sk.assign(M,vector(K,prior_sk));lb.assign(M,vector(K,0));obs.resize(M);\n et.assign(N,vector(M));for(int j=0;javail,idle;for(int i=0;iav(avail.begin(),avail.end());sort(av.begin(),av.end(),[](int a,int b){return cp[a]>cp[b];});\n // Extended reservation: check ALL tasks with 1-2 in-progress prerequisites\n mapres_cp;\n if(!av.empty()){\n double maxcp=cp[av[0]];\n for(int nxt=0;nxt2)continue;\n double max_rem=0;bool ok=true;\n for(int p:preds[nxt]){\n if(task_st[p]==2)continue;\n if(task_st[p]==0){ok=false;break;}\n int el=cur_day-task_sd[p];\n max_rem=max(max_rem,max(1.0,et[p][task_w[p]]-el));\n }\n if(!ok||max_rem<0.5||max_rem>3.0)continue;\n int bw=-1;double bet=1e18;\n for(int j:idle)if(et[nxt][j]1.5)continue;\n double sec=1e18;for(int j=0;j=2.0&&savings>max_rem+0.5){if(!res_cp.count(bw)||res_cp[bw]>asgn;setid=idle;\n for(int t:av){if(id.empty())break;int bw=-1;double bt=1e18;for(int j:id){if(res_cp.count(j)&&cp[t]asgn_set;for(auto&[w,t]:asgn)asgn_set.insert(t);for(int i=0;i<(int)asgn.size();i++){int wi=asgn[i].first,ti=asgn[i].second;if(et[ti][wi]<=3.0)continue;double rcp_ti=0;for(int v:succs[ti])rcp_ti=max(rcp_ti,cp[v]);double curr_cost=et[ti][wi]+rcp_ti;int best_tj=-1;double best_nc=curr_cost-2.0;for(int tj:avail){if(asgn_set.count(tj))continue;if(cp[tj]1.0)continue;double rcp_tj=0;for(int v:succs[tj])rcp_tj=max(rcp_tj,cp[v]);double nc=et[tj][wi]+rcp_tj;if(nc=2){vectorrcp_a(na,0.0);for(int i=0;i>nc;if(nc==-1)break;\n for(int i=0;i>w;w--;int t=worker_t[w];int tk=cur_day-task_sd[t]+1;obs[w].push_back({t,tk});if(tk==1)for(int k=0;k\nusing namespace std;\nconst int OX=400,OY=400,TOT=1000,K=50,NN=2*K+1;\nint A[TOT],B[TOT],C[TOT],D[TOT],sel[K],NX[NN],NY[NN];\nint md(int x1,int y1,int x2,int y2){return abs(x1-x2)+abs(y1-y2);}\nint ec(int u,int v){return md(NX[u],NY[u],NX[v],NY[v]);}\nvoid refresh(){NX[0]=OX;NY[0]=OY;for(int i=0;i&r){int s=0;for(int i=0;i+1<(int)r.size();i++)s+=ec(r[i],r[i+1]);return s;}\nbool feasible(const vector&r){bool p[K+1]={};for(int v:r){if(v>=1&&v<=K)p[v]=true;else if(v>K&&!p[v-K])return false;}return true;}\nvector build_nn(){bool vis[NN]={},has[K+1]={};vector r={0};vis[0]=true;for(int s=0;s<2*K;s++){int cur=r.back(),bv=-1,bd=INT_MAX;for(int v=1;vK&&!has[v-K]))continue;int dd=ec(cur,v);if(dd&r){int n=r.size();bool any=false;for(int i=1;i&r){int n=r.size();bool any=false;for(int i=1;ibd){bd=rem-ins;bj=j;}}if(bj<0)continue;vector nr;nr.reserve(n);for(int k=0;k&r){int n=r.size();bool any=false;for(int i=1;ibd){bd=rem-ins;bj=j;}}if(bj<0)continue;vector nr;nr.reserve(n);for(int k=0;k&r){int n=r.size();bool any=false;for(int i=1;i=i-1&&j<=i+2)continue;int inf=ec(r[j],u)+ec(w,r[j+1])-ec(r[j],r[j+1]);if(rem-inf>bd){bd=rem-inf;bj=j;rev=false;}int inr=ec(r[j],w)+ec(u,r[j+1])-ec(r[j],r[j+1]);if(rem-inr>bd){bd=rem-inr;bj=j;rev=true;}}if(bj<0)continue;vector nr;nr.reserve(n);for(int k=0;k&r){for(;;){bool a=two_opt_pass(r),b=or1_pass(r),c=or2_pass(r);if(!a&&!b&&!c)break;}}\nvoid quick_search(vector&r,int it=5){for(int i=0;i build_perturbed(const vector&base,int si){int pi=si+1,di=K+si+1;vector r;r.reserve(base.size()-2);for(int v:base)if(v!=pi&&v!=di)r.push_back(v);int n=r.size();int bc=INT_MAX,bp=0,bd2=1;for(int p=0;p res=r;res.insert(res.begin()+bp+1,pi);res.insert(res.begin()+bd2+1,di);return res;}\nvector double_bridge(const vector&r,mt19937&rng){int n=r.size();if(n<8)return r;int pos[4];do{for(int i=0;i<4;i++)pos[i]=1+rng()%(n-2);}while(pos[0]==pos[1]||pos[0]==pos[2]||pos[0]==pos[3]||pos[1]==pos[2]||pos[1]==pos[3]||pos[2]==pos[3]);sort(pos,pos+4);int a=pos[0],b=pos[1],c=pos[2],d=pos[3];vector nr;nr.reserve(n);for(int i=0;i&r){cout<(Clk::now()-T0).count();}\nint bcost=INT_MAX;vector broute;int bsel[K];bool inS[TOT]={};\nvoid trysel(){refresh();auto r=build_nn();full_search(r);int c=tcost(r);if(c pos(NN,-1);for(int i=0;i rem(K);for(int i=0;i> cands;\n for(int j=0;j0)cands.emplace_back(g,si,j);}}\n if(cands.empty())return false;\n int tk=min(10,(int)cands.size());partial_sort(cands.begin(),cands.begin()+tk,cands.end(),greater>());\n for(int ci=0;ci used(TOT,false);vector> pts={{OX,OY}};\n for(int k=0;k used(TOT,false);vector> pts={{OX,OY}};\n for(int k=0;k>A[i]>>B[i]>>C[i]>>D[i];\n {vector> sc(TOT);for(int i=0;i> sc(TOT);for(int i=0;i> sc(TOT);for(int i=0;i1.95)break;bool a=two_opt_pass(broute),b=or1_pass(broute),c=or2_pass(broute),d=or3_pass(broute);if(!a&&!b&&!c&&!d)break;}\n emit(broute);\n return 0;\n}","ahc007":"#include \nusing namespace std;\nconst int N=400,M=1995;\nint px[N],py[N],eu[M],ev[M];long long ed[M];\nstruct UF{int p[N],r[N];\nvoid init(){for(int i=0;i>>cadj(nc);\n for(int j=ie+1;j0&&((a==src&&b==dst)||(a==dst&&b==src)))continue;\n double w=2.0*ed[j];cadj[a].push_back({b,w});cadj[b].push_back({a,w});\n }\n vectordist(nc,1e18);vectorhops(nc,0);\n {priority_queue,vector>,greater<>>pq;\n dist[src]=0;pq.push({0.0,src});\n while(!pq.empty()){auto[dv,u]=pq.top();pq.pop();\n if(dv>dist[u]+1e-9)continue;if(u==dst)break;\n for(auto&[v,w]:cadj[u]){double nd=dist[u]+w;if(ndbn(nc,1e18);\n {priority_queue,vector>,greater<>>pq;\n bn[src]=0;pq.push({0.0,src});\n while(!pq.empty()){auto[bv,u]=pq.top();pq.pop();\n if(bv>bn[u]+1e-9)continue;if(u==dst)break;\n for(auto&[v,w]:cadj[u]){double nb=max(bn[u],w);if(nb0)sum_thr=dist[dst]*(3.0*n+1.0)/(2.0*n*(n+1.0));}\n if(bn[dst]<1e17)bn_thr=bn[dst];\n double indir=min(sum_thr,bn_thr);\n if(k==0)return(indir<1e17)?indir:2.0*ed[ie];\n double mn_avg=(eff_k>0)?(double)(mn+max_eff_d)/2.0:(double)mn;\n double ft;\n if(eff_k==0)ft=3.0*mn_avg;\n else if(eff_k==1)ft=2.0*mn_avg; // T=2, exact for 1 future\n else if(eff_k==2){\n // Exact optimal threshold for 2 future competitive alternatives [mn, max_eff_d]\n double D=(double)mn,D2=(double)max_eff_d;\n double pD=min(1.0,(2.0*D2-D)/(2.0*D));\n double eD=(pD>0)?pD*(D+2.0*D2)/2.0+(1.0-pD)*2.0*D2:2.0*D2;\n double pD2=max(0.0,(2.0*D-D2)/(2.0*D2));\n double eD2=pD2*(D2+2.0*D)/2.0+(1.0-pD2)*2.0*D;\n ft=0.5*eD+0.5*eD2;\n }\n else ft=mn_avg*(1.0+2.0/(eff_k+1.0)); // avg formula for eff_k>=3\n return(indir<1e17)?min(ft,indir):ft;\n}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n for(int i=0;i>px[i]>>py[i];\n for(int i=0;i>eu[i]>>ev[i];double dx=px[eu[i]]-px[ev[i]],dy=py[eu[i]]-py[ev[i]];ed[i]=llround(sqrt(dx*dx+dy*dy));}\n uf.init();\n for(int i=0;i>l;\n if(uf.same(eu[i],ev[i])){cout<<0<1){cout<<1<0){\n eff_k=0;max_eff_d=mn;\n long long eff_thresh=mn+mn/2;\n for(int j=i+1;jmax_eff_d)max_eff_d=ed[j];}}}\n }\n double thr=compute_thr(i,cu,cv,k,mn,max_eff_d,eff_k);\n if((double)l<=thr){cout<<1<\nusing namespace std;\nconst int G=30;\nint N,M,px[20],py[20],pt_arr[20],hx[10],hy[10];bool wall[G+2][G+2];\nint spx[20],spy[20],shx[10],shy[10];\nconst int ddx[]={-1,1,0,0},ddy[]={0,0,-1,1};\nconst char DIRS[]=\"UDLR\",WDIRS[]=\"udlr\";\nbool inb(int x,int y){return x>=1&&x<=G&&y>=1&&y<=G;}\nint dbuf[G+2][G+2];\nvoid bfs(int tx,int ty){\n for(int i=0;i<=G+1;i++)fill(dbuf[i],dbuf[i]+G+2,-1);\n dbuf[tx][ty]=0;queue>q;q.push({tx,ty});\n while(!q.empty()){auto[x,y]=q.front();q.pop();for(int d=0;d<4;d++){int nx=x+ddx[d],ny=y+ddy[d];if(!inb(nx,ny)||wall[nx][ny]||dbuf[nx][ny]!=-1)continue;dbuf[nx][ny]=dbuf[x][y]+1;q.push({nx,ny});}}\n}\nchar gmv(int sx,int sy,int tx,int ty){\n if(sx==tx&&sy==ty)return '.';bfs(tx,ty);if(dbuf[sx][sy]==-1)return '.';\n for(int d=0;d<4;d++){int nx=sx+ddx[d],ny=sy+ddy[d];if(!inb(nx,ny)||wall[nx][ny])continue;if(dbuf[nx][ny]==dbuf[sx][sy]-1)return DIRS[d];}return '.';\n}\nbool cpl(int wx,int wy){\n if(!inb(wx,wy)||wall[wx][wy])return false;\n for(int i=0;i=reg_r1&&hx[h]<=reg_r2&&hy[h]>=reg_c1&&hy[h]<=reg_c2;}\nstruct Task{int wx,wy,sx,sy,wd;};\nvector tasks;vector te(10),ct(10);\nint cur_wt=-1,cur_wp=-1;bool cur_hp=true;\nbool try_setup_phase(bool is_primary){\n auto cp=[&](int r1,int c1,int r2,int c2)->int{int c=0;for(int i=0;i=r1&&px[i]<=r2&&py[i]>=c1&&py[i]<=c2)c++;return c;};\n auto ch_fn=[&](int r1,int c1,int r2,int c2)->int{int c=0;for(int i=0;i=r1&&hx[i]<=r2&&hy[i]>=c1&&hy[i]<=c2)c++;return c;};\n int pr1=reg_r1,pr2=reg_r2,pc1=reg_c1,pc2=reg_c2;\n int total=cp(pr1,pc1,pr2,pc2);\n int prim_area=(pr2-pr1+1)*(pc2-pc1+1);\n if(prim_area<4)return false;\n double curr_score=(double)prim_area/900.0*pow(2.0,-(double)total);\n auto contam_est=[&](int wt2,int wp2,bool hp2)->double{\n if(is_primary)return 0.0;\n double c=0;\n for(int i=0;ipr2||py[i]pc2)continue;\n int d;bool on_pet;\n if(wt2==0){on_pet=hp2?(py[i]>=wp2):(py[i]=wp2):(px[i]double{\n double eff_n=n+contam_est(wt2,wp2,hp2)*0.4;\n return (double)area/900.0*pow(2.0,-eff_n)*(0.7+0.3*(double)hin/M);\n };\n double bv=-1e18;cur_wt=-1;cur_wp=-1;cur_hp=true;\n for(int c=pc1+1;c<=pc2;c++){\n int lp=cp(pr1,pc1,pr2,c-1),rp=cp(pr1,c,pr2,pc2);\n int lh=ch_fn(pr1,pc1,pr2,c-1),rh=ch_fn(pr1,c,pr2,pc2);\n double vl=ev((c-pc1)*(pr2-pr1+1),lp,lh,0,c,true),vr=ev((pc2-c+1)*(pr2-pr1+1),rp,rh,0,c,false);\n if(vl>bv){bv=vl;cur_wt=0;cur_wp=c;cur_hp=true;}if(vr>bv){bv=vr;cur_wt=0;cur_wp=c;cur_hp=false;}\n }\n for(int r=pr1+1;r<=pr2;r++){\n int tp=cp(pr1,pc1,r-1,pc2),bp=cp(r,pc1,pr2,pc2);\n int th=ch_fn(pr1,pc1,r-1,pc2),bh=ch_fn(r,pc1,pr2,pc2);\n double vt=ev((r-pr1)*(pc2-pc1+1),tp,th,1,r,true),vb=ev((pr2-r+1)*(pc2-pc1+1),bp,bh,1,r,false);\n if(vt>bv){bv=vt;cur_wt=1;cur_wp=r;cur_hp=true;}if(vb>bv){bv=vb;cur_wt=1;cur_wp=r;cur_hp=false;}\n }\n if(cur_wt<0)return false;\n if(!is_primary){\n if(bvhord(M);iota(hord.begin(),hord.end(),0);\n if(cur_wt==0)sort(hord.begin(),hord.end(),[&](int a,int b){return hx[a]>N;for(int i=0;i>px[i]>>py[i]>>pt_arr[i];\n cin>>M;for(int i=0;i>hx[i]>>hy[i];\n bool active=try_setup_phase(true);\n for(int turn=0;turn<300;turn++){\n for(int i=0;i0){\n bool done=true;for(auto&t:tasks)if(!wall[t.wx][t.wy]){done=false;break;}\n if(done){if(turn<250)active=try_setup_phase(false);else active=false;}\n }\n string acts(M,'.');\n if(active){\n int TT=tasks.size();\n bool all_safe=true;for(int h=0;h>pw;vectorisp(M,false);\n for(int h=0;h=(int)te[h])continue;\n Task&t=tasks[ct[h]];bool ig=(ct[h]==TT-1)&&!all_safe;\n if(hx[h]==t.sx&&hy[h]==t.sy&&!ig&&cpl(t.wx,t.wy)&&!pw.count({t.wx,t.wy})){\n acts[h]=WDIRS[t.wd];pw.insert({t.wx,t.wy});wall[t.wx][t.wy]=true;ct[h]++;isp[h]=true;\n }\n }\n for(int h=0;h=(int)te[h]){\n if(!on_side(h)){\n int tx,ty;\n if(cur_wt==0){tx=hx[h];ty=cur_hp?cur_wp-1:cur_wp;}\n else{tx=cur_hp?cur_wp-1:cur_wp;ty=hy[h];}\n char mv=gmv(hx[h],hy[h],tx,ty);\n acts[h]=mv;if(mv!='.')for(int d=0;d<4;d++)if(DIRS[d]==mv){hx[h]+=ddx[d];hy[h]+=ddy[d];break;}\n }\n continue;\n }\n Task&t=tasks[ct[h]];\n if(hx[h]==t.sx&&hy[h]==t.sy){acts[h]='.';continue;}\n char mv=gmv(hx[h],hy[h],t.sx,t.sy);\n acts[h]=mv;if(mv!='.')for(int d=0;d<4;d++)if(DIRS[d]==mv){hx[h]+=ddx[d];hy[h]+=ddy[d];break;}\n }\n }\n cout<>s;for(char c:s){if(c=='U')px[i]--;else if(c=='D')px[i]++;else if(c=='L')py[i]--;else if(c=='R')py[i]++;}}\n }\n return 0;\n}","ahc009":"#include \nusing namespace std;\nint si,sj,ti,tj; double pf;\nbool H[20][19],V[19][20];\nint nb[400][4],G;\ndouble PP[201][400],PE[201];\ndouble VA[201][400];\nvoid initNb(){for(int i=0;i<20;i++)for(int j=0;j<20;j++){int c=i*20+j;nb[c][0]=(i>0&&!V[i-1][j])?(i-1)*20+j:c;nb[c][1]=(i<19&&!V[i][j])?(i+1)*20+j:c;nb[c][2]=(j>0&&!H[i][j-1])?i*20+(j-1):c;nb[c][3]=(j<19&&!H[i][j])?i*20+(j+1):c;}}\nint dc(char c){return c=='U'?0:c=='D'?1:c=='L'?2:3;}\nvoid computeVA(){memset(VA,0,sizeof(VA));for(int t=199;t>=0;t--)for(int c=0;c<400;c++){if(c==G)continue;double best=-1e18;for(int d=0;d<4;d++){int nk=nb[c][d];double v=pf*VA[t+1][c]+(nk==G?(1-pf)*(400.-t):(1-pf)*VA[t+1][nk]);if(v>best)best=v;}VA[t][c]=best;}}\nvoid buildP(const string&s,int fr){for(int t=fr;t<200;t++){int d=dc(s[t]);double*a=PP[t],*b=PP[t+1];memset(b,0,3200);for(int k=0;k<400;k++){double v=a[k];if(v<1e-15)continue;b[k]+=v*pf;b[nb[k][d]]+=v*(1-pf);}double e=b[G]*(401.-(t+1));b[G]=0;PE[t+1]=PE[t]+e;}}\ndouble evalF(const string&s,int fr){double p[400],q[400];memcpy(p,PP[fr],3200);double E=PE[fr];for(int t=fr;t<200;t++){int d=dc(s[t]);memset(q,0,3200);for(int k=0;k<400;k++){double v=p[k];if(v<1e-15)continue;q[k]+=v*pf;q[nb[k][d]]+=v*(1-pf);}E+=q[G]*(401.-(t+1));q[G]=0;memcpy(p,q,3200);}return E;}\nvoid setP(const string&s){memset(PP[0],0,3200);PP[0][si*20+sj]=1;PE[0]=0;buildP(s,0);}\nchrono::time_pointT0;\ndouble el(){return chrono::duration(chrono::steady_clock::now()-T0).count();}\ndouble hc(string&s,double E0,double tl){double be=E0;for(;;){if(el()>tl)break;bool imp=false;for(int t=0;t<200;t++){int od=dc(s[t]);for(int d=0;d<4;d++){if(d==od)continue;s[t]=\"UDLR\"[d];double e=evalF(s,t);if(e>be+1e-12){be=e;od=d;buildP(s,t);imp=true;}else s[t]=\"UDLR\"[od];}}if(!imp)break;}return be;}\nstring bfsPath(){int ds[400];fill(ds,ds+400,-1);int pr[400],pd[400];int src=si*20+sj;queueq;q.push(src);ds[src]=0;while(!q.empty()){int k=q.front();q.pop();for(int d=0;d<4;d++){int nk=nb[k][d];if(nk==k||ds[nk]!=-1)continue;ds[nk]=ds[k]+1;pr[nk]=k;pd[nk]=d;q.push(nk);}}string r;for(int c=G;c!=src;c=pr[c])r+=\"UDLR\"[pd[c]];reverse(r.begin(),r.end());return r;}\nstring distanceGreedy(){int bd[400];fill(bd,bd+400,-1);queueq;q.push(G);bd[G]=0;while(!q.empty()){int k=q.front();q.pop();for(int d=0;d<4;d++){int nk=nb[k][d];if(nk==k||bd[nk]!=-1)continue;bd[nk]=bd[k]+1;q.push(nk);}}double prob[400]={},np[400];prob[si*20+sj]=1.0;string s(200,'D');for(int t=0;t<200;t++){double best=-1e18;int bestd=0;for(int d=0;d<4;d++){double g=0;for(int k=0;k<400;k++){if(prob[k]<1e-15)continue;g+=prob[k]*(1-pf)*(bd[k]-bd[nb[k][d]]);}if(g>best){best=g;bestd=d;}}s[t]=\"UDLR\"[bestd];memset(np,0,3200);for(int k=0;k<400;k++){if(prob[k]<1e-15)continue;np[k]+=prob[k]*pf;np[nb[k][bestd]]+=prob[k]*(1-pf);}np[G]=0;memcpy(prob,np,3200);}return s;}\ndouble la_val(const double*prob,int t,int depth){if(depth==0||t>=200){double v=0;for(int k=0;k<400;k++)if(prob[k]>1e-15)v+=prob[k]*(t<200?VA[t][k]:0.);return v;}double best=-1e18,np[400];for(int d=0;d<4;d++){memset(np,0,3200);for(int k=0;k<400;k++){double v=prob[k];if(v<1e-15)continue;np[k]+=v*pf;np[nb[k][d]]+=v*(1-pf);}double sc=np[G]*(400.-t);np[G]=0;double fv=la_val(np,t+1,depth-1);if(sc+fv>best)best=sc+fv;}return best;}\nstring kStepGreedy(int K){double prob[400]={},np[400];prob[si*20+sj]=1.0;string s(200,'D');for(int t=0;t<200;t++){double best=-1e18;int bestd=0;for(int d=0;d<4;d++){memset(np,0,3200);for(int k=0;k<400;k++){double v=prob[k];if(v<1e-15)continue;np[k]+=v*pf;np[nb[k][d]]+=v*(1-pf);}double sc=np[G]*(400.-t);np[G]=0;double fv=la_val(np,t+1,K-1);if(sc+fv>best){best=sc+fv;bestd=d;}}s[t]=\"UDLR\"[bestd];memset(np,0,3200);for(int k=0;k<400;k++){double v=prob[k];if(v<1e-15)continue;np[k]+=v*pf;np[nb[k][bestd]]+=v*(1-pf);}np[G]=0;memcpy(prob,np,3200);}return s;}\nint main(){\n ios::sync_with_stdio(0);cin.tie(0);\n cin>>si>>sj>>ti>>tj>>pf;\n for(int i=0;i<20;i++){string r;cin>>r;for(int j=0;j<19;j++)H[i][j]=(r[j]=='1');}\n for(int i=0;i<19;i++){string r;cin>>r;for(int j=0;j<20;j++)V[i][j]=(r[j]=='1');}\n initNb();G=ti*20+tj;T0=chrono::steady_clock::now();\n computeVA();\n string path=bfsPath();int K=(int)path.size();\n string s1(200,'D');for(int i=0;i<200;i++)s1[i]=path[i%K];\n string s2=kStepGreedy(3);\n string s3=distanceGreedy();\n setP(s1);double e1=hc(s1,PE[200],0.13);\n setP(s2);double e2=hc(s2,PE[200],0.27);\n setP(s3);double e3=hc(s3,PE[200],0.43);\n string gb;double gbE;\n if(e1>=e2&&e1>=e3){gb=s1;gbE=e1;}else if(e2>=e3){gb=s2;gbE=e2;}else{gb=s3;gbE=e3;}\n setP(gb);\n mt19937 rng(42);uniform_real_distributionud(0,1);\n {string sc=gb;double scE=gbE;double T=2.0;int sa_st=0;const int SA_MAX=6000;\n while(el()<1.2&&sa_st0||ud(rng)gbE){gbE=e;gb=sc;}}\n else sc[t]=\"UDLR\"[od];\n sa_st++;\n if(sa_st%500==0){T=2.0*exp(-7.0*(double)sa_st/SA_MAX);if(scEu1(0,1);\n double T=2.0;int st=0;\n while(st<500&&el()<1.23){\n int t=a1()%200,od=dc(sc[t]),nd=(od+1+(int)(a1()%3))%4;\n sc[t]=\"UDLR\"[nd];double e=evalF(sc,t),dlt=e-scE;\n if(dlt>0||u1(a1)gbE){gbE=e;gb=sc;}}\n else sc[t]=\"UDLR\"[od];\n st++;T=2.0*exp(-7.0*(double)st/500);\n if(st%100==0&&scEu2(0,1);\n double T=1.0;int st=0;\n while(st<200&&el()<1.26){\n int t=a2()%200,od=dc(sc[t]),nd=(od+1+(int)(a2()%3))%4;\n sc[t]=\"UDLR\"[nd];double e=evalF(sc,t),dlt=e-scE;\n if(dlt>0||u2(a2)gbE){gbE=e;gb=sc;}}\n else sc[t]=\"UDLR\"[od];\n st++;T=1.0*exp(-7.0*(double)st/200);\n }}\n setP(gb);\n while(el()<1.87){string p2=gb;int st=rng()%3;\n if(st==0){int M=5+(int)(rng()%21);for(int i=0;igbE+1e-12){gbE=e;gb=p2;}}\n cout<\nusing namespace std;\nconst int N=30,TOTAL=N*N*4;\nconst int to_t[8][4]={{1,0,-1,-1},{3,-1,-1,0},{-1,-1,3,2},{-1,2,1,-1},{1,0,3,2},{3,2,1,0},{2,-1,0,-1},{-1,3,-1,1}};\nconst int di[4]={0,-1,0,1},dj[4]={-1,0,1,0};\nint tiles[N][N],init_t[N][N],rots[N][N],best_rots[N][N];\nlong long global_best=0;mt19937 rng(42);int nxt[TOTAL];uint8_t col[TOTAL];\ninline int apply_rot(int t,int r){if(t<=3)return(t+r)&3;if(t<=5)return 4+((t-4+r)&1);return 6+((t-6+r)&1);}\ninline void update_nxt(int i,int j){int base=(i*N+j)*4,t=tiles[i][j];for(int d=0;d<4;d++){int d2=to_t[t][d];if(d2<0){nxt[base+d]=-1;continue;}int ni=i+di[d2],nj=j+dj[d2];if((unsigned)ni>=(unsigned)N||(unsigned)nj>=(unsigned)N){nxt[base+d]=-1;continue;}nxt[base+d]=(ni*N+nj)*4+((d2+2)&3);}}\nlong long evaluate(){memset(col,0,TOTAL);int t1=0,t2=0;for(int s=0;s=0&&!col[c]){col[c]=1;c=nxt[c];}if(c>=0&&col[c]==1){int len=0,cc=c;do{cc=nxt[cc];len++;}while(cc!=c);if(len>t1){t2=t1;t1=len;}else if(len>t2)t2=len;}c=s;while(c>=0&&col[c]==1){col[c]=2;c=nxt[c];}}return(long long)t1*t2;}\nconst auto TS=chrono::steady_clock::now();\ndouble gt(){return chrono::duration(chrono::steady_clock::now()-TS).count();}\nstatic unsigned cur_gen=0;\nstatic int dv_gen[TOTAL]={};\nstatic bool dvb[TOTAL]={},sm_mask[TOTAL]={};\nstatic int dirty_arr[N*N+2]={};\nstatic int n_dirty=0;\ntypedef array Pt;\nint dfs_loop(int si,int sj,int sd,const bool*occ){\n cur_gen++;n_dirty=0;\n if(occ&&occ[(si*N+sj)*4+sd])return 0;\n int i=si,j=sj,d=sd,len=0;\n while(len0)?len:0;\n if(occ&&occ[s])return 0;dv_gen[s]=cur_gen;\n int base=(i*N+j)*4;\n bool dc=false;for(int p=0;p<4&&!dc;p++)if(p!=d&&(dv_gen[base+p]==cur_gen||(occ&&occ[base+p])))dc=true;\n if(dc){int d2=to_t[tiles[i][j]][d];if(d2<0)return 0;int ni=i+di[d2],nj=j+dj[d2];if((unsigned)ni>=(unsigned)N||(unsigned)nj>=(unsigned)N)return 0;int nd=(d2+2)&3;if(occ&&occ[(ni*N+nj)*4+nd])return 0;len++;if(ni==si&&nj==sj&&nd==sd)return len;i=ni;j=nj;d=nd;continue;}\n int ti=init_t[i][j],br=-1,bp=-9999;\n for(int r=0;r<4;r++){\n int t=apply_rot(ti,r),d2=to_t[t][d];if(d2<0)continue;\n int ni=i+di[d2],nj=j+dj[d2];if((unsigned)ni>=(unsigned)N||(unsigned)nj>=(unsigned)N)continue;\n int nd=(d2+2)&3,ns=(ni*N+nj)*4+nd;if(occ&&occ[ns])continue;\n int nb=(ni*N+nj)*4;bool nc=false;\n for(int pp=0;pp<4&&!nc;pp++)if(pp!=nd&&(dv_gen[nb+pp]==cur_gen||(occ&&occ[nb+pp])))nc=true;\n if(nc&&to_t[tiles[ni][nj]][nd]<0)continue;\n int p=(dv_gen[ns]!=cur_gen)?100:0;\n if(ni==si&&nj==sj&&nd==sd&&len>4)p=50;\n int nti=init_t[ni][nj];if(nti==4||nti==5)p+=5;\n if(ni>0&&ni0&&njbp){bp=p;br=r;}\n }\n if(br<0)return 0;\n dirty_arr[n_dirty++]=i*N+j;\n rots[i][j]=br;tiles[i][j]=apply_rot(ti,br);update_nxt(i,j);\n int d2=to_t[tiles[i][j]][d];int ni=i+di[d2],nj=j+dj[d2],nd=(d2+2)&3;\n if(occ&&occ[(ni*N+nj)*4+nd])return 0;len++;if(ni==si&&nj==sj&&nd==sd)return len;i=ni;j=nj;d=nd;\n }return 0;\n}\nint build_loop(int n,const bool*occ,const vector*sm=nullptr,double end_t=1e18){\n int sr[N][N];memcpy(sr,rots,sizeof(rots));int bl=0,bs[N][N];memcpy(bs,sr,sizeof(sr));n_dirty=0;\n for(int a=0;a0&&a%100==0&>()>=end_t)break;\n for(int k=0;kempty()&&(int)(rng()%10)<7){const auto&p=(*sm)[rng()%sm->size()];si=p[0];sj=p[1];sd=p[2];}\n else{si=rng()%N;sj=rng()%N;sd=rng()%4;}\n int l=dfs_loop(si,sj,sd,occ);\n if(l>bl){bl=l;memcpy(bs,rots,sizeof(rots));for(int s=0;s=(unsigned)N||(unsigned)nj>=(unsigned)N)continue;if(to_t[tiles[ni][nj]][(d+2)%4]>=0)cnt++;}if(cnt>bc){bc=cnt;br=r;}}if(br!=rots[i][j]){rots[i][j]=br;tiles[i][j]=apply_rot(ti,br);update_nxt(i,j);c=true;}}if(!c)break;}}\nvoid run_sa(double Tf,double et){long long cur=evaluate();if(cur>global_best){global_best=cur;memcpy(best_rots,rots,sizeof(rots));}double si=max(10.0,(double)cur),e=gt(),s0=e;int cnt=0;while(e=0||rng()/4294967296.0global_best){global_best=ns;memcpy(best_rots,rots,sizeof(rots));}}else{tiles[i][j]=ot;update_nxt(i,j);}}}\nvoid run_greedy(long long&cur,double et){for(bool imp=true;imp&>()bl){bl=ns;bd=dr;}tiles[i][j]=st;update_nxt(i,j);}if(bd){rots[i][j]=(rots[i][j]+bd)&3;tiles[i][j]=apply_rot(ti,rots[i][j]);update_nxt(i,j);cur=bl;if(bl>global_best){global_best=bl;memcpy(best_rots,rots,sizeof(rots));}imp=true;}}}}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n for(int i=0;i>s;for(int j=0;j0){\n bool occ1[TOTAL];memcpy(occ1,dvb,TOTAL);\n vector smart;memset(sm_mask,0,TOTAL);\n for(int i=0;i0){memcpy(rots,pr,sizeof(rots));for(int i=0;i\nusing namespace std;\nint N,T,board[10][10],board_label[10][10],er,ec,tgt[10][10],avail[16];\nbool fixed_cells[10][10];string out;int total_edges;\nint uf_p[101],uf_rk[101];\nstruct UFCh{int ch,op,rt,ork;};vectoruf_ch;\nvoid uf_init(){for(int i=0;i<=N*N;i++){uf_p[i]=i;uf_rk[i]=0;}}\nint uf_find(int x){while(uf_p[x]!=x)x=uf_p[x];return x;}\nbool uf_union(int a,int b){int ra=uf_find(a),rb=uf_find(b);if(ra==rb)return false;if(uf_rk[ra]sv){UFCh c=uf_ch.back();uf_ch.pop_back();uf_p[c.ch]=c.op;uf_rk[c.rt]=c.ork;}}\nint sb_p[100],sb_sz[100];bool sb_cy[100];\nint sb_find(int x){while(sb_p[x]!=x){sb_p[x]=sb_p[sb_p[x]];x=sb_p[x];}return x;}\nint scoreBoard2(int b[10][10]){int NN=N*N;for(int i=0;i0&&b[i][j+1]>0&&(b[i][j]&4)&&(b[i][j+1]&1))add(i*N+j,i*N+j+1);for(int i=0;i0&&b[i+1][j]>0&&(b[i][j]&8)&&(b[i+1][j]&2))add(i*N+j,(i+1)*N+j);int best=0;for(int i=0;i0&&sb_find(i)==i&&!sb_cy[i])best=max(best,sb_sz[i]);return best;}\nint scoreBoard(){return scoreBoard2(board);}\nvoid read_input(){cin>>N>>T;for(int i=0;i>s;for(int j=0;j='0'&&c<='9')?c-'0':c-'a'+10;if(!board[i][j]){er=i;ec=j;}}}}\nbool valid_pos(int v,int i,int j){return!((v&1)&&!j)&&!((v&2)&&!i)&&!((v&4)&&j==N-1)&&!((v&8)&&i==N-1);}\nint g_ops,g_ops_limit;int g_vo[15];\nbool find_target(int pos){\n if(++g_ops>g_ops_limit)return false;\n if(pos==N*N)return total_edges==N*N-2;\n int i=pos/N,j=pos%N;if(i==N-1&&j==N-1){tgt[i][j]=0;return find_target(pos+1);}\n bool fl=(j>0),nl=fl&&(tgt[i][j-1]&4),fu=(i>0),nu=fu&&(tgt[i-1][j]&8);\n int new_ed=(fl?nl:0)+(fu?nu:0);if(total_edges+new_ed>N*N-2){tgt[i][j]=-1;return false;}\n for(int vi=0;vi<15;vi++){int v=g_vo[vi];\n if(!avail[v]||!valid_pos(v,i,j))continue;if(fl&&!!(v&1)!=nl)continue;if(fu&&!!(v&2)!=nu)continue;\n if(j0),nu2=fcu&&(tgt[i-1][nj]&8);for(int ui=0;ui<15&&!ok;ui++){int u=g_vo[ui];int cnt=avail[u]-(u==v?1:0);if(cnt<=0||!valid_pos(u,i,nj)||!!(u&1)!=n2||(fcu&&!!(u&2)!=nu2))continue;ok=true;}}if(!ok)continue;}\n if(i>cp,tp;for(int i=0;iused(tp.size(),false);for(auto[cr,cc]:cp){int best=-1,bd=INT_MAX;for(int k=0;k<(int)tp.size();k++){if(used[k])continue;int d=abs(cr-tp[k].first)+abs(cc-tp[k].second);if(d=0){board_label[cr][cc]=tp[best].first*N+tp[best].second;used[best]=true;}}}}\nbool check_solvable(){vectors;for(int i=0;i=0)s.push_back(board_label[i][j]);int inv=0;for(int a=0;a<(int)s.size();a++)for(int b=a+1;b<(int)s.size();b++)if(s[a]>s[b])inv++;if(N%2)return!(inv%2);return(inv+er)%2==1;}\nvoid fix_parity(){if(check_solvable())return;for(int v=1;v<=15;v++){vector>cp;for(int i=0;i=2){swap(board_label[cp[0].first][cp[0].second],board_label[cp[1].first][cp[1].second]);if(check_solvable())return;swap(board_label[cp[0].first][cp[0].second],board_label[cp[1].first][cp[1].second]);}}}\nvoid do_move(char m){int tr=er,tc=ec;if(m=='U')tr--;else if(m=='D')tr++;else if(m=='L')tc--;else tc++;board[er][ec]=board[tr][tc];board_label[er][ec]=board_label[tr][tc];board[tr][tc]=0;board_label[tr][tc]=-1;er=tr;ec=tc;out+=m;}\nstatic int me_prv[100],me_q[100];\nbool move_empty(int gr,int gc){if(er==gr&&ec==gc)return true;if((int)out.size()>=T)return false;if(fixed_cells[gr][gc])return false;int NN=N*N,s=er*N+ec,g=gr*N+gc;fill(me_prv,me_prv+NN,-2);me_prv[s]=-1;int qh=0,qt=0;me_q[qt++]=s;const int dr[]={-1,1,0,0},dc[]={0,0,-1,1};while(qh=N||nc<0||nc>=N||fixed_cells[nr][nc])continue;int nxt=nr*N+nc;if(me_prv[nxt]!=-2)continue;me_prv[nxt]=cur;me_q[qt++]=nxt;}}if(me_prv[g]==-2)return false;static int path[101];int plen=0,cur=g;while(cur!=s){path[plen++]=cur;cur=me_prv[cur];}for(int k=plen-1;k>=0;k--){if((int)out.size()>=T)return false;int nxt=path[k],nr=nxt/N,nc=nxt%N;char m;if(nr==er-1)m='U';else if(nr==er+1)m='D';else if(nc==ec-1)m='L';else m='R';do_move(m);}return true;}\nstatic int bt_prv[10000],bt_q[10001];static char bt_mv[10000],bt_path[10000];\nbool bfs_tile(int&tr,int&tc,int dr,int dc){if(tr==dr&&tc==dc)return true;if((int)out.size()>=T)return false;int NN=N*N,t0=tr*N+tc,e0=er*N+ec,tg=dr*N+dc,tot=NN*NN;memset(bt_prv,-1,tot*sizeof(int));int start=t0*NN+e0;bt_prv[start]=start;int qh=0,qt=0;bt_q[qt++]=start;const int ddr[]={-1,1,0,0},ddc[]={0,0,-1,1};const char dch[]={'U','D','L','R'};int goal=-1;while(qh=N||nc<0||nc>=N||fixed_cells[nr][nc])continue;int np=nr*N+nc,nt=(np==ct)?ce:ct,ne=np;if(nt==ne)continue;int nst=nt*NN+ne;if(nst<0||nst>=tot||bt_prv[nst]!=-1)continue;bt_prv[nst]=cur;bt_mv[nst]=dch[d];bt_q[qt++]=nst;}}if(goal<0){for(int e=0;e=0;k--){if((int)out.size()>=T)return false;do_move(bt_path[k]);}tr=dr;tc=dc;return true;}\npairfind_lbl(int lbl){for(int i=0;i=T)return;for(int col=0;col<=N-3&&(int)out.size()=T)return;auto[ar,ac]=find_lbl(row*N+(N-2));auto[br,bc]=find_lbl(row*N+(N-1));if(ar<0||br<0)return;if(ar==row&&ac==N-2&&br==row&&bc==N-1){fixed_cells[row][N-2]=fixed_cells[row][N-1]=true;return;}bfs_tile(ar,ac,row,N-1);if((int)out.size()>=T)return;auto[br2,bc2]=find_lbl(row*N+(N-1));if(br2<0)return;fixed_cells[row][N-1]=true;bfs_tile(br2,bc2,row+1,N-1);fixed_cells[row][N-1]=false;if((int)out.size()>=T)return;fixed_cells[row][N-1]=fixed_cells[row+1][N-1]=true;move_empty(row,N-2);fixed_cells[row][N-1]=fixed_cells[row+1][N-1]=false;if((int)out.size()=T)return;auto[ar,ac]=find_lbl((N-2)*N+col);auto[br,bc]=find_lbl((N-1)*N+col);if(ar<0||br<0)return;if(ar==N-2&&ac==col&&br==N-1&&bc==col){fixed_cells[N-2][col]=fixed_cells[N-1][col]=true;return;}bfs_tile(ar,ac,N-1,col);if((int)out.size()>=T)return;auto[br2,bc2]=find_lbl((N-1)*N+col);if(br2<0)return;fixed_cells[N-1][col]=true;bfs_tile(br2,bc2,N-1,col+1);fixed_cells[N-1][col]=false;if((int)out.size()>=T)return;fixed_cells[N-1][col]=fixed_cells[N-1][col+1]=true;move_empty(N-2,col);fixed_cells[N-1][col]=fixed_cells[N-1][col+1]=false;if((int)out.size()=T)return;int p0=(N-2)*N+(N-2),p1=(N-2)*N+(N-1),p2=(N-1)*N+(N-2);int a=board_label[N-2][N-2],b=board_label[N-2][N-1],c=board_label[N-1][N-2],d=board_label[N-1][N-1];if(a==p0&&b==p1&&c==p2&&d==-1)return;auto el=[&](int l)->int{if(l==p0)return 0;if(l==p1)return 1;if(l==p2)return 2;return 3;};auto enc=[](int v0,int v1,int v2,int v3){return v0*64+v1*16+v2*4+v3;};int gs=enc(0,1,2,3),ss=enc(el(a),el(b),el(c),el(d));if(ss==gs)return;static int par[256];static char mfr[256];fill(par,par+256,-2);par[ss]=-1;static int bq[256];int bqh=0,bqt=0;bq[bqt++]=ss;const int adj[4][2]={{1,2},{0,3},{0,3},{1,2}};const char amv[4][2]={{'R','D'},{'L','D'},{'U','R'},{'U','L'}};while(bqh>6)&3,(cur>>4)&3,(cur>>2)&3,cur&3};int ep=-1;for(int p=0;p<4;p++)if(v[p]==3){ep=p;break;}if(ep<0)continue;for(int k=0;k<2;k++){int np=adj[ep][k];char m=amv[ep][k];int nv[4]={v[0],v[1],v[2],v[3]};nv[ep]=nv[np];nv[np]=3;int nst=enc(nv[0],nv[1],nv[2],nv[3]);if(par[nst]==-2){par[nst]=cur;mfr[nst]=m;bq[bqt++]=nst;}}}if(par[gs]==-2)return;static char path[20];int plen=0;int cur=gs;while(cur!=ss){path[plen++]=mfr[cur];cur=par[cur];}for(int k=plen-1;k>=0;k--){if((int)out.size()>=T)break;do_move(path[k]);}}\nvoid solve(){for(int row=0;row<=N-3&&(int)out.size()=T)return;\n int init_b[10][10],init_l[10][10];int init_er=er,init_ec=ec;string init_out=out;\n memcpy(init_b,board,sizeof(board));memcpy(init_l,board_label,sizeof(board_label));\n int gbsc=scoreBoard();\n int gb[10][10],gl[10][10];int ger2=er,gec2=ec;string gpath=out;\n memcpy(gb,board,sizeof(board));memcpy(gl,board_label,sizeof(board_label));\n const int dr[4]={-1,1,0,0},dc[4]={0,0,-1,1};const char mvs[4]={'U','D','L','R'};\n for(int run=0;run<15&&gbsc=N||nc<0||nc>=N)continue;\n int sb[10][10];memcpy(sb,board,sizeof(board));int se=er,sf=ec;\n int tr2=er,tc2=ec;if(mvs[d]=='U')tr2--;else if(mvs[d]=='D')tr2++;else if(mvs[d]=='L')tc2--;else tc2++;\n board[er][ec]=board[tr2][tc2];board[tr2][tc2]=0;er=tr2;ec=tc2;\n int sc=scoreBoard();memcpy(board,sb,sizeof(board));er=se;ec=sf;\n if(sc>bsc2){bsc2=sc;best_d=d;}}\n if(best_d>=0){\n do_move(mvs[best_d]);int sc=scoreBoard();\n if(sc>lbsc){lbsc=sc;memcpy(lb,board,sizeof(board));memcpy(ll,board_label,sizeof(board_label));ler=er;lec=ec;lpath=out;}\n no_imp=0;if(lbsc==N*N-1)break;\n }else{\n int np2=min(5+no_imp,20);\n for(int i=0;i=0&&nr=0&&nc100){memcpy(board,lb,sizeof(board));memcpy(board_label,ll,sizeof(board_label));er=ler;ec=lec;out=lpath;no_imp=0;}\n }}\n if(lbsc>gbsc){gbsc=lbsc;memcpy(gb,lb,sizeof(board));memcpy(gl,ll,sizeof(board_label));ger2=ler;gec2=lec;gpath=lpath;if(gbsc==N*N-1)break;}}\n memcpy(board,gb,sizeof(board));memcpy(board_label,gl,sizeof(board_label));er=ger2;ec=gec2;out=gpath;}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);read_input();\n memset(avail,0,sizeof(avail));for(int i=0;i0)avail[board[i][j]]++;\n memset(tgt,-1,sizeof(tgt));memset(fixed_cells,0,sizeof(fixed_cells));memset(board_label,-1,sizeof(board_label));\n total_edges=0;\n bool found=find_target_multi();\n if(found){init_labels();fix_parity();solve();}\n if(scoreBoard()\nusing namespace std;\ntypedef long long ll;\ntypedef unsigned long long ull;\ntypedef pair puu;\nstruct PH{size_t operator()(const puu&p)const{size_t h=hash()(p.first);h^=hash()(p.second)+0x9e3779b9ULL+(h<<6)+(h>>2);return h;}};\nmt19937 rng(42);\nint N,K,a[11],stx[5501],sty[5501];\nstruct Line{ll px,py,qx,qy;};\nconst int MK=100;\nLine cur_lines[MK],best_lines[MK];\nint8_t sgn_data[5501][MK];\null slo[5501],shi[5501];\nunordered_mapgrps;\nint b_arr[12],cscore,best_score;\nstruct Change{int idx;puu old_sig,new_sig;int8_t new_sgn;};\nvectorpending;\nvector>dvec;\nbool is_dummy[MK];\nll ecross(const Line&l,ll x,ll y){return(l.qx-l.px)*(y-l.py)-(l.qy-l.py)*(x-l.px);}\nvoid upd(int oc,int nc){if(oc>=1&&oc<=10){cscore-=min(a[oc],b_arr[oc]);b_arr[oc]--;cscore+=min(a[oc],b_arr[oc]);}if(nc>=1&&nc<=10){cscore-=min(a[nc],b_arr[nc]);b_arr[nc]++;cscore+=min(a[nc],b_arr[nc]);}}\nvoid build(){grps.clear();grps.reserve(32768);grps.max_load_factor(0.3f);memset(b_arr,0,sizeof(b_arr));cscore=0;for(int i=0;i=0)?1:-1;sgn_data[i][j]=s;if(s==1){if(j<64)slo[i]|=(1ULL<second,it->second+1);it->second++;}}\nint try_ch(int j,const Line&nl){pending.clear();dvec.clear();for(int i=0;i=0)?1:-1;if(ns==sgn_data[i][j])continue;puu os{slo[i],shi[i]};ull nl2=slo[i],nh2=shi[i];if(j<64){if(ns==1)nl2|=(1ULL<second:0,nc=c+d;if(c>=1&&c<=10){nsc-=min(a[c],nb[c]);nb[c]--;nsc+=min(a[c],nb[c]);}if(nc>=1&&nc<=10){nsc-=min(a[nc],nb[nc]);nb[nc]++;nsc+=min(a[nc],nb[nc]);}}i=j2;}return nsc;}\nvoid do_ch(int j,const Line&nl){for(auto&ch:pending){{auto it=grps.find(ch.old_sig);upd(it->second,it->second-1);if(!--it->second)grps.erase(it);}slo[ch.idx]=ch.new_sig.first;shi[ch.idx]=ch.new_sig.second;sgn_data[ch.idx][j]=ch.new_sgn;{auto[it2,ins]=grps.emplace(ch.new_sig,0);upd(it2->second,it2->second+1);it2->second++;}}cur_lines[j]=nl;}\nLine rline(){double th=(rng()%314159)*(M_PI/314159.0);double r=(int)(rng()%18001)-9000;double cx=r*cos(th),cy=r*sin(th),sdx=-sin(th)*9000,sdy=cos(th)*9000;return{llround(cx+sdx),llround(cy+sdy),llround(cx-sdx),llround(cy-sdy)};}\nLine pline(const Line&l,int s){ll dx=(ll)(rng()%(2*s+1))-s,dy=(ll)(rng()%(2*s+1))-s;int t=rng()%3;if(t==0)return{l.px+dx,l.py+dy,l.qx,l.qy};if(t==1)return{l.px,l.py,l.qx+dx,l.qy+dy};return{l.px+dx,l.py+dy,l.qx-dx,l.qy-dy};}\nLine pline_perp(const Line&l,int s){ll ddx=l.qx-l.px,ddy=l.qy-l.py;double len=hypot((double)ddx,(double)ddy);if(len<1.0)return l;ll delta=(ll)(rng()%(2*s+1))-s;ll dx2=llround(delta*(-ddy)/len),dy2=llround(delta*ddx/len);return{l.px+dx2,l.py+dy2,l.qx+dx2,l.qy+dy2};}\nLine pline_rot(const Line&l,int mr){double mx=(l.px+l.qx)*0.5,my=(l.py+l.qy)*0.5;double hdx=(l.qx-l.px)*0.5,hdy=(l.qy-l.py)*0.5;double angle=((int)(rng()%(2*mr+1))-mr)*0.001;double ca=cos(angle),sa=sin(angle);ll ndx=llround(hdx*ca-hdy*sa),ndy=llround(hdx*sa+hdy*ca);return{llround(mx)-ndx,llround(my)-ndy,llround(mx)+ndx,llround(my)+ndy};}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>N>>K;for(int d=1;d<=10;d++)cin>>a[d];for(int i=0;i>stx[i]>>sty[i];\n for(int i=0;i<25;i++){ll y=llround(-9000.0+18000.0*i/24.0);cur_lines[i]={-10000,y,10000,y};is_dummy[i]=false;}\n for(int i=0;i<25;i++){ll x=llround(-9000.0+18000.0*i/24.0);cur_lines[25+i]={x,-10000,x,10000};is_dummy[25+i]=false;}\n for(int i=50;i(chrono::steady_clock::now()-t0).count();\n if(e>2.90)break;\n T=max(0.05,15.0*pow(0.05/15.0,e/2.90));\n }\n int j=rng()%MK;Line nl;\n if(is_dummy[j]){nl=rline();}\n else{\n int sel=rng()%100;\n if(sel<22)nl=pline(cur_lines[j],30);\n else if(sel<30)nl=pline_perp(cur_lines[j],20);\n else if(sel<40)nl=pline_perp(cur_lines[j],50);\n else if(sel<48)nl=pline_perp(cur_lines[j],200);\n else if(sel<60)nl=pline_rot(cur_lines[j],10);\n else if(sel<72)nl=pline(cur_lines[j],300);\n else if(sel<86)nl=pline(cur_lines[j],2000);\n else nl=rline();\n }\n if(nl.px==nl.qx&&nl.py==nl.qy)continue;\n int ns=try_ch(j,nl);int ds=ns-cscore;bool acc=(ds>=0);\n if(!acc&&T>0.01)acc=((double)(rng()>>8)/(double)(1u<<24))best_score){best_score=cscore;memcpy(best_lines,cur_lines,sizeof(cur_lines));}}\n }\n cout<\nusing namespace std;\nconst int MAXN=65;\nint N,M,cc;\nbool dots[MAXN][MAXN],h_seg[MAXN][MAXN],v_seg[MAXN][MAXN],d1_seg[MAXN][MAXN],d2_seg[MAXN][MAXN],inPQ[MAXN][MAXN];\nvector row_dots[MAXN],col_dots[MAXN],diag_dots[130],ad_dots[130];\nstruct Op{int x1,y1,x2,y2,x3,y3,x4,y4;};\nvector ops,best_ops;\npriority_queue>> work_pq;\nlong long best_score=0;\nint init_M; pair init_list[400];\nmt19937 rng(0); int run_mode=0;\nvoid ins(vector&v,int x){v.insert(lower_bound(v.begin(),v.end(),x),x);}\nvoid addDot(int x,int y){dots[x][y]=true;ins(row_dots[y],x);ins(col_dots[x],y);ins(diag_dots[x-y+64],x);ins(ad_dots[x+y],x);}\nbool ec(int x1,int y1,int x2,int y2){\n if(x1==x2){for(int y=min(y1,y2);yx1)==(y2>y1)){int xm=min(x1,x2),ym=min(y1,y2);for(int t=0;tx1)?1:-1,dy=(y2>y1)?1:-1;for(int t=1;tx1)==(y2>y1)){int xm=min(x1,x2),ym=min(y1,y2);for(int t=0;t=N||y2<0||y2>=N||x3<0||x3>=N||y3<0||y3>=N||x4<0||x4>=N||y4<0||y4>=N)return false;\n if(!dots[x2][y2]||!dots[x3][y3]||!dots[x4][y4])return false;\n if(!en(nx,ny,x2,y2)||!en(x2,y2,x3,y3)||!en(x3,y3,x4,y4)||!en(x4,y4,nx,ny))return false;\n if(!ec(nx,ny,x2,y2)||!ec(x2,y2,x3,y3)||!ec(x3,y3,x4,y4)||!ec(x4,y4,nx,ny))return false;\n ops.push_back({nx,ny,x2,y2,x3,y3,x4,y4});addDot(nx,ny);de(nx,ny,x2,y2);de(x2,y2,x3,y3);de(x3,y3,x4,y4);de(x4,y4,nx,ny);return true;}\nbool fap(int nx,int ny){\n if(dots[nx][ny])return false;\n vector> cands;\n for(int x2:row_dots[ny]){if(x2==nx)continue;for(int y2:col_dots[nx]){if(y2==ny||!dots[x2][y2])continue;cands.emplace_back((abs(x2-nx)+abs(y2-ny))*2,x2,ny,x2,y2,nx,y2);}}\n for(int xa:diag_dots[nx-ny+64]){if(xa==nx)continue;int a=xa-nx;for(int xb:ad_dots[nx+ny]){if(xb==nx)continue;int b=xb-nx;int x3=nx+a+b,y3=ny+a-b;if(x3>=0&&x3=0&&y3(c)+=rng()%8;sort(cands.begin(),cands.end());}\n else shuffle(cands.begin(),cands.end(),rng);\n for(auto&[p,x2,y2,x3,y3,x4,y4]:cands)if(cando(nx,ny,x2,y2,x3,y3,x4,y4))return true;\n return false;}\nvoid addWork(int x,int y){if(x<0||x>=N||y<0||y>=N||dots[x][y]||inPQ[x][y])return;inPQ[x][y]=true;work_pq.push({(x-cc)*(x-cc)+(y-cc)*(y-cc)+1,{x,y}});}\nvoid afterPlace(int x,int y){\n for(int i=0;i=4||run_mode==2)for(int xb:ad_dots[x+y])for(int xa:diag_dots[x-y+64])addWork(xa+xb-x,y+xa-xb);}\nvoid resetRun(){\n memset(dots,0,sizeof(dots));memset(h_seg,0,sizeof(h_seg));memset(v_seg,0,sizeof(v_seg));\n memset(d1_seg,0,sizeof(d1_seg));memset(d2_seg,0,sizeof(d2_seg));memset(inPQ,0,sizeof(inPQ));\n for(int i=0;i>>();\n for(int i=0;i(chrono::steady_clock::now()-t0).count()>=lim)return;\n auto[w,pos]=work_pq.top();work_pq.pop();auto[x,y]=pos;inPQ[x][y]=false;\n if(dots[x][y])continue;if(fap(x,y))afterPlace(x,y);}}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>N>>M;cc=(N-1)/2;init_M=M;\n for(int i=0;i>init_list[i].first>>init_list[i].second;}\n vector>> pts;\n for(int x=0;x(chrono::steady_clock::now()-t0).count();};\n for(int run=0;el()<4380;run++){\n run_mode=run;\n if(run>=2){\n long long s=(run==4)?2LL*31337+12345:\n (run==5)?3LL*31337+12345:\n (run==8)?0LL:\n (long long)run*31337+12345;\n rng.seed(s);\n }\n resetRun();\n // Adaptive timing: deterministic modes get full 550ms; shuffle modes 500ms; noise modes 430ms\n long long tpr;\n if(run_mode<=2) tpr=550LL; // modes 0,1,2: deterministic, need full time\n else if(run_mode==6||run_mode==7) tpr=500LL; // shuffle modes: slightly more time\n else tpr=430LL; // noise modes 3,4,5,8: 430ms (proven in sub10)\n // Total: 3*550+2*500+4*430 = 1650+1000+1720 = 4370ms < 4380ms\n long long re=min(4380LL,el()+tpr);\n drainQ(re,t0);\n bool changed=true;\n while(changed&&el()=re)break;\n auto[x,y]=pos;if(dots[x][y])continue;\n if(fap(x,y)){changed=true;afterPlace(x,y);drainQ(re,t0);}\n }\n }\n long long sc=0;\n for(int x=0;xbest_score){best_score=sc;best_ops=ops;}\n }\n cout<\nusing namespace std;\ntypedef array,10> Grid;\nGrid applyTilt(Grid g, char dir) {\n if(dir=='L'){for(int i=0;i<10;i++){int p=0;for(int j=0;j<10;j++)if(g[i][j])g[i][p++]=g[i][j];for(;p<10;p++)g[i][p]=0;}}\n else if(dir=='R'){for(int i=0;i<10;i++){int p=9;for(int j=9;j>=0;j--)if(g[i][j])g[i][p--]=g[i][j];for(;p>=0;p--)g[i][p]=0;}}\n else if(dir=='F'){for(int j=0;j<10;j++){int p=0;for(int i=0;i<10;i++)if(g[i][j])g[p++][j]=g[i][j];for(;p<10;p++)g[p][j]=0;}}\n else{for(int j=0;j<10;j++){int p=9;for(int i=9;i>=0;i--)if(g[i][j])g[p--][j]=g[i][j];for(;p>=0;p--)g[p][j]=0;}}\n return g;\n}\nlong long evalLeaf(const Grid& g, int nf=0){\n int rc[10][4]={},cc[10][4]={};\n bool vis[10][10]={};long long sum=0;int stk[100][2];\n const int dx[]={-1,1,0,0},dy[]={0,0,-1,1};\n for(int si=0;si<10;si++)for(int sj=0;sj<10;sj++){\n if(!g[si][sj])continue;\n rc[si][g[si][sj]]++;cc[sj][g[si][sj]]++;\n if(vis[si][sj])continue;\n int f=g[si][sj],sz=0,top=0;\n stk[top][0]=si;stk[top][1]=sj;top++;vis[si][sj]=true;\n while(top>0){--top;int x=stk[top][0],y=stk[top][1];sz++;\n for(int d=0;d<4;d++){int nx=x+dx[d],ny=y+dy[d];\n if(nx>=0&&nx<10&&ny>=0&&ny<10&&!vis[nx][ny]&&g[nx][ny]==f){vis[nx][ny]=true;stk[top][0]=nx;stk[top][1]=ny;top++;}}}\n sum+=(long long)sz*sz;}\n for(int i=0;i<10;i++)for(int f=1;f<=3;f++)\n sum+=(long long)(rc[i][f]*rc[i][f]+cc[i][f]*cc[i][f]);\n if(nf>=1&&nf<=3)\n for(int i=0;i<10;i++) sum+=(long long)(rc[i][nf]*rc[i][nf]+cc[i][nf]*cc[i][nf]);\n return sum;\n}\nGrid placeCandy(Grid g,int p,int flav){\n int cnt=0;for(int i=0;i<10;i++)for(int j=0;j<10;j++)if(!g[i][j]&&++cnt==p){g[i][j]=flav;return g;}return g;\n}\nconst char DIRS[]={'F','B','L','R'};\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n int fl[100];for(int t=0;t<100;t++)cin>>fl[t];\n Grid grid={};\n mt19937 rng(20230101);\n const int S=8;\n for(int t=0;t<100;t++){\n int p;cin>>p;grid=placeCandy(grid,p,fl[t]);\n char bestDir='F';\n if(t<99){\n int nc1=99-t,nc2=98-t;\n int s3[S],s_cnt=0;\n if(t+2<100){s_cnt=min(S,nc2);\n if(nc2<=S){for(int s=0;supc[nf3]) nf3=f;\n }\n long long best=-1;\n for(char d1:DIRS){\n Grid g1=applyTilt(grid,d1);long long total=0;\n for(int p2=1;p2<=nc1;p2++){\n Grid g2=placeCandy(g1,p2,fl[t+1]);long long mx=0;\n for(char d2:DIRS){\n Grid g2t=applyTilt(g2,d2);long long val;\n if(s_cnt==0){val=evalLeaf(g2t,t+2<100?fl[t+2]:0);}\n else{long long sum3=0;\n for(int s=0;sbest){best=total;bestDir=d1;}}\n }\n cout<\n#include \nusing namespace std;using namespace Eigen;\nint M,N;double eps;\ndouble normalCDF(double x){return 0.5*erfc(-x*M_SQRT1_2);}\nvector getDeg(const string&s,int n){vectord(n,0);int idx=0;for(int i=0;i getEig(const string&s,int n){MatrixXd A(n,n);A.setZero();int idx=0;for(int i=0;isol(A,EigenvaluesOnly);vectorev(n);for(int i=0;iint{if(a>b)swap(a,b);return a*(2*n-a-1)/2+(b-a-1);};int cnt=0;for(int d=1;d,string>> enumDistinctSeqs(int n,int maxSeqs){\n int me=n*(n-1)/2;\n long long cap=(me<=21)?(1LL<,string>seen;\n for(long long mask=0;maskd(n,0);int idx=0;\n for(int i=0;i,string>>r;for(auto&p:seen)r.push_back(p);return r;\n}\ntuple> greedyPackSeqs(const vector,string>>&seqs,int M,int n){\n int S=seqs.size();if(Ssel(S,false);vectorminD(S,1e18);vectorselIdx;double achMin=1e18;\n sel[0]=true;selIdx.push_back(0);\n for(int j=1;jbestD){bestD=minD[j];best=j;}}\n if(best<0||bestD<=0)break;\n achMin=min(achMin,bestD);sel[best]=true;selIdx.push_back(best);\n for(int j=0;jg;for(int idx:selIdx)g.push_back(seqs[idx].second);\n return{achMin,avgK,g};\n}\ndouble predictCustomScore(int n,int M,double eps,double minL2,double avgK){\n if(eps<1e-9)return 1e9/n;\n double s1D=sqrt(eps*(1-eps)*(n-1));if(s1D<1e-12)return 1e9/n;\n double snr=(1-2*eps)*minL2/s1D;\n double p1=1.0-normalCDF(snr/2.0);\n double pe=min((double)(M-1)/M,1.0-pow(max(0.0,1.0-p1),avgK));\n return(1e9/n)*pow(0.9,100.0*pe);\n}\npair computeOptNScore(int M,double eps){\n int Nm=4;while((long long)Nm*(Nm-1)/2>c(M);\n for(int k=0;kbs){bs=sc;on=n;}\n }\n return{on,bs};\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>M>>eps;\n double bcs=0;int bcN=-1;vectorbcG;\n for(int n=4;n<=7;n++){\n auto seqs=enumDistinctSeqs(n,M+200);\n if((int)seqs.size()bcs){bcs=sc;bcN=n;bcG=g;}\n }\n auto[Nb,sb]=computeOptNScore(M,eps);\n bool uc=(bcN>0&&bcs>sb);\n N=uc?bcN:Nb;\n vectorG(M);\n if(uc){G=bcG;}\n else{int ME=N*(N-1)/2;for(int k=0;k=20);int NS,FD;\n if(uE){NS=min(500,NSE);FD=2*N;}\n else{long long opSD=(long long)N*N;NS=max(30,min(1000,(int)(budget/max(1LL,(long long)M*opSD))));FD=N;}\n vector>C(M,vector(FD,0.0));\n if(eps<1e-9){for(int k=0;ku(0.0,1.0);\n for(int k=0;k>h;vectorhf(FD);auto dh=getDeg(h,N);for(int i=0;i\nusing namespace std;\ntypedef long long ll;typedef pair pli;\nconst ll INF=1e18;const int MXN=1005,MXM=3005,MXD=35,MAXCP=10;\nint N,M,D,K,EU[MXM],EV[MXM];ll EW[MXM];\nvector> G[MXN];ll gd[MXN][MXN];\ndouble imp[MXM];int aday[MXM];double ADJ[MXM][MXD];int cutD[MXM][MXD];\nvector ladj[MXM],cpairs[MXM],dayE[MXD];int dpos[MXM];ll dtmp2[MXN];\nuint64_t rs=0xdeadbeef123ULL;\nuint64_t rng(){rs^=rs<<13;rs^=rs>>7;rs^=rs<<17;return rs;}\nint ri(int n){return(int)(rng()%(unsigned)n);}double rd(){return(rng()>>11)*(1.0/(1ull<<53));}\nvoid dijk(int s){fill(gd[s]+1,gd[s]+N+1,INF);gd[s][s]=0;priority_queue,greater>pq;pq.push({0,s});while(!pq.empty()){auto[d,u]=pq.top();pq.pop();if(d>gd[s][u])continue;for(auto&[v,e]:G[u]){ll nd=d+EW[e];if(nd,greater>pq;pq.push({0,s});while(!pq.empty()){auto[dd,u]=pq.top();pq.pop();if(dd>d[u])continue;if(u==t)return d[t];for(auto&[v,e]:G[u]){if(e==sk)continue;ll nd=dd+EW[e];if(nd&srcs){double tot=0.0;for(int s:srcs){fill(dtmp2+1,dtmp2+N+1,INF);dtmp2[s]=0;priority_queue,greater>pq;pq.push({0,s});while(!pq.empty()){auto[dd,u]=pq.top();pq.pop();if(dd>dtmp2[u])continue;for(auto&[v,ei]:G[u]){if(aday[ei]==d)continue;ll nd=dd+EW[ei];if(ndgd[s][t])tot+=(double)(dtmp2[t]-gd[s][t]);}return tot/((double)srcs.size()*(N-1));}\nstruct BrFr{int u,pe,ix;};struct BrI{int e,sz;};int bdt[MXN],blv[MXN];vector bstk;\nvoid findBr(int sk,vector&br){fill(bdt+1,bdt+N+1,-1);int tm=0;bstk.clear();if((int)bstk.capacity()bdt[p.u])br.push_back({pe,sz});}}}}\nbool cvis[MXN];int cq[MXN];\nint main(){\n ios_base::sync_with_stdio(0);cin.tie(0);\n auto tst=chrono::steady_clock::now();\n cin>>N>>M>>D>>K;\n for(int i=0;i>EU[i]>>EV[i]>>EW[i];G[EU[i]].push_back({EV[i],i});G[EV[i]].push_back({EU[i],i});}\n for(int i=1;i<=N;i++){int x,y;cin>>x>>y;}\n for(int s=1;s<=N;s++)dijk(s);\n {vectorpar(N+1,-1),sv(N);vectorsz(N+1,1);iota(sv.begin(),sv.end(),1);for(int s=1;s<=N;s++){fill(par.begin(),par.end(),-1);fill(sz.begin(),sz.end(),1LL);sort(sv.begin(),sv.end(),[s](int a,int b){return gd[s][a]=0;i--){int v=sv[i];if(par[v]<0)continue;int p=(EU[par[v]]==v)?EV[par[v]]:EU[par[v]];sz[p]+=sz[v];}for(int v:sv){if(par[v]<0)continue;imp[par[v]]+=(double)sz[v];}}}\n for(int e=0;ebr;for(int e=0;emin(b.sz,N-b.sz);});for(auto&bi:br){if((int)cpairs[e].size()>=MAXCP)break;auto it=lower_bound(cpairs[e].begin(),cpairs[e].end(),bi.e);if(it==cpairs[e].end()||*it!=bi.e)cpairs[e].insert(it,bi.e);}}}\n for(int u=1;u<=N;u++){int dg=G[u].size();for(int i=0;ieo(M);iota(eo.begin(),eo.end(),0);sort(eo.begin(),eo.end(),[](int a,int b){return imp[a]>imp[b];});\n for(int e:eo){int best=-1;double bs=1e18;int bc=INT_MAX;\n for(int d=0;d=K)continue;int cuts=0;for(int f:cpairs[e])if(aday[f]==d)cuts++;double cf=0;for(int e2:ladj[e])if(aday[e2]==d)cf+=imp[e2];double sc=cf+1e-12*dc[d];if(cuts0)continue;\n double dl=imp[e1]*(ADJ[e1][d2]-ADJ[e1][d1])+imp[e2]*(ADJ[e2][d1]-ADJ[e2][d2])-2.*isAdj(e1,e2)*imp[e1]*imp[e2];\n sm+=fabs(dl);c++;}\n if(c>0)T=sm/c;if(T<1e-9)T=1.0;}\n double T0=T;\n // Phase 1: Proxy SA (0.5s)\n for(long long step=0;;step++){\n if(step%200000==0){double el=chrono::duration(chrono::steady_clock::now()-tst).count();if(el>0.5)break;T=T0*exp(-10.*el/0.5);}\n int d1=ri(D),d2=ri(D);if(d1==d2||dayE[d1].empty()||dayE[d2].empty())continue;\n int e1=dayE[d1][ri(dayE[d1].size())],e2=dayE[d2][ri(dayE[d2].size())];\n int ic=isCut(e1,e2)?1:0;int dlc=(cutD[e1][d2]-ic)+(cutD[e2][d1]-ic)-cutD[e1][d1]-cutD[e2][d2];if(dlc>0)continue;\n double dl=imp[e1]*(ADJ[e1][d2]-ADJ[e1][d1])+imp[e2]*(ADJ[e2][d1]-ADJ[e2][d2])-2.*isAdj(e1,e2)*imp[e1]*imp[e2];\n if(dl<=0||(T>1e-9&&rd() srcs;\n {setused;while((int)srcs.size() sfk(D);\n for(int d=0;d(chrono::steady_clock::now()-tst).count();if(el>5.3)break;\n // d1 = worst of 4 random (same as v13)\n int d1=ri(D);for(int k=0;k<3;k++){int d=ri(D);if(sfk[d]>sfk[d1])d1=d;}\n if(dayE[d1].empty())continue;\n // d2 = lightest of 4 random (RESTORED to v13 approach, NOT absolute lightest)\n int d2=-1;for(int k=0;k<4;k++){int d=ri(D);if(d!=d1&&!dayE[d].empty()&&(d2<0||sfk[d]0)continue;\n double old_f1=sfk[d1],old_f2=sfk[d2];\n aday[e1]=d2;aday[e2]=d1;\n double new_f1=diagFk(d1,srcs),new_f2=diagFk(d2,srcs);\n aday[e1]=d1;aday[e2]=d2;\n if(new_f1+new_f20){\n fill(cvis+1,cvis+N+1,false);int h=0,t=0;cvis[1]=true;cq[t++]=1;\n while(h=K)continue;double cost=0;for(int ef:ladj[e])if(aday[ef]==dd)cost+=imp[e]*imp[ef];if(bdd<0||cost=0){for(int ef:ladj[e]){ADJ[ef][d]-=imp[e];ADJ[ef][bdd]+=imp[e];}for(int f:cpairs[e]){cutD[f][d]--;cutD[f][bdd]++;}\n {int p=dpos[e],L=dayE[d].back();dayE[d][p]=L;dpos[L]=p;dayE[d].pop_back();}dpos[e]=dayE[bdd].size();dayE[bdd].push_back(e);aday[e]=bdd;fx=true;}}\n if(!fx)break;}}\n for(int i=0;i\nusing namespace std;\nint D;string Fs[2][14],Rs[2][14];int bid,B[2][2744];bool occ[2][2744];\nstruct Box{int x,y,z,a,b,c;};\nbool bf(int r,int x0,int y0,int z0,int a,int b,int c){for(int i=0;it0,vectort1){double sc=0;int r0=0,r1=0,i0=0,i1=0;while(true){if(!r0&&i0<(int)t0.size())r0=t0[i0++];if(!r1&&i1<(int)t1.size())r1=t1[i1++];if(!r0||!r1)break;int ml=min(r0,r1);sc+=1.0/ml;r0-=ml;r1-=ml;}sc+=r0;while(i0<(int)t0.size())sc+=t0[i0++];sc+=r1;while(i1<(int)t1.size())sc+=t1[i1++];return sc;}\ntemplate\nvoid runBestTP(vector>brv0,vector>brv1,const vector&F0,const vector&F1,auto fillFn){\n vectorl0,l1;for(auto[l,i]:brv0)l0.push_back(l);for(auto[l,i]:brv1)l1.push_back(l);\n double bsc=1e18;vector>rv0=brv0,rv1=brv1;mt19937 rng(42);\n auto tryOrd=[&](vector>r0,vector>r1){vectort0,t1;for(auto[l,i]:r0)t0.push_back(l);for(auto[l,i]:r1)t1.push_back(l);double sc=simTP(t0,t1);if(scb.first;});sort(r1.begin(),r1.end(),[=](auto&a,auto&b){return o1?a.firstb.first;});tryOrd(r0,r1);}\n for(int rep=0;rep<10;rep++){auto r0=brv0,r1=brv1;shuffle(r0.begin(),r0.end(),rng);shuffle(r1.begin(),r1.end(),rng);tryOrd(r0,r1);}\n struct SO{int idx,off;};dequer0d,r1d;for(auto[l,i]:rv0)r0d.push_back({i,0});for(auto[l,i]:rv1)r1d.push_back({i,0});\n while(!r0d.empty()&&!r1d.empty()){auto&[i0,o0]=r0d.front();auto&[i1,o1]=r1d.front();int ml=min(F0[i0].len-o0,F1[i1].len-o1);bid++;fillFn(0,F0[i0],bid,o0,ml);fillFn(1,F1[i1],bid,o1,ml);o0+=ml;o1+=ml;if(o0==F0[i0].len)r0d.pop_front();if(o1==F1[i1].len)r1d.pop_front();}\n while(!r0d.empty()){auto[i0,o0]=r0d.front();r0d.pop_front();bid++;fillFn(0,F0[i0],bid,o0,F0[i0].len-o0);}\n while(!r1d.empty()){auto[i1,o1]=r1d.front();r1d.pop_front();bid++;fillFn(1,F1[i1],bid,o1,F1[i1].len-o1);}\n}\nvectoreB(int arr){vectorv;uint16_t fz[14]={},rz[14]={};for(int z=0;zgRL(int arr,int ax){vectorL;if(ax==0){for(int y=0;y=0){L.push_back({s,y,z,x-s,0});s=-1;}}}}else if(ax==1){for(int x=0;x=0){L.push_back({x,s,z,y-s,1});s=-1;}}}}else{for(int x=0;x=0){L.push_back({x,y,s,z-s,2});s=-1;}}}}return L;}\ndouble mS(const vector&L0,const vector&L1){mapc0,c1;for(auto&l:L0)c0[l.len]++;for(auto&l:L1)c1[l.len]++;double sc=0;int v0=0,v1=0;for(auto&[l,c]:c0){int cl=c1.count(l)?c1[l]:0;sc+=min(c,cl)*1.0/l;v0+=(c-min(c,cl))*l;}for(auto&[l,c]:c1){int cl=c0.count(l)?c0[l]:0;if(c>cl)v1+=(c-cl)*l;}return sc+max(v0,v1);}\nvoid doBox(){auto bx0=eB(0),bx1=eB(1);typedef arrayKey;auto gk=[](const Box&b)->Key{Key k={b.a,b.b,b.c};sort(k.begin(),k.end());return k;};map>g0,g1;for(int i=0;i<(int)bx0.size();i++)g0[gk(bx0[i])].push_back(i);for(int i=0;i<(int)bx1.size();i++)g1[gk(bx1[i])].push_back(i);vector>grps;for(auto&[k,v]:g0)if(g1.count(k))grps.push_back({k[0]*k[1]*k[2],k});sort(grps.rbegin(),grps.rend());for(auto&[vol,key]:grps){auto&v0=g0[key];auto&v1=g1[key];int p1=0;for(int i0:v0){auto&B0=bx0[i0];if(!bf(0,B0.x,B0.y,B0.z,B0.a,B0.b,B0.c))continue;while(p1<(int)v1.size()&&!bf(1,bx1[v1[p1]].x,bx1[v1[p1]].y,bx1[v1[p1]].z,bx1[v1[p1]].a,bx1[v1[p1]].b,bx1[v1[p1]].c))p1++;if(p1>=(int)v1.size())break;auto&B1=bx1[v1[p1++]];bid++;fB(0,B0.x,B0.y,B0.z,B0.a,B0.b,B0.c,bid);fB(1,B1.x,B1.y,B1.z,B1.a,B1.b,B1.c,bid);}}\n int bax0=1,bax1=1;double bsc=1e18;for(int a0=0;a0<3;a0++){auto Lt0=gRL(0,a0);for(int a1=0;a1<3;a1++){auto Lt1=gRL(1,a1);double sc=mS(Lt0,Lt1);if(sc>gl0,gl1;for(int i=0;i<(int)L0.size();i++)gl0[L0[i].len].push_back(i);for(int i=0;i<(int)L1.size();i++)gl1[L1[i].len].push_back(i);vectorlu0(L0.size(),false),lu1(L1.size(),false);for(auto&[l,v0]:gl0){auto it=gl1.find(l);if(it==gl1.end())continue;auto&v1=it->second;int mc=min((int)v0.size(),(int)v1.size());for(int j=0;jtuple{return{s.x+(s.ax==0?off:0),s.y+(s.ax==1?off:0),s.z+(s.ax==2?off:0)};};auto[x0,y0,z0]=gp(L0[v0[j]],0);fL(0,x0,y0,z0,l,L0[v0[j]].ax,bid);auto[x1,y1,z1]=gp(L1[v1[j]],0);fL(1,x1,y1,z1,l,L1[v1[j]].ax,bid);lu0[v0[j]]=lu1[v1[j]]=true;}}\n vector>rv0,rv1;for(int i=0;i<(int)L0.size();i++)if(!lu0[i])rv0.push_back({L0[i].len,i});for(int i=0;i<(int)L1.size();i++)if(!lu1[i])rv1.push_back({L1[i].len,i});\n auto gp=[&](const Ln&s,int off)->tuple{return{s.x+(s.ax==0?off:0),s.y+(s.ax==1?off:0),s.z+(s.ax==2?off:0)};};auto fillLn=[&](int arr,const Ln&s,int id,int off,int len){auto[x,y,z]=gp(s,off);fL(arr,x,y,z,len,s.ax,id);};\n runBestTP(rv0,rv1,L0,L1,fillLn);}\nstruct Seg{int x,y,z,len,ax;};\nvectorbuildSegs(int arr,int ax){vectorc;if(ax==2)for(int x=0;x=0){c.push_back({x,y,zs,z-zs,2});zs=-1;}}}else if(ax==1)for(int x=0;x=0){c.push_back({x,ys,z,y-ys,1});ys=-1;}}}else for(int y=0;y=0){c.push_back({xs,y,z,x-xs,0});xs=-1;}}}return c;}\nvectorgreedyFill(vectorc){bool cx[14][14]={},cy[14][14]={};vectorsel;for(auto&s:c){bool u=false;for(int k=0;kmF(int arr,int ax){auto c=buildSegs(arr,ax);sort(c.begin(),c.end(),[](const Seg&a,const Seg&b){return a.len>b.len;});return greedyFill(c);}\nvectormFbiased(int arr,int ax,const multiset&prefer){auto c=buildSegs(arr,ax);sort(c.begin(),c.end(),[&](const Seg&a,const Seg&b){int pa=prefer.count(a.len),pb=prefer.count(b.len);if(pa!=pb)return pa>pb;return a.len>b.len;});return greedyFill(c);}\nvectormFspatial(int arr,int ax,int mode){auto c=buildSegs(arr,ax);sort(c.begin(),c.end(),[mode](const Seg&a,const Seg&b){if(a.len!=b.len)return a.len>b.len;if(mode==0){if(a.x!=b.x)return a.xmFbiasedSpatial(int arr,int ax,const multiset&prefer,int mode){auto c=buildSegs(arr,ax);sort(c.begin(),c.end(),[&](const Seg&a,const Seg&b){int pa=(int)prefer.count(a.len),pb=(int)prefer.count(b.len);if(pa!=pb)return pa>pb;if(a.len!=b.len)return a.len>b.len;if(mode==0){if(a.x!=b.x)return a.xmFtarget(int arr,int ax,int tv,int dim){auto c=buildSegs(arr,ax);sort(c.begin(),c.end(),[tv,dim](const Seg&a,const Seg&b){if(a.len!=b.len)return a.len>b.len;bool ap=(dim==1?a.y==tv:a.x==tv),bp=(dim==1?b.y==tv:b.x==tv);if(ap!=bp)return ap>bp;if(a.x!=b.x)return a.xmFzstart(int arr,int ax){auto c=buildSegs(arr,ax);sort(c.begin(),c.end(),[](const Seg&a,const Seg&b){if(a.len!=b.len)return a.len>b.len;if(a.z!=b.z)return a.zmFtarget2(int arr,int ax,int tv1,int tv2,int dim){auto c=buildSegs(arr,ax);sort(c.begin(),c.end(),[tv1,tv2,dim](const Seg&a,const Seg&b){if(a.len!=b.len)return a.len>b.len;bool ap=(dim==1?(a.y==tv1||a.y==tv2):(a.x==tv1||a.x==tv2)),bp=(dim==1?(b.y==tv1||b.y==tv2):(b.x==tv1||b.x==tv2));if(ap!=bp)return ap>bp;if(a.x!=b.x)return a.xcomputeCP(int arr,int ax,const vector&c){\n int other=1-arr;vectorcp(c.size());\n for(int i=0;i<(int)c.size();i++){const Seg&s=c[i];int cnt=0;\n for(int k=0;kmFcommon(int arr,int ax){\n auto c=buildSegs(arr,ax);auto cp=computeCP(arr,ax,c);\n vectoridx(c.size());iota(idx.begin(),idx.end(),0);\n sort(idx.begin(),idx.end(),[&](int a,int b){if(cp[a]!=cp[b])return cp[a]>cp[b];return c[a].len>c[b].len;});\n vectorsc2;for(int i:idx)sc2.push_back(c[i]);return greedyFill(sc2);}\nvectormFcommonTarget(int arr,int ax,int tv,int dim){\n auto c=buildSegs(arr,ax);auto cp=computeCP(arr,ax,c);\n vectoridx(c.size());iota(idx.begin(),idx.end(),0);\n sort(idx.begin(),idx.end(),[&](int a,int b){\n if(cp[a]!=cp[b])return cp[a]>cp[b];\n bool ap=(dim==1?c[a].y==tv:c[a].x==tv),bp=(dim==1?c[b].y==tv:c[b].x==tv);\n if(ap!=bp)return ap>bp;\n if(c[a].x!=c[b].x)return c[a].xc[b].len;});\n vectorsc2;for(int i:idx)sc2.push_back(c[i]);return greedyFill(sc2);}\nvectormFrandom(int arr,int ax,uint32_t seed){\n auto c=buildSegs(arr,ax);sort(c.begin(),c.end(),[](const Seg&a,const Seg&b){return a.len>b.len;});\n mt19937 rng(seed);int i=0;\n while(i<(int)c.size()){int j=i;while(j<(int)c.size()&&c[j].len==c[i].len)j++;shuffle(c.begin()+i,c.begin()+j,rng);i=j;}\n return greedyFill(c);}\nvectormFrandomCommon(int arr,int ax,uint32_t seed){\n auto c=buildSegs(arr,ax);auto cp=computeCP(arr,ax,c);\n vectoridx(c.size());iota(idx.begin(),idx.end(),0);\n sort(idx.begin(),idx.end(),[&](int a,int b){return cp[a]>cp[b];});\n mt19937 rng(seed);int i=0;\n while(i<(int)idx.size()){int j=i;while(j<(int)idx.size()&&cp[idx[j]]==cp[idx[i]])j++;shuffle(idx.begin()+i,idx.begin()+j,rng);i=j;}\n vectorsc2;for(int ii:idx)sc2.push_back(c[ii]);return greedyFill(sc2);}\nvoid fS(int arr,const Seg&s,int id,int off,int len){for(int k=0;k&F0,const vector&F1){map>g0,g1;for(int i=0;i<(int)F0.size();i++)g0[F0[i].len].push_back(i);for(int i=0;i<(int)F1.size();i++)g1[F1[i].len].push_back(i);vectoru0(F0.size(),false),u1(F1.size(),false);for(auto&[l,v0]:g0){auto it=g1.find(l);if(it==g1.end())continue;auto&v1=it->second;int mc=min((int)v0.size(),(int)v1.size());for(int j=0;j>rv0,rv1;for(int i=0;i<(int)F0.size();i++)if(!u0[i])rv0.push_back({F0[i].len,i});for(int i=0;i<(int)F1.size();i++)if(!u1[i])rv1.push_back({F1[i].len,i});\n auto fillSeg=[&](int arr,const Seg&s,int id,int off,int len){fS(arr,s,id,off,len);};runBestTP(rv0,rv1,F0,F1,fillSeg);}\ndouble cScore(int mb){vectorv0(mb+1,0),v1(mb+1,0);for(int i=0;i0&&v1[k]>0)sc+=1.0/v0[k];else if(v0[k]>0)sc+=v0[k];else sc+=v1[k];}return sc;}\ndouble doMFboxed(const vector&F0,const vector&F1){\n uint16_t f0[14][14]={},f1[14][14]={};\n auto buildF=[&](uint16_t f[14][14],const vector&segs){for(auto&s:segs)for(int k=0;kvector{vectorv;for(int x0=0;x0bool{bool*lo=r?lo1:lo0;for(int i=0;iKey;auto gk=[](const Box&b)->Key{Key k={b.a,b.b,b.c};sort(k.begin(),k.end());return k;};\n map>gb0,gb1;for(int i=0;i<(int)bxs0.size();i++)gb0[gk(bxs0[i])].push_back(i);for(int i=0;i<(int)bxs1.size();i++)gb1[gk(bxs1[i])].push_back(i);\n vector>grps;for(auto&[k,v]:gb0)if(gb1.count(k))grps.push_back({k[0]*k[1]*k[2],k});sort(grps.rbegin(),grps.rend());\n for(auto&[vol,key]:grps){auto&v0=gb0[key];auto&v1=gb1[key];int p1=0;for(int i0:v0){if(!bfL(0,bxs0[i0]))continue;while(p1<(int)v1.size()&&!bfL(1,bxs1[v1[p1]]))p1++;if(p1>=(int)v1.size())break;bid++;fBL(0,bxs0[i0],bid);fBL(1,bxs1[v1[p1++]],bid);}}\n auto getR=[&](bool*lo,uint16_t f[14][14])->vector{vectorsegs;for(int x=0;x=0){segs.push_back({x,y,zs,z-zs,2});zs=-1;}}}return segs;};\n auto rem0=getR(lo0,f0),rem1=getR(lo1,f1);\n map>gr0,gr1;for(int i=0;i<(int)rem0.size();i++)gr0[rem0[i].len].push_back(i);for(int i=0;i<(int)rem1.size();i++)gr1[rem1[i].len].push_back(i);\n vectorur0(rem0.size(),false),ur1(rem1.size(),false);for(auto&[l,v0]:gr0){auto it=gr1.find(l);if(it==gr1.end())continue;auto&v1=it->second;int mc=min((int)v0.size(),(int)v1.size());for(int j=0;j>rv0,rv1;for(int i=0;i<(int)rem0.size();i++)if(!ur0[i])rv0.push_back({rem0[i].len,i});for(int i=0;i<(int)rem1.size();i++)if(!ur1[i])rv1.push_back({rem1[i].len,i});\n auto fillSeg=[&](int arr,const Seg&s,int id,int off,int len){fS(arr,s,id,off,len);};runBestTP(rv0,rv1,rem0,rem1,fillSeg);\n return cScore(bid);}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>D;for(int i=0;i<2;i++){for(int z=0;z>Fs[i][z];for(int z=0;z>Rs[i][z];}\n struct Res{int bid;int B[2][2744];};\n double best=1e18;Res bestR;bestR.bid=0;memset(bestR.B,0,sizeof(bestR.B));\n auto tryIt=[&](auto fn){memset(B,0,sizeof(B));bid=0;double s=fn();if(svector{\n vectorsig(D,0);\n for(int tv=0;tvL0,L1;for(auto&s:F0u)L0.insert(s.len);for(auto&s:F1u)L1.insert(s.len);\n auto F0b=mFbiased(0,a0,L1),F1b=mFbiased(1,a1,L0);\n tryIt([&,F0b,F1b]{doMF(F0b,F1b);return cScore(bid);});\n tryIt([&,F0b,F1b]{return doMFboxed(F0b,F1b);});\n multisetL0b,L1b;for(auto&s:F0b)L0b.insert(s.len);for(auto&s:F1b)L1b.insert(s.len);\n auto F0b2=mFbiased(0,a0,L1b),F1b2=mFbiased(1,a1,L0b);\n tryIt([&,F0b2,F1b2]{doMF(F0b2,F1b2);return cScore(bid);});\n tryIt([&,F0b2,F1b2]{return doMFboxed(F0b2,F1b2);});\n for(int mode=0;mode<2;mode++){\n auto F0s=mFspatial(0,a0,mode),F1s=mFspatial(1,a1,mode);\n tryIt([&,F0s,F1s]{doMF(F0s,F1s);return cScore(bid);});\n tryIt([&,F0s,F1s]{return doMFboxed(F0s,F1s);});\n auto F0bs=mFbiasedSpatial(0,a0,L1,mode),F1bs=mFbiasedSpatial(1,a1,L0,mode);\n tryIt([&,F0bs,F1bs]{return doMFboxed(F0bs,F1bs);});}\n for(int tv=0;tv>>pairs;\n for(int tv0=0;tv00)\n pairs.push_back({sig0[tv0],{tv0,tv1}});}\n sort(pairs.rbegin(),pairs.rend());\n int K=min((int)pairs.size(),5);\n for(int k=0;k\nusing namespace std;\ntypedef long long ll;\nint main() {\n auto tStart = chrono::steady_clock::now();\n auto msElapsed = [&]() { return (int)chrono::duration_cast(chrono::steady_clock::now()-tStart).count(); };\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int N,M,K; cin>>N>>M>>K;\n vector X(N),Y(N); for(int i=0;i>X[i]>>Y[i];\n vector EU(M),EV(M); vector EW(M);\n for(int j=0;j>EU[j]>>EV[j]>>EW[j];EU[j]--;EV[j]--;}\n vector A(K),B(K); for(int k=0;k>A[k]>>B[k];\n const ll MAXP=5000,MAXP2=MAXP*MAXP,INF=(ll)4e18;\n vector> D2(N,vector(K)),D2T(K,vector(N));\n for(int i=0;i>> adj(N);\n for(int j=0;jll{if(!d2)return 0;ll p=(ll)sqrt((double)d2);while(p*p> spD(N,vector(N,INF)); vector> spE(N,vector(N,-1)),spPr(N,vector(N,-1));\n for(int s=0;s,vector>,greater<>>pq;pq.push({0,s});\n while(!pq.empty()){auto[d,v]=pq.top();pq.pop();if(d>spD[s][v])continue;\n for(auto&[u,j]:adj[v]){ll nd=d+EW[j];if(nd term)->vector{\n term[0]=true;vectorT;for(int i=0;iin(TN,false);vectorkey(TN,INF);vectorpar(TN,-1);key[0]=0;\n for(int it=0;it=INF)break;in[u]=true;\n for(int w=0;weo(M,false);\n for(int i=0;i&reach,bool with2c=false)->pair,ll>{\n vector>vR(N);vectorvMx(N,0);\n for(int k=0;kMAXP2)return{{},INF};vR[bv].push_back(k);vMx[bv]=max(vMx[bv],best);}\n vectorPv(N,0);for(int i=0;itp(N);\n for(int u=0;utp[u].d[0]){tp[u].d[4]=tp[u].d[3];tp[u].k[4]=tp[u].k[3];tp[u].d[3]=tp[u].d[2];tp[u].k[3]=tp[u].k[2];tp[u].d[2]=tp[u].d[1];tp[u].k[2]=tp[u].k[1];tp[u].d[1]=tp[u].d[0];tp[u].k[1]=tp[u].k[0];tp[u].d[0]=d;tp[u].k[0]=k;}\n else if(d>tp[u].d[1]){tp[u].d[4]=tp[u].d[3];tp[u].k[4]=tp[u].k[3];tp[u].d[3]=tp[u].d[2];tp[u].k[3]=tp[u].k[2];tp[u].d[2]=tp[u].d[1];tp[u].k[2]=tp[u].k[1];tp[u].d[1]=d;tp[u].k[1]=k;}\n else if(d>tp[u].d[2]){tp[u].d[4]=tp[u].d[3];tp[u].k[4]=tp[u].k[3];tp[u].d[3]=tp[u].d[2];tp[u].k[3]=tp[u].k[2];tp[u].d[2]=d;tp[u].k[2]=k;}\n else if(d>tp[u].d[3]){tp[u].d[4]=tp[u].d[3];tp[u].k[4]=tp[u].k[3];tp[u].d[3]=d;tp[u].k[3]=k;}\n else if(d>tp[u].d[4]){tp[u].d[4]=d;tp[u].k[4]=k;}}}\n ll bD=0;int bU=-1,bV=-1,bT=-1;\n for(int u=0;u=0){ll d1v=D2T[tp[u].k[1]][v];if(d1v<=MAXP2){ll nPu=pVal(tp[u].d[2]),nPv=pVal(max({vMx[v],d0v,d1v}));ll dd=nPu*nPu+nPv*nPv-Pu2-Pv2;if(dd=0){ll d1v=D2T[tp[u].k[1]][v],d2v=D2T[tp[u].k[2]][v];if(d1v<=MAXP2&&d2v<=MAXP2){ll nPu=pVal(tp[u].d[3]),nPv=pVal(max({vMx[v],d0v,d1v,d2v}));ll dd=nPu*nPu+nPv*nPv-Pu2-Pv2;if(dd=0){ll d1v=D2T[tp[u].k[1]][v],d2v=D2T[tp[u].k[2]][v],d3v=D2T[tp[u].k[3]][v];if(d1v<=MAXP2&&d2v<=MAXP2&&d3v<=MAXP2){ll nPu=pVal(tp[u].d[4]),nPv=pVal(max({vMx[v],d0v,d1v,d2v,d3v}));ll dd=nPu*nPu+nPv*nPv-Pu2-Pv2;if(ddu&&f0&&tp[v].k[0]>=0){ll d0u=D2T[tp[v].k[0]][u];if(d0u<=MAXP2){ll nMxU=max(tp[u].d[1],d0u),nMxV=max(tp[v].d[1],d0v);ll nPu=pVal(nMxU),nPv=pVal(nMxV);ll dd=nPu*nPu+nPv*nPv-Pu2-Pv2;if(ddcan;ll fmU=0,fmV=0;vectormustU,mustV;\n for(int k:vR[u]){ll dv=D2T[k][v];if(dv<=MAXP2)can.push_back({D2T[k][u],dv,k});else{fmU=max(fmU,D2T[k][u]);mustU.push_back(k);}}\n for(int k:vR[v]){ll du=D2T[k][u];if(du<=MAXP2)can.push_back({du,D2T[k][v],k});else{fmV=max(fmV,D2T[k][v]);mustV.push_back(k);}}\n if((int)can.size()<2)continue;\n int m=can.size();\n ll bestC=Pv[u]*Pv[u]+Pv[v]*Pv[v];int bestT=-1;bool sortDv=false;\n // Direction 1: sort by du (first t\u2192u)\n sort(can.begin(),can.end(),[](const Res&a,const Res&b){return a.dusfDv(m+1,fmV);for(int i=m-1;i>=0;i--)sfDv[i]=max(sfDv[i+1],can[i].dv);\n ll mxU=fmU;for(int t=0;t<=m;t++){if(sfDv[t]<=MAXP2){ll pu=pVal(mxU),pv=pVal(sfDv[t]);ll c=pu*pu+pv*pv;if(csfDu(m+1,fmU);for(int i=m-1;i>=0;i--)sfDu[i]=max(sfDu[i+1],can[i].du);\n ll mxV=fmV;for(int t=0;t<=m;t++){if(sfDu[t]<=MAXP2){ll pu=pVal(sfDu[t]),pv=pVal(mxV);ll c=pu*pu+pv*pv;if(cP(N,0);for(int i=0;i&eo)->tuple,ll,bool>{\n vectorreach(N,false);queueq;q.push(0);reach[0]=true;\n while(!q.empty()){int v=q.front();q.pop();for(auto&[u,j]:adj[v])if(eo[j]&&!reach[u]){reach[u]=true;q.push(u);}}\n ll ec=0;for(int j=0;jmstPar(N,-1),mstPE(N,-1);vector>mstCh(N);\n {vectorvis(N,false);vectorkey(N,INF);key[0]=0;priority_queue,vector>,greater<>>pq;pq.push({0,0});\n while(!pq.empty()){auto[d,v]=pq.top();pq.pop();if(vis[v])continue;vis[v]=true;for(auto&[u,j]:adj[v])if(!vis[u]&&EW[j]act(N,true);vector>vRes(N);vectorvmx(N,0),Pv(N,0);\n for(int k=0;k>bAs;vector>bAf;\n for(int v=1;vtmp;vector>ta;bool ok=true;\n for(int k:vRes[v]){ll best=INF;int bu=-1;for(int u=0;uMAXP2){ok=false;break;}ta.push_back({k,bu});if(!tmp.count(bu))tmp[bu]=vmx[bu];tmp[bu]=max(tmp[bu],best);}\n if(!ok)continue;for(auto&[u,nd]:tmp){ll np=pVal(nd);delta+=np*np-Pv[u]*Pv[u];}\n if(delta=0){act[bV]=false;ec0-=EW[mstPE[bV]];pc0-=Pv[bV]*Pv[bV];Pv[bV]=0;vmx[bV]=0;vRes[bV].clear();\n for(auto&[k,u]:bAs)vRes[u].push_back(k);\n for(auto&[u,nd]:bAf){pc0-=Pv[u]*Pv[u];vmx[u]=nd;Pv[u]=pVal(nd);pc0+=Pv[u]*Pv[u];}imp2=true;}}\n ll bestCost=INF;vectorbestEO(M,false);vectorbestP(N,0);\n auto updateBest=[&](const vector&eo,const vector&P,ll cost){if(costeo(M,false);for(int v=1;vterm,int maxIt=20){term[0]=true;\n for(int sit=0;sitnt(N,false);nt[0]=true;for(int i=0;i0)nt[i]=true;if(nt==term)break;term=nt;}};\n {vectort(N,false);for(int i=0;i0)t[i]=true;runSteiner(t);}\n {vectort(N,true);runSteiner(t);}\n auto getTerms=[&]()->vector{vectort(N,false);t[0]=true;for(int i=0;i0)t[i]=true;return t;};\n vectorvPri(N,0);bool sysImp=true;\n while(sysImp&&msElapsed()<1850){sysImp=false;vectorcurT=getTerms();\n vectorntd(K,INF);for(int k=0;k,int>>addV,remV;\n for(int v=1;v1850)break;if(curT[v])continue;vectort=curT;t[v]=true;auto eo=buildSteiner(t);auto[sp,sc,sf]=evalEO(eo);if(sf&&sc1850)break;if(!curT[v])continue;vectort=curT;t[v]=false;auto eo=buildSteiner(t);auto[sp,sc,sf]=evalEO(eo);if(sf&&sccurT=getTerms();\n vectorntd(K,INF);for(int k=0;k>addC,remC;\n for(int v=1;vt=curT;t[v1]=true;t[v2]=true;auto eo=buildSteiner(t);auto[sp,sc,sf]=evalEO(eo);if(sf&&sct=curT;t[v1]=false;t[v2]=false;auto eo=buildSteiner(t);auto[sp,sc,sf]=evalEO(eo);if(sf&&sct=curT;t[v1]=true;t[v2]=false;auto eo=buildSteiner(t);auto[sp,sc,sf]=evalEO(eo);if(sf&&screach(N,false);queueq;q.push(0);reach[0]=true;\n while(!q.empty()){int v=q.front();q.pop();for(auto&[u,j]:adj[v])if(bestEO[j]&&!reach[u]){reach[u]=true;q.push(u);}}\n ll ec=0;for(int j=0;jcurT=getTerms();int loopIt=0;bool cont=true;\n while(cont&&loopIt++<100&&msElapsed()<1850){cont=false;\n auto eo=buildSteiner(curT);vectorreach(N,false);queueq;q.push(0);reach[0]=true;\n while(!q.empty()){int v=q.front();q.pop();for(auto&[u,j]:adj[v])if(eo[j]&&!reach[u]){reach[u]=true;q.push(u);}}\n ll ec=0;for(int j=0;jnewT(N,false);newT[0]=true;for(int i=0;i0)newT[i]=true;\n if(newT==curT)break;curT=newT;cont=true;}}\n for(int i=0;i\nusing namespace std;\nconst int N = 30;\nint init_board[N][N], board[N][N];\nvoid sift(int cx,int cy,vector>&ops){\n while(cx>&ops){\n memcpy(board,init_board,sizeof(board));ops.clear();int ys[N];\n for(int x=N-2;x>=0;x--){for(int y=0;y<=x;y++)ys[y]=y;\n if(mode==4||mode==5){bool done[N]={};bool mkbig=(mode==4);\n for(int p=0;p<=x;p++){int by=-1,bv=mkbig?INT_MIN:INT_MAX;\n for(int y=0;y<=x;y++)if(!done[y]){int val=board[x][y]-min(board[x+1][y],board[x+1][y+1]);if(mkbig?val>bv:valboard[x][b];});break;\n default:if(rng)for(int i=x;i>0;i--)swap(ys[i],ys[(*rng)()%(i+1)]);break;}\n for(int i=0;i<=x;i++)sift(x,ys[i],ops);}}}\n// Try extension from given (lx,ly) position\nbool try_extend(int lx,int ly,vector>&prefix,vector>&best,\n vector>&v,vector>&bv_saved){\n int p6[6][4]={{lx,ly,lx,ly+1},{lx,ly,lx+1,ly},{lx,ly,lx+1,ly+1},\n {lx,ly-1,lx,ly},{lx-1,ly-1,lx,ly},{lx-1,ly,lx,ly}};\n int ex1=-1,ey1=-1,ex2=-1,ey2=-1;size_t ext_cand=best.size();\n for(auto&p:p6){int x1=p[0],y1=p[1],x2=p[2],y2=p[3];\n if(x1<0||x1>=N||y1<0||y1>x1||x2<0||x2>=N||y2<0||y2>x2)continue;\n swap(init_board[x1][y1],init_board[x2][y2]);\n for(int m:{0,2,3,4}){do_heapify(nullptr,m,v);size_t cand=prefix.size()+1+v.size();\n if(cand(chrono::steady_clock::now()-t0).count();};\n for(int x=0;x>init_board[x][y];\n mt19937 rng(42);\n vector>best,v,bv_saved;\n best.reserve(6000);v.reserve(6000);bv_saved.reserve(6000);\n vector>prefix;prefix.reserve(100);\n auto upd=[&](vector>&ops_v){\n if(prefix.size()+ops_v.size()1400)break;\n int bx1=-1,by1=-1,bx2=-1,by2=-1;size_t best_cand=best.size();\n for(int x1=0;x1=N||y2>x2)continue;\n swap(init_board[x1][y1],init_board[x2][y2]);\n for(int m:{0,2,3,4}){do_heapify(nullptr,m,v);size_t cand=prefix.size()+1+v.size();\n if(cand\nusing namespace std;\nconst int MAXD=9;\nint D,N,M,er,ec;bool obs[MAXD][MAXD],hasc[MAXD][MAXD];\nint cnum[MAXD][MAXD],sr[MAXD*MAXD],sc[MAXD*MAXD],pk[MAXD][MAXD];\nconst int DR[4]={-1,1,0,0},DC[4]={0,0,-1,1};\nbool np[MAXD*MAXD]={};\nbool in_(int r,int c){return(unsigned)r<(unsigned)D&&(unsigned)c<(unsigned)D;}\nvoid build_sigma(){int dist[MAXD][MAXD];memset(dist,-1,sizeof dist);queue>q;q.push({er,ec});dist[er][ec]=0;while(!q.empty()){auto[x,y]=q.front();q.pop();for(int i=0;i<4;i++){int nx=x+DR[i],ny=y+DC[i];if(!in_(nx,ny)||dist[nx][ny]>=0||obs[nx][ny])continue;dist[nx][ny]=dist[x][y]+1;q.push({nx,ny});}}vector>pos;for(int r=0;r&a,const pair&b){if(dist[a.first][a.second]!=dist[b.first][b.second])return dist[a.first][a.second]1)ga[r][c]=true;if(pr!=-1&&gl[nr][nc]>=gd[r][c])ga[r][c]=true;}else if(!(nr==pr&&nc==pc))gl[r][c]=min(gl[r][c],gd[nr][nc]);}}\nint sgd2[MAXD][MAXD],sgl3[MAXD][MAXD],sgT3;bool sga3[MAXD][MAXD];\nvoid sapdfs(int r,int c,int pr,int pc,bool sh[MAXD][MAXD]){sgd2[r][c]=sgl3[r][c]=sgT3++;int ch=0;for(int i=0;i<4;i++){int nr=r+DR[i],nc=c+DC[i];if(!in_(nr,nc)||obs[nr][nc]||sh[nr][nc])continue;if(sgd2[nr][nc]==-1){ch++;sapdfs(nr,nc,r,c,sh);sgl3[r][c]=min(sgl3[r][c],sgl3[nr][nc]);if(pr==-1&&ch>1)sga3[r][c]=true;if(pr!=-1&&sgl3[nr][nc]>=sgd2[r][c])sga3[r][c]=true;}else if(!(nr==pr&&nc==pc))sgl3[r][c]=min(sgl3[r][c],sgd2[nr][nc]);}}\npairplace_sim_v1(int v,bool sh[MAXD][MAXD]){memset(sgd2,-1,sizeof sgd2);memset(sgl3,-1,sizeof sgl3);memset(sga3,0,sizeof sga3);sgT3=0;sapdfs(er,ec,-1,-1,sh);int ir=sr[v],ic=sc[v];if(sgd2[ir][ic]>=0&&!sga3[ir][ic])return{ir,ic};pairb={-1,-1};int bd=INT_MAX,brk=-1;bool gots=false;for(int r=0;rbrk)));if(better){b={r,c};bd=d;brk=rk;gots=s;}}return b;}\nvoid bfsr(bool st[MAXD][MAXD],bool reach[MAXD][MAXD]){static pairQ[MAXD*MAXD];memset(reach,0,MAXD*MAXD*sizeof(bool));int h=0,t=0;Q[t++]={er,ec};reach[er][ec]=true;while(h&fut,int tv,int tr,int tc){bool sh[MAXD][MAXD];memcpy(sh,sh0,sizeof sh);int sc2[MAXD][MAXD];memcpy(sc2,sc0,sizeof sc2);sh[tr][tc]=true;sc2[tr][tc]=tv;for(int v:fut){auto[r,c]=place_sim_v1(v,sh);if(r<0)continue;sh[r][c]=true;sc2[r][c]=v;}int bit[MAXD*MAXD+2]={};auto upd=[&](int v){for(v++;v<=M;v+=v&-v)bit[v]++;};auto qry=[&](int v){int s=0;for(v++;v>0;v-=v&-v)s+=bit[v];return s;};int inv=0,n=0;bool h2[MAXD][MAXD];memcpy(h2,sh,sizeof h2);for(int s=0;s=0&&sga3[nr][nc]&&!ga[nr][nc])return true;return false;}\npairpick(int t){\n memset(gd,-1,sizeof gd);memset(gl,-1,sizeof gl);memset(ga,0,sizeof ga);gT=0;apdfs(er,ec,-1,-1);\n int ir=sr[t],ic=sc[t];\n bool ideal_safe=(gd[ir][ic]>=0&&!ga[ir][ic]);\n if(ideal_safe&&!any_new_ap_if_place(ir,ic))return{ir,ic};\n vector>safe;for(int r=0;r=0&&!(r==er&&c==ec)&&!ga[r][c])safe.emplace_back(r,c);\n if(safe.empty())for(int r=0;r=0&&!(r==er&&c==ec))safe.emplace_back(r,c);\n sort(safe.begin(),safe.end(),[&](const pair&a,const pair&b){int da=abs(pk[a.first][a.second]-t),db=abs(pk[b.first][b.second]-t);if(da!=db)return dapk[b.first][b.second];});\n vectorunplaced;unplaced.reserve(M);for(int v=0;vtotals(K_pos,0);vectorfut=unplaced;\n for(int trial=0;trialb;});\n else shuffle(fut.begin(),fut.end(),rng_s);\n for(int pi=0;pibp=safe[0];\n for(int pi=0;pi&prefix,int limit){bool h[MAXD][MAXD];memcpy(h,hin,sizeof h);int bit[MAXD*MAXD+2]={};auto upd=[&](int v){for(v++;v<=M;v+=v&-v)bit[v]++;};auto qry=[&](int v){int s=0;for(v++;v>0;v-=v&-v)s+=bit[v];return s;};int inv=0,n=0;for(int v:prefix){inv+=n-qry(v);upd(v);n++;if(inv>limit)return limit+1;}while(inv<=limit){bool reach[MAXD][MAXD];bfsr(h,reach);int bn=INT_MAX,br=-1,bc=-1;for(int r=0;rlimit)return limit+1;}return inv;}\nvector>transport(){bool h[MAXD][MAXD];memcpy(h,hasc,sizeof h);vector>ord;ord.reserve(M);vectorcommitted;for(int s=0;s>acc;for(int r=0;rbest_pos={mr,mc};if(acc.size()==1){committed.push_back(mn);ord.emplace_back(mr,mc);h[mr][mc]=false;continue;}bool hg[MAXD][MAXD];memcpy(hg,h,sizeof hg);hg[mr][mc]=false;vectorsg=committed;sg.push_back(mn);int best_inv=sim_inv(hg,sg,M*(M-1)/2);if(best_inv>0){for(auto&[nx,rx,cx]:acc){if(nx==mn)continue;bool h2[MAXD][MAXD];memcpy(h2,h,sizeof h2);h2[rx][cx]=false;vectorsx=committed;sx.push_back(nx);int inv_x=sim_inv(h2,sx,best_inv-1);if(inv_x>D>>N;memset(obs,false,sizeof obs);memset(hasc,false,sizeof hasc);memset(cnum,-1,sizeof cnum);memset(np,false,sizeof np);er=0;ec=(D-1)/2;for(int i=0;i>r>>c;obs[r][c]=true;}build_sigma();for(int d=0;d>t;auto[r,c]=pick(t);hasc[r][c]=true;cnum[r][c]=t;np[t]=true;cout<\nusing namespace std;using namespace chrono;\nint n,m,g[50][50],og[50][50];bool adj[102][102];\nint ac[102][102],cc[102],dp[102];bool ic[2500];\nconst int dr[]={0,0,1,-1},dc[]={1,-1,0,0};\nauto t0=steady_clock::now();\nint TL=1400;\nbool tok(){return duration_cast(steady_clock::now()-t0).count()=n||c<0||c>=n)?0:g[r][c];}\nvoid cajad(){memset(adj,0,sizeof(adj));for(int i=0;iq;for(int c=0;c<=m;c++)if(adj[c][0]){dp[c]=0;q.push(c);}dp[0]=0;while(!q.empty()){int u=q.front();q.pop();for(int v=1;v<=m;v++)if(adj[u][v]&&dp[v]>dp[u]+1){dp[v]=dp[u]+1;q.push(v);}}}\nvoid rcp(){memset(ac,0,sizeof(ac));memset(cc,0,sizeof(cc));for(int i=0;i>q;q.push({sr,sc});v[sr][sc]=1;int cnt=1;while(!q.empty()){auto[cr,cc2]=q.front();q.pop();for(int d=0;d<4;d++){int nr=cr+dr[d],nc=cc2+dc[d];if(nr>=0&&nr=0&&nc=0&&nr=0&&nc=2&&!cok(r,c,col))return 0;for(int d=0;d<4;d++){int nc=gc(r+dr[d],c+dc[d]);if(nc&&nc!=col&&ac[col][nc]<=1)return 0;}return 1;}\nvoid dtr(int r,int c){ic[r*n+c]=0;int col=g[r][c];bool s[102]={};for(int d=0;d<4;d++){int nc=gc(r+dr[d],c+dc[d]);if(nc!=col&&!s[nc]){ac[col][nc]--;s[nc]=1;}}g[r][c]=0;cc[col]--;cc[0]++;for(int d=0;d<4;d++){int nr=r+dr[d],nc=c+dc[d];if(nr<0||nr>=n||nc<0||nc>=n)continue;int ncol=g[nr][nc];if(!ncol)continue;bool hz=0;for(int d2=0;d2<4;d2++){int nr2=nr+dr[d2],nc2=nc+dc[d2];if(nr2==r&&nc2==c)continue;if(nr2<0||nr2>=n||nc2<0||nc2>=n){hz=1;break;}if(!g[nr2][nc2]){hz=1;break;}}if(!hz)ac[ncol][0]++;if(ncol==col)continue;bool sc2=0;for(int d2=0;d2<4;d2++){int nr2=nr+dr[d2],nc2=nc+dc[d2];if(nr2==r&&nc2==c)continue;if(nr2>=0&&nr2=0&&nc2=n||c<0||c>=n||!g[r][c])return;int idx=r*n+c;if(!gbi[idx]){gbi[idx]=1;gbq[qt++]=idx;}};\n for(int i=0;i=0&&nr=0&&nc=n||nc<0||nc>=n)continue;int ncol=g[nr][nc];if(!ncol)continue;if(ncol!=col){bool st=0;for(int d2=0;d2<4;d2++){int nr2=nr+dr[d2],nc2=nc+dc[d2];if(nr2==r&&nc2==c)continue;if(nr2>=0&&nr2=0&&nc2=0&&nr2=0&&nc2=2&&!cok(r,c,col))return 0;int best=-1,bd=dp[col]+1;for(int d=0;d<4;d++){int nr=r+dr[d],nc=c+dc[d];if(nr<0||nr>=n||nc<0||nc>=n)continue;int c2=g[nr][nc];if(!c2||c2==col||dp[c2]>dp[col])continue;bool ok=1;for(int d2=0;d2<4;d2++){int dc2=gc(r+dr[d2],c+dc[d2]);if(dc2&&dc2!=col&&dc2!=c2&&!adj[c2][dc2]){ok=0;break;}}if(!ok)continue;ok=1;for(int d2=0;d2<4;d2++){int dc2=gc(r+dr[d2],c+dc[d2]);if(dc2&&dc2!=col&&dc2!=c2&&ac[col][dc2]<=1){ok=0;break;}}if(!ok)continue;if(dp[c2]=0){co=best;return 1;}return 0;}\nint czero(){int c=0;for(int i=0;i&ord){rcp();gtrim();int pz=czero();while(tok()){rcp();for(int p=0;p<15;p++){bool a=0;for(int idx:ord){if(!ic[idx])continue;int i=idx/n,j=idx%n,col=g[i][j],co;if(!col||adj[col][0]){ic[idx]=0;continue;}if(cra(i,j,co)){dra(i,j,col,co);a=1;}}if(!a)break;}gtrim();int z=czero();if(z<=pz)break;pz=z;}}\nint mg[50][50],mac[102][102],mcc[102];\nbool wconn(int W){int sr=-1,sc_=-1,wc=0;for(int a=0;a>q;q.push({sr,sc_});v[sr][sc_]=1;int cnt=1;while(!q.empty()){auto[cr,c2]=q.front();q.pop();for(int d=0;d<4;d++){int nr=cr+dr[d],nc=c2+dc[d];if(nr>=0&&nr=0&&nc=n||nj<0||nj>=n)continue;\n int E=g[ni][nj];if(!E||!adj[E][0]||!adj[I][E])continue;\n bool bad=false;for(int d2=0;d2<4;d2++){int a2=ni+dr[d2],b2=nj+dc[d2];if(a2==i&&b2==j)continue;if(a2<0||a2>=n||b2<0||b2>=n||!g[a2][b2]){bad=true;break;}}\n if(!bad){\n int sz=czero();memcpy(mg,g,sizeof(g));memcpy(mac,ac,sizeof(ac));memcpy(mcc,cc,sizeof(cc));\n dra(ni,nj,E,I);dra(i,j,I,E);\n if(wconn(E)){rcp();bool vd=true;for(int a=1;a<=m&&vd;a++){if(adj[a][0]!=(ac[a][0]>0))vd=false;for(int b=1;b0))vd=false;}if(vd)for(int w=1;w<=m&&vd;w++)if(!wconn(w))vd=false;if(vd){gtrim();if(czero()>sz)continue;}}\n memcpy(g,mg,sizeof(g));memcpy(ac,mac,sizeof(ac));memcpy(cc,mcc,sizeof(cc));\n }\n for(int d12=0;d12<4;d12++){\n int r2=ni+dr[d12],c2=nj+dc[d12];if(r2<0||r2>=n||c2<0||c2>=n||(r2==i&&c2==j))continue;\n int E2=g[r2][c2];if(!E2||!adj[E2][0]||!adj[I][E2]||E2==I)continue;\n bool bad2=false;for(int d2=0;d2<4;d2++){int a2=r2+dr[d2],b2=c2+dc[d2];if(a2==ni&&b2==nj)continue;if(a2<0||a2>=n||b2<0||b2>=n||!g[a2][b2]){bad2=true;break;}}\n if(bad2)continue;\n int sz=czero();memcpy(mg,g,sizeof(g));memcpy(mac,ac,sizeof(ac));memcpy(mcc,cc,sizeof(cc));\n dra(ni,nj,E,I);dra(i,j,I,E);dra(r2,c2,E2,I);dra(ni,nj,I,E2);\n if(wconn(E)&&wconn(E2)){rcp();bool vd=true;for(int a=1;a<=m&&vd;a++){if(adj[a][0]!=(ac[a][0]>0))vd=false;for(int b=1;b0))vd=false;}if(vd)for(int w=1;w<=m&&vd;w++)if(!wconn(w))vd=false;if(vd){gtrim();if(czero()>sz)continue;}}\n memcpy(g,mg,sizeof(g));memcpy(ac,mac,sizeof(ac));memcpy(cc,mcc,sizeof(cc));\n }\n }\n }\n}\nstatic int tg[50][50],tac[102][102],tcc[102];\nvoid teleport_micro_opt(){\n bool improved=true;\n while(improved&&tok()){\n improved=false;\n for(int i=0;i5)continue;\n int ni=i+dr2,nj=j+dc2;if(ni<0||ni>=n||nj<0||nj>=n)continue;\n int E=g[ni][nj];\n if(!E||!adj[I][E])continue; // Removed adj[E][0] requirement - allows interior\u2192interior swaps\n bool bad=false;\n for(int d2=0;d2<4;d2++){\n int a2=ni+dr[d2],b2=nj+dc[d2];\n if(a2<0||a2>=n||b2<0||b2>=n||!g[a2][b2]){bad=true;break;}\n }\n if(bad)continue;\n memcpy(tg,g,sizeof(g));memcpy(tac,ac,sizeof(ac));memcpy(tcc,cc,sizeof(cc));\n dra(ni,nj,E,I);dra(i,j,I,E);\n rcp();bool valid=true;\n for(int a=1;a<=m&&valid;a++){\n if(adj[a][0]!=(ac[a][0]>0))valid=false;\n for(int b=1;b0))valid=false;\n }\n if(valid)for(int w=1;w<=m&&valid;w++)if(!wconn(w))valid=false;\n if(valid){gtrim();if(czero()>sz){found=true;improved=true;break;}}\n memcpy(g,tg,sizeof(g));memcpy(ac,tac,sizeof(ac));memcpy(cc,tcc,sizeof(cc));\n }\n }\n }\n }\n}\nstatic int bg[50][50];int bz=-1;\nvoid sv(){int z=czero();if(z>bz){bz=z;memcpy(bg,g,sizeof(g));}}\nvector centroid_last_ord(){\n vectorcx(102,0),cy(102,0);vectorcnt(102,0);\n for(int i=0;icidx(102,-1);vectorbd(102,1e18);\n for(int i=0;i,int>>keys;\n for(int i=0;iord;for(auto&[k,idx]:keys)ord.push_back(idx);return ord;\n}\nint main(){\n t0=steady_clock::now();ios_base::sync_with_stdio(0);cin.tie(0);\n cin>>n>>m;for(int i=0;i>g[i][j];og[i][j]=g[i][j];}\n cajad();cdep();mt19937 rng(42);\n // Phase 1: Multiple trials\n TL=1400;\n for(int trial=0;trial==0||tok();trial++){\n memcpy(g,og,sizeof(g));init_ic();\n vectorord(n*n);iota(ord.begin(),ord.end(),0);\n if(trial==1)reverse(ord.begin(),ord.end());\n else if(trial==2){for(int j2=0;j2abs(b/n-cx)+abs(b%n-cy);});}\n else if(trial==4){int cx=n/2,cy=n/2;sort(ord.begin(),ord.end(),[&](int a,int b){return abs(a/n-cx)+abs(a%n-cy)=0;i--)for(int j=0;j=0;j--)ord[k++]=i*n+j;}\n else shuffle(ord.begin(),ord.end(),rng);\n run(ord);micro_opt();sv();\n }\n // Phase 2: Post-processing on best result with extended time\n if(bz>0){\n TL=1900; // Extend time limit for post-processing\n memcpy(g,bg,sizeof(g));\n for(int i=0;i0&&!adj[g[i][j]][0]);\n rcp();\n teleport_micro_opt(); // Distance 1-5, any adjacent ward (incl. interior)\n micro_opt(); // 1-2 step moves\n vectorord0(n*n);iota(ord0.begin(),ord0.end(),0);\n run(ord0); // Additional reassignment + trim\n sv();\n }\n for(int i=0;i\nusing namespace std;\nint N, D, Q, q_used = 0;\nchar bq(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; q_used++;\n char c; cin >> c; return c;\n}\nint slm;\nvector ms(vector a) {\n if ((int)a.size() <= 1 || q_used >= slm) return a;\n int m = a.size() / 2;\n auto L = ms(vector(a.begin(), a.begin() + m));\n auto R = ms(vector(a.begin() + m, a.end()));\n vector r; int i = 0, j = 0;\n while (i < (int)L.size() && j < (int)R.size()) {\n if (q_used >= slm) break;\n if (bq({L[i]}, {R[j]}) != '>') r.push_back(L[i++]);\n else r.push_back(R[j++]);\n }\n while (i < (int)L.size()) r.push_back(L[i++]);\n while (j < (int)R.size()) r.push_back(R[j++]);\n return r;\n}\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(nullptr);\n cin >> N >> D >> Q;\n auto t0 = chrono::high_resolution_clock::now();\n auto el = [&]() { return chrono::duration(chrono::high_resolution_clock::now() - t0).count(); };\n slm = Q / 2;\n vector ini(N); iota(ini.begin(), ini.end(), 0);\n vector ord = ms(ini);\n vector pos(N);\n for (int i = 0; i < N; i++) pos[ord[i]] = i;\n int est_end = Q * 4 / 5;\n vector w(N, 1.0), ps(N + 1, 0.0);\n w[ord[0]] = 1.0; ps[1] = 1.0;\n for (int i = 1; i < N; i++) {\n if (q_used >= est_end) { w[ord[i]] = w[ord[i-1]]; ps[i+1] = ps[i] + w[ord[i]]; continue; }\n int lo = 0, hi = i;\n while (lo < hi && q_used < est_end) {\n int mid = (lo + hi) / 2;\n if (bq({ord[i]}, vector(ord.begin(), ord.begin() + mid + 1)) == '>') lo = mid + 1;\n else hi = mid;\n }\n double wlo = ps[lo], whi = (lo < i) ? ps[lo + 1] : ps[i] * 2.0;\n w[ord[i]] = max(w[ord[i-1]], (wlo + whi) / 2.0);\n ps[i+1] = ps[i] + w[ord[i]];\n }\n vector oi(N); iota(oi.begin(), oi.end(), 0);\n sort(oi.begin(), oi.end(), [&](int a, int b) { return fabs(w[a]-w[b]) > 1e-12 ? w[a] > w[b] : pos[a] > pos[b]; });\n vector gw(D, 0.0); vector asgn(N, 0);\n for (int x : oi) { int g = (int)(min_element(gw.begin(), gw.end()) - gw.begin()); asgn[x] = g; gw[g] += w[x]; }\n double total = 0; for (double x : gw) total += x;\n double mean = total / D;\n for (int p = 0; p < 5000 && el() < 1.5; p++) {\n bool imp = false;\n for (int x = 0; x < N; x++) {\n int g0 = asgn[x]; int bg = g0; double bd = 0, d0 = gw[g0] - mean;\n for (int g = 0; g < D; g++) {\n if (g == g0) continue;\n double d1 = gw[g] - mean;\n double dc = d0*d0 + d1*d1 - (d0-w[x])*(d0-w[x]) - (d1+w[x])*(d1+w[x]);\n if (dc > bd) { bd = dc; bg = g; }\n }\n if (bg != g0) { gw[g0] -= w[x]; gw[bg] += w[x]; asgn[x] = bg; imp = true; }\n }\n for (int i = 0; i < N && el() < 1.45; i++) for (int j = i+1; j < N; j++) {\n if (asgn[i] == asgn[j]) continue;\n int g1 = asgn[i], g2 = asgn[j];\n double d1 = gw[g1]-mean, d2 = gw[g2]-mean, d1n = d1-w[i]+w[j], d2n = d2+w[i]-w[j];\n if (d1*d1 + d2*d2 > d1n*d1n + d2n*d2n + 1e-9) {\n gw[g1] += w[j]-w[i]; gw[g2] += w[i]-w[j]; asgn[i] = g2; asgn[j] = g1; imp = true;\n }\n }\n if (!imp) break;\n }\n vector> gi(D);\n for (int x = 0; x < N; x++) gi[asgn[x]].push_back(x);\n for (int g = 0; g < D; g++) sort(gi[g].begin(), gi[g].end(), [&](int a, int b){ return pos[a] < pos[b]; });\n auto cpos = [&](int a, int b){ return pos[a] < pos[b]; };\n // Phase 5: Always run rank-list approach (Phase 5a removed)\n {\n vector grank;\n for (int g = 0; g < D; g++) if (!gi[g].empty()) grank.push_back(g);\n int ng = (int)grank.size();\n if (ng >= 2) {\n function mgsort=[&](int lo,int hi){\n if(hi-lo<=1||q_used>=Q) return;\n int mid=(lo+hi)/2; mgsort(lo,mid); mgsort(mid,hi);\n vector tmp; int i=lo,j=mid;\n while(i=2&&q_used+8<=Q&&el()<1.9){\n while(ng>0&&gi[grank[0]].empty()){grank.erase(grank.begin());ng--;}\n while(ng>0&&gi[grank[ng-1]].empty()){grank.pop_back();ng--;}\n if(ng<2) break;\n int gh=grank[0],gl=grank[ng-1];\n char cmp=bq(gi[gh],gi[gl]);\n if(cmp=='='){if(++eqst>=3) break;continue;} eqst=0;\n if(cmp=='<'){\n int mx=grank[0];\n for(int i=1;i=1&&q_used') mn=grank[i];}\n if(mn!=-1){auto it2=find(grank.begin(),grank.begin()+ng,mn);if(it2!=grank.begin()+ng-1) rotate(it2,it2+1,grank.begin()+ng);}\n gh=grank[0];gl=grank[ng-1];\n if(q_used>=Q) break;\n char c2=bq(gi[gh],gi[gl]);if(c2!='>'){ if(++nimi>=3) break; continue;}\n }\n auto& hv=gi[gh];auto& lt=gi[gl];\n if((int)hv.size()<=1){grank.erase(grank.begin());ng--;continue;}\n bool se=false; int lo=0,hi=(int)hv.size()-1;\n while(loL2,R2=lt;\n for(int k=0;k<(int)hv.size();k++) if(k!=mid) L2.push_back(hv[k]);R2.push_back(hv[mid]);\n char r=bq(L2,R2);if(r=='='){lo=hi=mid;se=true;break;}else if(r=='>') lo=mid+1;else hi=mid;\n }\n lo=min(lo,(int)hv.size()-1);\n int lo_orig=lo;\n bool mm=se,lo_overshot=false;\n if(!se&&q_used+1<=Q){\n vectorvL,vR=lt;for(int k=0;k<(int)hv.size();k++) if(k!=lo) vL.push_back(hv[k]);vR.push_back(hv[lo]);\n if(!vL.empty()){char v=bq(vL,vR);if(v=='>'||v=='=') mm=true;\n else{lo_overshot=true;if(lo>0&&q_used+1<=Q){vectorvL2,vR2=lt;for(int k=0;k<(int)hv.size();k++) if(k!=lo-1) vL2.push_back(hv[k]);vR2.push_back(hv[lo-1]);char v2=bq(vL2,vR2);if(v2=='>'||v2=='='){lo--;mm=true;}}}}\n }\n int swap_src=(lo_overshot?lo_orig:lo);\n bool usw=false;int syi=0;\n if(!se&&!lt.empty()&&(lo_overshot||!mm)){\n int ll=(int)(log2((double)lt.size())+2);\n if(q_used+ll+1<=Q&&el()<1.87){\n int y0=0,y1=(int)lt.size()-1;bool s2=false;\n while(y0L2,R2;\n for(int k=0;k<(int)hv.size();k++) if(k!=swap_src) L2.push_back(hv[k]);\n for(int k=0;k<(int)lt.size();k++) if(k!=ym) R2.push_back(lt[k]);\n L2.push_back(lt[ym]);R2.push_back(hv[swap_src]);\n if(L2.empty()||R2.empty()) break;\n char r=bq(L2,R2);if(r=='='){y0=y1=ym;s2=true;break;}else if(r=='>') y0=ym+1;else y1=ym;\n }\n if(s2){usw=true;syi=min(y0,(int)lt.size()-1);lo=swap_src;}\n }\n }\n auto do_bub=[&](){\n for(int i=0;i+10&&q_used+1<=Q;i--){if(gi[grank[i]].empty()||gi[grank[i-1]].empty()) break;if(bq(gi[grank[i]],gi[grank[i-1]])=='>') swap(grank[i],grank[i-1]);else break;}\n };\n if(usw){\n int xm=hv[lo],ym=lt[syi];asgn[xm]=gl;asgn[ym]=gh;gw[gh]+=w[ym]-w[xm];gw[gl]+=w[xm]-w[ym];\n hv.erase(hv.begin()+lo);lt.erase(lt.begin()+syi);\n hv.insert(lower_bound(hv.begin(),hv.end(),ym,cpos),ym);lt.insert(lower_bound(lt.begin(),lt.end(),xm,cpos),xm);\n nimi=0;do_bub();\n } else if(mm){\n int mv=hv[lo];asgn[mv]=gl;gw[gh]-=w[mv];gw[gl]+=w[mv];\n hv.erase(hv.begin()+lo);lt.insert(lower_bound(lt.begin(),lt.end(),mv,cpos),mv);\n bool undo=false;\n if(!se&&q_used+1<=Q&&!hv.empty()&&!lt.empty()){\n char pt=bq(gi[gh],gi[gl]);\n if(pt=='<'){undo=true;asgn[mv]=gh;gw[gh]+=w[mv];gw[gl]-=w[mv];\n auto it=lower_bound(lt.begin(),lt.end(),mv,cpos);if(it!=lt.end()&&*it==mv) lt.erase(it);\n hv.insert(lower_bound(hv.begin(),hv.end(),mv,cpos),mv);}\n }\n if(!undo){nimi=0;do_bub();}else{if(++nimi>=3) break;}\n } else{if(++nimi>=3) break;}\n }\n }\n }\n while(q_used\nusing namespace std;\nusing Clock = chrono::steady_clock;\nint n, m;\nstruct Dec{int ars,t,rs,re;};\nlong long greedy(int mode,long long noise,vector>sts,vectorstk,vectorpidx,vectorsm,vector>&ops,mt19937_64&rng,Dec*od=nullptr,int*on=nullptr){\n if(on)*on=0;bool psfx=(mode<=1),pat=(mode==1||mode==3);ops.clear();long long e=0;\n auto rc=[&](int t){sm[t]=sts[t].empty()?n+1:*min_element(sts[t].begin(),sts[t].end());};\n for(int v=1;v<=n;v++){int s=stk[v],j=pidx[v];while((int)sts[s].size()>j+1){\n int re=(int)sts[s].size()-1,rs=re;while(rs>j+1&&sts[s][rs-1]>sts[s][rs])rs--;\n int fu1=sts[s][rs],ars=rs,bt=-1;\n if(psfx){for(int sp=rs;sp<=re&&bt==-1;sp++){int u1c=sts[s][sp];long long bs=LLONG_MIN;int bk=-1;for(int t=0;tu1c&&mt>u1c){long long sc=(long long)n-tt;if(noise>0)sc+=(long long)(rng()%(2*noise+1))-noise;if(sc>bs){bs=sc;bk=t;}}}if(bk!=-1){ars=sp;bt=bk;}}}\n if(bt==-1){long long best=LLONG_MIN;for(int t=0;tfu1)sc=(mt>fu1)?3LL*n*n+(n-tt):(long long)n*n+mt;else sc=mt-(long long)n*n;}else{if(emp)sc=(long long)n;else if(tt>fu1)sc=2LL*n*n+(n-tt);else sc=tt-(long long)n*n;}if(noise>0)sc+=(long long)(rng()%(2*noise+1))-noise;if(sc>best){best=sc;bt=t;}}}\n if(od&&on&&*on<2000)od[(*on)++]={ars,bt,rs,re};\n e+=(re-ars+1)+1;ops.push_back({sts[s][ars],bt+1});\n int nb=(int)sts[bt].size(),osz=(int)sts[s].size();\n for(int p=ars;p>&is,const vector&ist,const vector&ip,const vector&ism,const Dec*fxd,int nfx,Dec*od,int*on,long long budget=LLONG_MAX,vector>*ops=nullptr){\n if(on)*on=0;if(ops)ops->clear();\n vector>sts=is;vectorstk=ist,pidx=ip,sm=ism;long long e=0;int d=0;\n auto rc=[&](int t){sm[t]=sts[t].empty()?n+1:*min_element(sts[t].begin(),sts[t].end());};\n for(int v=1;v<=n;v++){int s=stk[v],j=pidx[v];while((int)sts[s].size()>j+1){\n if(e>budget)return e;\n int re=(int)sts[s].size()-1,rs=re;while(rs>j+1&&sts[s][rs-1]>sts[s][rs])rs--;\n int fu1=sts[s][rs],ars,bt;\n if(du1c&&mt>u1c){long long sc=(long long)n-tt;if(sc>bs){bs=sc;bk=t;}}}if(bk!=-1){ars=sp;bt=bk;}}\n if(bt==-1){long long best=LLONG_MIN;for(int t=0;tfu1)sc=(mt>fu1)?3LL*n*n+(n-tt):(long long)n*n+mt;else sc=mt-(long long)n*n;if(sc>best){best=sc;bt=t;}}}}\n d++;if(od&&on&&*on<2000)od[(*on)++]={ars,bt,rs,re};\n e+=(re-ars+1)+1;if(ops)ops->push_back({sts[s][ars],bt+1});\n if(bt==s)continue;\n int nb=(int)sts[bt].size(),osz=(int)sts[s].size();\n for(int p=ars;ppush_back({v,0});sts[s].pop_back();rc(s);}\n return e;}\nint main(){\n auto t0=Clock::now();ios_base::sync_with_stdio(false);cin.tie(NULL);\n cin>>n>>m;int h=n/m;\n vector>is(m,vector(h));vectorist(n+1),ip(n+1),ism(m,n+1);\n for(int i=0;i>is[i][j];ist[is[i][j]]=i;ip[is[i][j]]=j;}ism[i]=*min_element(is[i].begin(),is[i].end());}\n long long be=LLONG_MAX;vector>bops;mt19937_64 rng(42);\n auto tms=[&](){return chrono::duration_cast(Clock::now()-t0).count();};\n static Dec d4[4][2000];int nd4[4];long long e4[4];\n for(int mode=0;mode<4;mode++){mt19937_64 d(0);vector>ops;nd4[mode]=0;\n e4[mode]=greedy(mode,0,is,ist,ip,ism,ops,d,d4[mode],&nd4[mode]);if(e4[mode]bool{\n bool imp=false;int dummy;\n for(int di=0;di0;p++){int di=ils_rng()%cnd;\n if(ils_rng()%2==0||cd[di].rs==cd[di].re){int ot=cd[di].t;int nt;do{nt=ils_rng()%m;}while(nt==ot);cd[di].t=nt;}\n else{int r=cd[di].re-cd[di].rs;cd[di].ars=cd[di].rs+ils_rng()%(r+1);}\n ce=simfx(is,ist,ip,ism,cd,di+1,td,&cnd);memcpy(cd,td,cnd*sizeof(Dec));}\n imp=true;}\n imp=ls_pass(cd,cnd,ce);}\n if(ce>ops_gen;simfx(is,ist,ip,ism,gcd,gnd,nullptr,nullptr,LLONG_MAX,&ops_gen);bops=ops_gen;}\n vector>ops;ops.reserve(5000);\n for(uint64_t it=0;;it++){if(it%10==0&&tms()>=1800)break;\n rng.seed(it*6364136223846793005ULL+1442695040888963407ULL);\n long long e=greedy(it%4,2000,is,ist,ip,ism,ops,rng);if(e\nusing namespace std;\nconst int MAXN=41,MAXC=1601,BUD=100000;\nint N,n;bool hw[MAXN][MAXN],vw[MAXN][MAXN];int dv[MAXN][MAXN];\nconst int DI[]={0,1,0,-1},DJ[]={1,0,-1,0};const char DC[]=\"RDLU\";\nint C(int i,int j){return i*N+j;}int RI(int c){return c/N;}int RJ(int c){return c%N;}\nbool OK(int i,int j,int d){int ni=i+DI[d],nj=j+DJ[d];if(ni<0||ni>=N||nj<0||nj>=N)return false;if(d==0)return!vw[i][j];if(d==1)return!hw[i][j];if(d==2)return!vw[i][nj];return!hw[ni][j];}\nshort AP[MAXC][MAXC];int AF[MAXC][MAXC];\nvoid bfs(int s){memset(AP[s],0xFF,n*sizeof(short));int fs[MAXC];AP[s][s]=0;fs[s]=s;static int q[MAXC];int h=0,tail=0;q[tail++]=s;while(h>N;n=N*N;\n for(int i=0;i>s;for(int j=0;j>s;for(int j=0;j>dv[i][j];\n for(int s=0;s lv(n,0);int pos=0,t=0;\n {vector vis(n,false);vis[0]=true;vector> stk;stk.reserve(n);stk.push_back({0,0});\n while(!stk.empty()){int u=stk.back().first;int&nd=stk.back().second;bool found=false;\n while(nd<4){int d=nd++;if(OK(RI(u),RJ(u),d)){int v=C(RI(u)+DI[d],RJ(u)+DJ[d]);if(!vis[v]){route+=DC[d];t++;pos=v;lv[v]=t;vis[v]=true;stk.push_back({v,0});found=true;break;}}}\n if(!found){stk.pop_back();if(!stk.empty()){int par=stk.back().first;for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==par){route+=DC[d];t++;pos=par;lv[par]=t;break;}}}};}\n for(int c=0;c=20);\n if(!rrt&&t+(int)AP[pos][committed]+(int)D_home[committed]+2>BUD)rrt=true;\n if(rrt){\n const short*Ap=AP[pos];int best=-1;float bu=0.0f;\n for(int c=0;cBUD)continue;\n // Age-at-arrival: estimate dirtiness when we actually arrive\n float u=sqd[c]*(float)(t+dc-lv[c]+1)/sqrtf((float)dc+1.0f);\n if(u>bu){bu=u;best=c;}}\n committed=best;sr=0;if(committed<0)break;}\n int nx=AF[pos][committed];bool moved=false;\n for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==nx){route+=DC[d];pos=nx;t++;sr++;lv[pos]=t;moved=true;break;}\n if(!moved)break;}\n while(pos!=0){int nx=AF[pos][0];for(int d=0;d<4;d++)if(OK(RI(pos),RJ(pos),d)&&C(RI(pos)+DI[d],RJ(pos)+DJ[d])==nx){route+=DC[d];pos=nx;t++;break;}}\n cout<\nusing namespace std;\nint N,M,si,sj;\nvector targets;\nvector> charPos[26];\nint ovM[200][200],tCI[200][200];\nint16_t EV[200][200];\nfloat amd[26][26],tC[200][200];\nconst int SCALE=100,OV_W=350,CL_K=20;\nint cands_cl[200][20],pos_of[200];\nvoid computeAll(){\n for(int i=0;i=1;k--){bool ok=true;for(int l=0;l> sc;\n for(int j=0;j&p){int s=0;for(int i=1;i<(int)p.size();i++)s+=EV[p[i-1]][p[i]];return s;}\nvoid rebuildPos(const vector&p){for(int i=0;i<(int)p.size();i++)pos_of[p[i]]=i;}\nvector greedyP(int s){vector used(M,false);vector p;p.reserve(M);p.push_back(s);used[s]=true;while((int)p.size()bcs){bcs=EV[last][j];best=j;}p.push_back(best);used[best]=true;}return p;}\nint swapCG(const vector&p,int i,int j){int m=p.size(),a=p[i],b=p[j],cg=0;if(i>0)cg+=EV[p[i-1]][b]-EV[p[i-1]][a];if(j0)cg+=EV[p[j-1]][a]-EV[p[j-1]][b];}return cg;}\nbool swapOpt(vector&p){\n int m=p.size(),bg=0,bi=-1,bj=-1;\n for(int i=0;ibg){bg=g;bi=ii;bj=jj;}\n }\n }\n if(bi==-1)return false;\n pos_of[p[bi]]=bj;pos_of[p[bj]]=bi;\n swap(p[bi],p[bj]);return true;}\nbool orOpt(vector&p){\n int m=p.size(),bg=0,bk=-1,bp=-1;static int sr[200];\n for(int k=0;k0)?EV[p[k-1]][x]:0,ro=(k0&&k0)?EV[sr[q-1]][x]:0,nr=(q0&&qbg){bg=g;bk=k;bp=q;}}}\n if(bk==-1)return false;\n if(bp<=bk)rotate(p.begin()+bp,p.begin()+bk,p.begin()+bk+1);\n else rotate(p.begin()+bk,p.begin()+bk+1,p.begin()+bp+1);\n rebuildPos(p);return true;}\nbool revOpt(vector&p){int m=p.size();if(m<2)return false;vector cd(m-1),cp(m,0);for(int k=0;k0)g+=EV[p[i-1]][p[j]]-EV[p[i-1]][p[i]];if(jbg){bg=g;bi=i;bj=j;}}if(bi==-1)return false;reverse(p.begin()+bi,p.begin()+bj+1);rebuildPos(p);return true;}\nvoid localS(vector&p,int maxP=1000){rebuildPos(p);bool imp=true;int pass=0;while(imp&&pass&p,mt19937&rng){int m=p.size();if(m<4)return;uniform_int_distribution d(1,m-1);int a,b,c;do{a=d(rng);b=d(rng);c=d(rng);}while(a==b||b==c||a==c);if(a>b)swap(a,b);if(b>c)swap(b,c);if(a>b)swap(a,b);vector np;np.reserve(m);for(int i=0;i&p){string s=targets[p[0]];for(int i=1;i<(int)p.size();i++)s+=targets[p[i]].substr(ovM[p[i-1]][p[i]]);return s;}\npair>,int> dpSolve(const string&s){\n int L=s.size(),G=N*N;const int INF=1e9;vector dp((L+1)*G,INF),prv((L+1)*G,-1);dp[si*N+sj]=0;\n for(int i=0;i> path(L);int pos=bp;for(int i=L;i>=1;i--){path[i-1]={pos/N,pos%N};pos=prv[i*G+pos];}return{path,bc};}\nint main(){\n ios::sync_with_stdio(false);cin.tie(nullptr);\n auto t0=chrono::steady_clock::now();\n auto ms=[&](){return chrono::duration_cast(chrono::steady_clock::now()-t0).count();};\n cin>>N>>M>>si>>sj;\n for(int i=0;i>row;for(int j=0;j>targets[i];\n computeAll();\n vector>> cands;\n for(int s=0;s best;vector> bestPath;int bestT=INT_MAX;\n for(int k=0;k\n#include \n#include \n#include \n#include \n#include \nusing namespace std;\ntypedef pair pii;\nint main(){\n int N,M,MAX_OPS,ops=0;double eps,coef;\n scanf(\"%d%d%lf\",&N,&M,&eps);MAX_OPS=2*N*N;coef=1.0-2.0*eps;\n struct Oil{int hi,hj;vectorcells,pos;vectorrp,cp;};\n vectorF(M);\n for(int k=0;k>prob(M);\n for(int k=0;k0?sz:1,sz>0?1.0/sz:1.0);}\n vector>drld(N,vector(N,-1));\n vectorrobs(N,0),cobs(N,0);int nrr=0,nrc=0;\n auto qdiv=[&](const vector&c)->double{ops++;printf(\"q %d\",(int)c.size());for(auto&p:c)printf(\" %d %d\",p.first,p.second);printf(\"\\n\");fflush(stdout);int v;scanf(\"%d\",&v);return(double)v;};\n auto qdrl=[&](int i,int j)->int{ops++;printf(\"q 1 %d %d\\n\",i,j);fflush(stdout);int v;scanf(\"%d\",&v);drld[i][j]=v;return v;};\n auto qans=[&](const vector&oil)->bool{ops++;printf(\"a %d\",(int)oil.size());for(auto&p:oil)printf(\" %d %d\",p.first,p.second);printf(\"\\n\");fflush(stdout);int r;scanf(\"%d\",&r);return r==1;};\n auto run_mf=[&](int nit){\n if(!nrr&&!nrc)return;\n double vr=max(1e-9,(double)nrr*N*eps*(1-eps)),vc=max(1e-9,(double)nrc*N*eps*(1-eps));\n vectortmr(N,0),tmc(N,0);\n for(int k=0;kkmr(N,0),kmc(N,0);\n for(int p=0;p>drow(N,vector(F[k].hi+1,0)),dcol(N,vector(F[k].hj+1,0));\n for(int i=0;iop2=prob[k],ll(np,0.0);double mx=-1e300;\n for(int p=0;pmx)mx=lp;}\n double s=0;for(int p=0;p1e-15)for(int p=0;p1e-15)for(double&pp:prob[k])pp/=s;else fill(prob[k].begin(),prob[k].end(),1.0/max(1,(int)prob[k].size()));}\n }\n };\n auto get_oil=[&]()->vector>{\n vector>noc(N,vector(N,1.0));\n for(int k=0;k>cvk(N,vector(N,0.0));int np=(int)F[k].pos.size();for(int p=0;p>op(N,vector(N,0));for(int i=0;i>&op,double thr=0.5)->vector{\n vectorr;for(int i=0;i0||(drld[i][j]<0&&op[i][j]>thr))r.push_back({i,j});return r;\n };\n auto shape_q=[&](int k)->bool{\n if(ops>=MAX_OPS-5)return false;int np=(int)F[k].pos.size();if(!np)return false;\n int p1=0;for(int p=1;pprob[k][p1])p1=p;\n if(prob[k][p1]>0.98)return false;\n int p2=-1;for(int p=0;pprob[k][p2]))p2=p;\n int di1=F[k].pos[p1].first,dj1=F[k].pos[p1].second;\n setSs;\n if(p2>=0){setc2;int di2=F[k].pos[p2].first,dj2=F[k].pos[p2].second;for(auto&c:F[k].cells)c2.insert({di2+c.first,dj2+c.second});for(auto&c:F[k].cells){pii cc={di1+c.first,dj1+c.second};if(cc.first>=0&&cc.first=0&&cc.second=0&&cc.first=0&&cc.secondS(Ss.begin(),Ss.end());\n vectorSm(N*N,0);for(auto&p:S)Sm[p.first*N+p.second]=1;\n vectorovl(np,0);\n for(int p=0;p=0&&i=0&&j=0&&i=0&&jll2(np);\n for(int p=0;pmx2)mx2=ll2[p];}\n if(mx2>-1e290){double s=0;for(int p=0;pmx2-500)?exp(ll2[p]-mx2):0.0;s+=prob[k][p];}if(s>1e-15)for(int p=0;pdouble{double H=0;for(double p:prob[k])if(p>1e-12)H-=p*log(p);return H;};\n auto find_best=[&](int nr2,int nit)->vector{\n if(!nrr&&!nrc){vectorst(M);for(int k=0;kprob[k][p1])p1=p;st[k]=p1;}return st;}\n double vr=max(1e-9,(double)nrr*N*eps*(1-eps)),vc=max(1e-9,(double)nrc*N*eps*(1-eps));\n auto cE=[&](const vector&er,const vector&ec)->double{\n double E=0;for(int i=0;i>vps(M);\n for(int k=0;kur(0,1);\n vectorgbest(M,0);double gbest_E=1e300;\n for(int restart=0;restartstate(M);\n if(restart==0){for(int k=0;kprob[k][p1])p1=p;state[k]=p1;}}\n else{for(int k=0;k=r2){state[k]=vp[pi];break;}}}}\n for(int k=0;ker(N,0),ec(N,0);\n for(int k=0;kbest=state;double best_E=cur_E;\n for(int it=0;it&state)->vector{\n setoil_set;\n for(int k=0;k0)oil_set.insert({i,j});\n return vector(oil_set.begin(),oil_set.end());\n };\n // Phase 1: Row/col queries - KEY CHANGE: adaptive n_reps for large N with high eps\n int ideal_nr = eps>=0.15 ? min(5,1+N/5) : eps>=0.08 ? 2 : 1;\n int max_nr = max(1,(MAX_OPS-N*N-20-5)/(2*N));\n int nr = min(max_nr, ideal_nr);\n for(int rep=0;repc;for(int j=0;jc;for(int i=0;iprob[k][p1])p1=p;\n if(prob[k][p1]>0.98)continue;\n double h=entropy(k);if(h>be){be=h;bk=k;}\n }\n if(bk<0||be<0.05)break;\n shape_q(bk);run_mf(10);\n }\n }\n apply_hard();run_mf(100);\n // Phase 3: SA guess + MF fallback\n {\n auto bs=find_best(5,200000);\n {auto g=sa_guess(bs);if(ops=0)continue;double u=min(op[i][j],1.0-op[i][j]);if(u>bu){bu=u;bi=i;bj=j;}}\n if(bi<0||bu<0.1)break;\n qdrl(bi,bj);\n if(drld[bi][bj]==0){for(int k=0;k1e-15)for(double&pp:prob[k])pp/=s;else fill(prob[k].begin(),prob[k].end(),1.0/max(1,(int)prob[k].size()));}}\n run_mf(5);op=get_oil();\n }\n apply_hard();run_mf(20);\n {auto g=make_g(get_oil());if(ops\nusing namespace std;\ntypedef long long ll;\ntypedef tuple T3;\nint W,D,N;\nvector>a;\nstruct CS{\nint s0,st,nc,cw;\nint r(int d,int k)const{return a[d][s0+k*st];}\nvectorch(const vector&days)const{\n vectorh(nc,1);\n auto be=[&](int k,int cur)->ll{ll b=0;for(int d:days){int df=r(d,k)-cur*cw;if(df>0)b+=(ll)min(cw,df);}return b;};\n priority_queuepq;\n for(int k=0;k0)pq.push({b,k,1});}\n for(int rem=W-nc;rem>0&&!pq.empty();){auto[b,kk,cu]=pq.top();pq.pop();if(b<=0)break;h[kk]++;rem--;ll nb=be(kk,h[kk]);if(nb>0)pq.push({nb,kk,h[kk]});}\n sort(h.begin(),h.end());\n {int s=0;for(int x:h)s+=x;if(s&h)const{ll c=0;for(int k=0;k0)c+=(ll)df*100;}return c;}\nsetgb(const vector&arr)const{setS;int y=0;for(int i=0;i+1<(int)arr.size();i++){y+=arr[i];S.insert(y);}return S;}\nll bd(const set&A,const set&B)const{ll c=0;for(int x:A)if(!B.count(x))c++;for(int x:B)if(!A.count(x))c++;return c*(ll)cw;}\nvectorag(const vector&h,const set&t)const{\n vectortg(t.begin(),t.end());multisetav(h.begin(),h.end());\n vectorarr;int S=0,j=0,nt=(int)tg.size();\n while(!av.empty()){while(j=tg[j])j++;if(j>=nt){for(int x:av)arr.push_back(x);break;}\n int nd=tg[j]-S;auto it=av.find(nd);\n if(it!=av.end()){arr.push_back(nd);S+=nd;av.erase(it);j++;}\n else{auto ub=av.upper_bound(nd);\n if(ub!=av.begin()){--ub;arr.push_back(*ub);S+=*ub;av.erase(ub);while(j=tg[j])j++;}\n else{it=av.begin();arr.push_back(*it);S+=*it;av.erase(it);while(j=tg[j])j++;}\n }\n }return arr;\n}\nvectorhc(vectorarr,const set&t)const{\n if(t.empty()||(int)arr.size()<=1)return arr;\n int n2=arr.size();vectorps(n2+1,0);for(int i=0;i0){swap(arr[i],arr[j]);for(int k=i+1;k<=j;k++)ps[k]+=dl;im=true;}\n }}return arr;\n}\npair>>solve()const{\n vector>C;vectorai(D);iota(ai.begin(),ai.end(),0);\n C.push_back(ch(ai));\n for(int d=0;d>SS(NC);for(int L=0;L>AR(D,vector(NC));for(int d=0;d>pcg(NC,vector(NC,0));\n for(int L1=0;L1>pcgt(NC,vector(NC,0));\n for(int L1=0;L1zr(NC,0LL);\n const ll INF=2e18;\n vector>dp(D,vector(NC,INF));vector>frm(D,vector(NC,-1));\n for(int L=0;Ldpseq(D);dpseq[D-1]=bL;for(int d=D-2;d>=0;d--)dpseq[d]=frm[d+1][dpseq[d+1]];\n // DLS with configurable max iterations\n auto dls=[&](vectors,int mi=80)->vector{\n vectordc(D);\n for(int d=0;d0&&s[d]!=s[d-1])dc[d]+=pcg[s[d-1]][s[d]];}\n auto step=[&](int d)->bool{\n int bL2=s[d];ll bDl=0;ll od=dc[d],od1=(d+10)?pcg[s[d-1]].data():zr.data();\n const ll*rt=(d+10&&s[d]!=s[d-1]?pcg[s[d-1]][s[d]]:0LL);\n if(d+1=0;d--)any|=step(d);\n if(!any)break;}\n return s;\n };\n auto sa2phase=[&](vectors,int sid)->vector{\n vectordc(D);\n for(int d=0;d0&&s[d]!=s[d-1])dc[d]+=pcg[s[d-1]][s[d]];}\n ll total=0;for(auto x:dc)total+=x;\n ll best_total=total;vectorbest_s=s;\n uint64_t rs=(uint64_t)(nc+1)*(uint64_t)(cw+1)*(uint64_t)(D*NC+sid*7+1)+42;\n auto rng=[&]()->uint64_t{rs^=rs<<13;rs^=rs>>7;rs^=rs<<17;return rs;};\n auto do_sa=[&](double T0,double TF,int NS){\n const double dec=pow(TF/T0,1.0/NS);double T=T0;\n for(int step=0;step0?pcg[s[d-1]][L]:0LL);\n ll nd21=(d+10.01&&(double)delta<5.0*T)\n acc=((double)(rng()>>11)*(1.0/(1LL<<53))0&&s[d]!=s[d-1])dc[d]+=pcg[s[d-1]][s[d]];}\n total=best_total;\n do_sa(10000.0,0.5,200000);\n return best_s;\n };\n auto pcg_cost=[&](const vector&sv)->ll{\n ll t=0;for(int d=0;d0&&sv[d]!=sv[d-1])t+=pcg[sv[d-1]][sv[d]];}return t;\n };\n auto fs=[&](const vector&s)->pair>>{\n vector>arrs(D);ll cost=0;arrs[0]=C[s[0]];cost+=AR[0][s[0]];setcur=gb(arrs[0]);\n for(int d=1;dns=gb(arrs[d]);cost+=AR[d][s[d]]+bd(cur,ns);cur=ns;}}\n return{cost,arrs};\n };\n auto slow_dls=[&](vectors,int ni)->vector{\n vector>Sv(D);vectordc(D);\n {setprev;for(int d=0;dpv=prev;\n if(d>0&&s[d]==s[d-1]){Sv[d]=Sv[d-1];dc[d]=AR[d][s[d]];}\n else{auto arr=ag(C[s[d]],pv);Sv[d]=gb(arr);dc[d]=AR[d][s[d]]+(d>0?bd(pv,Sv[d]):0LL);}\n prev=Sv[d];}}\n for(int it=0;itpv=(d>0)?Sv[d-1]:set();\n for(int L=0;L0?bd(pv,nSd):0LL);ll nd21=0;\n if(d+10?bd(pv,Sv[d]):0LL);\n if(d+1pv2=Sv[d];\n if(s[d+1]==s[d]){Sv[d+1]=Sv[d];dc[d+1]=AR[d+1][s[d+1]];}\n else{auto na1=ag(C[s[d+1]],pv2);Sv[d+1]=gb(na1);dc[d+1]=AR[d+1][s[d+1]]+bd(pv2,Sv[d+1]);}}\n any=true;}}\n if(!any)break;}\n return s;\n };\n auto run=[&](vectorsq,int sid)->pair>>{\n auto s0=dls(sq,80);auto[c0,a0]=fs(s0);\n auto bsa1=sa2phase(s0,sid);\n auto bsa2=sa2phase(s0,sid+4);\n auto best_sa=(pcg_cost(bsa1)<=pcg_cost(bsa2))?bsa1:bsa2;\n auto s1=dls(best_sa,80);auto[c1,a1]=fs(s1);\n if(c1gseq(D);{int L0=0;for(int L=0;Lapseq(D);for(int d=0;dfseq(D,0);\n auto[c4,a4]=run(fseq,3);\n auto[cs,as_]=fs(slow_dls(dpseq,10));\n // Best from structured runs\n ll bc2=min({c1,c2,c3,c4,cs});\n pair>>best_r;\n if(bc2==c1)best_r={c1,a1};else if(bc2==c2)best_r={c2,a2};else if(bc2==c3)best_r={c3,a3};\n else if(bc2==c4)best_r={c4,a4};else best_r={cs,as_};\n // Random DLS restarts: explore completely different basins of attraction\n {\n uint64_t rr=(uint64_t)(nc+1)*(uint64_t)(cw+1)*(uint64_t)(D+NC+1)*98765ULL+12345ULL;\n auto rnxt=[&]()->uint64_t{rr^=rr<<13;rr^=rr>>7;rr^=rr<<17;return rr;};\n for(int tr=0;tr<6;tr++){\n vectorrs(D);for(int d=0;d>W>>D>>N;a.resize(D,vector(N));\n for(int d=0;d>a[d][k];\n ll best=2e18;int bK=1;\n vector>>>bcr;\n for(int K=1;K<=N;K++){\n if(N%K!=0||W%K!=0)continue;\n int npc=N/K,cw=W/K;\n if(npc==1){\n ll tc=0;vector>>>cr(K);\n for(int c=0;c0)cc+=(ll)df*100;}\n cr[c]={cc,vector>(D,vector(1,W))};tc+=cc;}\n if(tc10)continue;\n vector>>>cr(K);ll tc=0;\n for(int c=0;c>rects(N);\n for(int c=0;cy(npc+1);y[0]=0;for(int j=0;j>strips(npc);for(int j=0;j\nusing namespace std;using namespace chrono;\nconstexpr long long MOD=998244353;\nint N,M,K;long long sv[20][3][3],b[9][9],cur_score;\nlong long base_b[9][9];long long base_score;\ninline long long add_mod(long long a,long long c){long long s=a+c;return s>=MOD?s-MOD:s;}\ninline long long sub_mod(long long a,long long c){return a>=c?a-c:a-c+MOD;}\nvoid apply_s(int m,int p,int q){for(int i=0;i<3;i++)for(int j=0;j<3;j++){long long&c=b[p+i][q+j];long long nv=add_mod(c,sv[m][i][j]);cur_score+=nv-c;c=nv;}}\nvoid undo_s(int m,int p,int q){for(int i=0;i<3;i++)for(int j=0;j<3;j++){long long&c=b[p+i][q+j];long long nv=sub_mod(c,sv[m][i][j]);cur_score+=nv-c;c=nv;}}\nstruct Op{int m,p,q;};\nconst int TK=17;\nlong long gdtv[3][3],gdts,gdtbest;int gdbs[9],gdcs[9],gdord[20],gdfl;bool gdto;steady_clock::time_point gddl;\nvoid tile_dfs(int dep,int mi){\n if(gdto)return;\n if(dep==9){if(++gdfl%200000==0&&steady_clock::now()>=gddl){gdto=true;return;}if(gdts>gdtbest){gdtbest=gdts;for(int d=0;d<9;d++)gdbs[d]=gdord[gdcs[d]];}return;}\n long long ub=gdts;for(int i=0;i<3;i++)for(int j=0;j<3;j++)ub+=(MOD-1)-gdtv[i][j];if(ub<=gdtbest)return;\n for(int idx=mi;idx&ops){\n bool changed=true;while(changed){changed=false;\n for(int k=0;k<(int)ops.size();k++){Op oo=ops[k];undo_s(oo.m,oo.p,oo.q);\n long long g_old=0;for(int i=0;i<3;i++)for(int j=0;j<3;j++)g_old+=add_mod(b[oo.p+i][oo.q+j],sv[oo.m][i][j])-b[oo.p+i][oo.q+j];\n long long bg=g_old;int bm=oo.m,bp=oo.p,bq=oo.q;\n for(int pp=0;pp<=N-3;pp++)for(int qq=0;qq<=N-3;qq++)for(int m=0;mbg){bg=g;bm=m;bp=pp;bq=qq;}}\n apply_s(bm,bp,bq);if(bm!=oo.m||bp!=oo.p||bq!=oo.q){ops[k]={bm,bp,bq};changed=true;}}}\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);cin>>N>>M>>K;cur_score=0;\n for(int i=0;i>b[i][j];b[i][j]%=MOD;cur_score+=b[i][j];}\n for(int m=0;m>sv[m][i][j];\n memcpy(base_b,b,sizeof(b));base_score=cur_score;\n auto t0=steady_clock::now();const long long TL_US=1850000;\n vectorops;ops.reserve(K);\n const int tpos[9][2]={{0,0},{0,3},{0,6},{3,0},{3,3},{3,6},{6,0},{6,3},{6,6}};\n gdfl=0;gdto=false;gddl=t0+milliseconds(1300);\n for(int tile=0;tile<9;tile++){\n int p=tpos[tile][0],q=tpos[tile][1];long long itv[3][3];long long its=0;\n for(int i=0;i<3;i++)for(int j=0;j<3;j++){itv[i][j]=b[p+i][q+j];its+=itv[i][j];}\n long long gn[20];int ord[20];iota(ord,ord+20,0);\n for(int m=0;mgn[b_];});\n long long grtv[3][3];memcpy(grtv,itv,sizeof(itv));long long grts=its;int grs[9];\n for(int d=0;d<9;d++){long long bg=0;int bm=0;for(int m=0;mbg){bg=g;bm=m;}}grs[d]=bm;for(int i=0;i<3;i++)for(int j=0;j<3;j++){long long nv=add_mod(grtv[i][j],sv[bm][i][j]);grts+=nv-grtv[i][j];grtv[i][j]=nv;}}\n memcpy(gdtv,itv,sizeof(itv));gdts=its;gdtbest=grts;for(int d=0;d<9;d++)gdbs[d]=grs[d];for(int m=0;m<20;m++)gdord[m]=ord[m];\n tile_dfs(0,0);\n int best_s[9];memcpy(best_s,gdbs,sizeof(gdbs));long long best_ts=gdtbest;\n bool imp=true;while(imp){imp=false;for(int d=0;d<9;d++){int om=best_s[d];for(int m=0;mbest_ts){best_ts=ts;memcpy(best_s,tmp,sizeof(tmp));imp=true;}}}}\n bool imp2=true;while(imp2){imp2=false;long long b2ts=best_ts;int bd1=-1,bd2=-1,bm1=-1,bm2=-1;for(int d1=0;d1<9;d1++)for(int d2=d1+1;d2<9;d2++)for(int m1=0;m1b2ts){b2ts=ts;bd1=d1;bd2=d2;bm1=m1;bm2=m2;}}if(bd1>=0){best_ts=b2ts;best_s[bd1]=bm1;best_s[bd2]=bm2;imp2=true;}}\n for(int d=0;d<9;d++){apply_s(best_s[d],p,q);ops.push_back({best_s[d],p,q});}\n }\n long long overall_best=cur_score;vectoroverall_best_ops=ops;\n double T_cal=1e8;\n {mt19937 rc(777);long long sumd=0;int cnt=0;for(int i=0;i<3000&&!ops.empty();i++){int L=ops.size(),idx=rc()%L;Op oo=ops[idx];Op no={(int)(rc()%M),(int)(rc()%(N-2)),(int)(rc()%(N-2))};long long s0=cur_score;undo_s(oo.m,oo.p,oo.q);apply_s(no.m,no.p,no.q);long long d=cur_score-s0;sumd+=(d<0?-d:d);cnt++;undo_s(no.m,no.p,no.q);apply_s(oo.m,oo.p,oo.q);}if(cnt>0)T_cal=max(1.0,(double)sumd/cnt);}\n global_greedy(ops);\n if(cur_score>overall_best){overall_best=cur_score;overall_best_ops=ops;}\n mt19937 rng(42);const int POS=N-2;\n auto rand_op=[&]()->Op{return{(int)(rng()%M),(int)(rng()%POS),(int)(rng()%POS)};};\n double T=T_cal,T_end=max(T_cal*1e-7,1.0);\n // Restart boost: temperature that decays with half-life 30K iters\n double T_restart=0.0;\n const double T_restart_init=T_cal*0.05;\n const double T_restart_decay=pow(0.5,1.0/30000.0); // halves every 30K iters\n long long since_improvement=0;\n const long long RESTART_THRESHOLD=500000LL;\n for(long long it=0;;it++){\n if(it%50000==0){long long el=duration_cast(steady_clock::now()-t0).count();if(el>=TL_US-50000)break;T=T_cal*pow(T_end/T_cal,max(0.0,min(1.0,(double)el/TL_US)));}\n T_restart*=T_restart_decay; // Decay boost\n if(since_improvement>=RESTART_THRESHOLD){\n memcpy(b,base_b,sizeof(b));cur_score=base_score;\n ops=overall_best_ops;\n for(auto&op:ops)apply_s(op.m,op.p,op.q);\n T_restart=T_restart_init; // Fresh boost at restart\n since_improvement=0;}\n double T_eff=max(T,T_restart);\n int L=ops.size();Op n1=rand_op(),o1{},o2{},n2{};int i1=-1,i2=-1,mt;\n if(L==0){mt=0;}else{int r=rng()%10;if(L==K)mt=(r<2)?1:(r<7)?2:3;else mt=(r<2)?0:(r<3)?1:(r<7)?2:3;if(mt==3&&L<2)mt=2;}\n if(mt==1||mt==2){i1=rng()%L;o1=ops[i1];}\n if(mt==3){i1=rng()%L;do{i2=rng()%L;}while(i2==i1);o1=ops[i1];o2=ops[i2];n2=rand_op();}\n long long s0=cur_score;\n switch(mt){case 0:apply_s(n1.m,n1.p,n1.q);break;case 1:undo_s(o1.m,o1.p,o1.q);break;case 2:undo_s(o1.m,o1.p,o1.q);apply_s(n1.m,n1.p,n1.q);break;case 3:undo_s(o1.m,o1.p,o1.q);undo_s(o2.m,o2.p,o2.q);apply_s(n1.m,n1.p,n1.q);apply_s(n2.m,n2.p,n2.q);break;}\n long long delta=cur_score-s0;bool acc=(delta>=0)||(T_eff>0.5&&(double)(rng()%1000000)overall_best){overall_best=cur_score;overall_best_ops=ops;since_improvement=0;}\n else since_improvement++;}\n else{switch(mt){case 0:undo_s(n1.m,n1.p,n1.q);break;case 1:apply_s(o1.m,o1.p,o1.q);break;case 2:undo_s(n1.m,n1.p,n1.q);apply_s(o1.m,o1.p,o1.q);break;case 3:undo_s(n2.m,n2.p,n2.q);undo_s(n1.m,n1.p,n1.q);apply_s(o2.m,o2.p,o2.q);apply_s(o1.m,o1.p,o1.q);break;}\n since_improvement++;}\n }\n memcpy(b,base_b,sizeof(b));cur_score=base_score;\n ops=overall_best_ops;\n for(auto&op:ops)apply_s(op.m,op.p,op.q);\n global_greedy(ops);\n if(cur_score>overall_best){overall_best=cur_score;overall_best_ops=ops;}\n cout<\nusing namespace std;\nconst int N=5;\nint A[N][N],posR[N*N],posP[N*N],grid[N][N];\nint craneR,craneC;bool craneHolding;int craneContainer;\nstring result;\nint smR_[N-1],smC_[N-1];bool smH_[N-1];int smCont_[N-1];\nbool smBombed_[N-1];int smStaged_[N-1];string smResult_[N-1];\nint recvSent[N],lgPU[N],dispatchCount[N];bool done_[N*N];\nmap> bufPos;set> usedBufs;\ninline bool gl(){return result.size()<9900;}\nchar getSmA(int i){\n if(smBombed_[i])return '.';if(smStaged_[i]>=N)return 'B';\n int r=i+1;\n if(!smH_[i])return smC_[i]==0?(grid[r][0]!=-1?'P':'.'):'L';\n if(smC_[i]==0)return grid[r][1]==-1?'R':'.';\n return 'Q';\n}\nvoid applySmA(int i,char a){\n smResult_[i]+=a;if(a=='B'){smBombed_[i]=true;return;}if(smBombed_[i])return;\n int r=i+1;\n if(a=='P'){smH_[i]=true;smCont_[i]=grid[r][smC_[i]];grid[r][smC_[i]]=-1;}\n else if(a=='Q'){grid[r][smC_[i]]=smCont_[i];smH_[i]=false;smCont_[i]=-1;smStaged_[i]++;}\n else if(a=='R')smC_[i]++;else if(a=='L')smC_[i]--;\n}\nvoid sRecv_(){\n for(int r=0;r=1&&lgPU[r]==p&&smStaged_[r-1]>lgPU[r])return true;\n return false;\n}\npair freeBuf(int tR=-1){\n auto ok=[&](int r,int c)->bool{\n if(r>=1&&c==1&&!smBombed_[r-1])return false;\n if(c==0&&!(recvSent[r]==N&&(r==0||smBombed_[r-1])))return false;\n return !usedBufs.count({r,c})&&grid[r][c]==-1;\n };\n if(tR>=0)for(int c=N-2;c>=1;c--)if(ok(tR,c))return{tR,c};\n for(int c=N-2;c>=1;c--)for(int r=0;r=1&&smStaged_[r-1]<=lgPU[r])return;\n int bl=A[r][lgPU[r]],gbl=bl/N;\n for(int i=0;i=1&&lgPU[pr]==pp&&smStaged_[pr-1]>lgPU[pr]){dStaged(pr,gbl);}\n else if(pr>=1&&lgPU[pr]==pp-1&&rec){\n int bl2=A[pr][lgPU[pr]];\n if(nNext(bl2/N)==bl2){int pv=lgPU[pr];clearB(pr,false);if(lgPU[pr]>pv&&lgPU[pr]==pp)dStaged(pr,gbl);else break;}\n else break;\n } else break;\n }\n if(nNext(gbl)==bl){if(r==0)dGate(gbl);else dStaged(r,gbl);return;}\n auto[br,bc]=freeBuf(gbl);\n if(br!=-1){if(r==0)bGate(br,bc);else bStaged(r,br,bc);}\n else{if(r==0)dGate(gbl);else dStaged(r,gbl);}\n}\nbool canC(int bl){\n int gbl=bl/N,bp=bl%N,d=dispatchCount[gbl];\n if(d>bp)return false;\n for(int pos=d;pos=1&&lgPU[r]==p-1){int bl2=A[r][lgPU[r]];if(nNext(bl2/N)==bl2)continue;}\n return false;\n }return true;\n}\nvoid deliverFG(int gate){\n int k=nNext(gate);if(k<0||done_[k])return;\n if(bufPos.count(k)){auto[br,bc]=bufPos[k];dBuf(br,bc,gate);return;}\n int r=posR[k],p=posP[k];\n while(lgPU[r]=1&&smStaged_[r-1]<=lgPU[r])break;clearB(r);}\n if(!gl())return;\n if(lgPU[r]==p&&(r==0||smStaged_[r-1]>lgPU[r])){if(r==0)dGate(gate);else dStaged(r,gate);}\n}\nvector planOrd(int initR=0,int initC=0){\n const int ND=N+1;int DB=1;for(int i=0;id,int r,int c)->int{int s=0;for(int i=0;i&d,int&r,int&c){c=s%N;s/=N;r=s%N;s/=N;for(int i=N-1;i>=0;i--){d[i]=s%ND;s/=ND;}};\n vectordist(NS,INT_MAX/2),pS(NS,-1),pG(NS,-1);\n priority_queue,vector>,greater<>>pq;\n arrayd0{};for(int i=0;idist[s])continue;\n arrayd;int r,c;dec(s,d,r,c);\n for(int g=0;g=N)continue;int k=N*g+d[g];\n int sR,sC,tc;\n if(bufPos.count(k)){auto&bp=bufPos[k];sR=bp.first;sC=bp.second;tc=abs(r-sR)+abs(c-sC)+abs(sR-g)+abs(sC-(N-1))+2+posP[k]*12;}\n else if(posR[k]==0){sR=0;sC=0;tc=abs(r)+abs(c-(N-1))+g+2*(N-1)+2+posP[k]*12;}\n else{sR=posR[k];sC=1;tc=abs(r-sR)+abs(c-(N-1))+abs(sR-g)+2*(N-2)+2+posP[k]*12;}\n auto nd=d;nd[g]++;int ns=enc(nd,g,N-1);\n if(dist[s]+tcgD;for(int i=0;iord;if(best!=-1)for(int s=best;pS[s]!=-1;s=pS[s])ord.push_back(pG[s]);\n reverse(ord.begin(),ord.end());return ord;\n}\nvoid solve(){\n for(int r=0;r=1&&lgPU[posR[k]]==posP[k]&&smStaged_[posR[k]-1]>lgPU[posR[k]]){sR=posR[k];sC=N-1;t=1;sc=abs(craneR-sR)+abs(craneC-(N-1))+abs(sR-g)+2*(N-2)+2;}\n else continue;\n int fut=0;for(int j=dispatchCount[g]+1;j=0){if(bType==0)dGate(bK/N);else if(bType==1)dStaged(bSR,bK/N);else dBuf(bSR,bSC,bK/N);continue;}\n int bGc=-1,bDc=INT_MAX,bGb=-1,bDb=INT_MAX;\n for(int g=0;g=1&&smStaged_[r-1]<=lgPU[r])continue;\n int bl=A[r][lgPU[r]],dd=abs(craneR-r)+abs(craneC-(r==0?0:N-1));\n if(canC(bl)){if(dd=0)?bGc:bGb;\n if(bG>=0){clearB(posR[nNext(bG)]);continue;}\n turn_('.');\n }\n}\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(nullptr);\n int n;cin>>n;for(int r=0;r>A[r][p];\n solve();cout<\nusing namespace std;\nint N,h[20][20],origH[20][20],curR,curC,curLoad;\nvectorops;long long totalCost;\nint g_dpv=0;\nvoid doLoad(int d){if(d<=0)return;totalCost+=d;ops.push_back(\"+\"+to_string(d));h[curR][curC]-=d;curLoad+=d;}\nvoid doUnload(int d){d=min(d,curLoad);if(d<=0)return;totalCost+=d;ops.push_back(\"-\"+to_string(d));h[curR][curC]+=d;curLoad-=d;}\nvoid moveStep(char dir,int dr,int dc){totalCost+=100LL+curLoad;curR+=dr;curC+=dc;ops.push_back(string(1,dir));if(h[curR][curC]>0)doLoad(h[curR][curC]);else if(h[curR][curC]<0&&curLoad>0)doUnload(min(curLoad,-h[curR][curC]));}\nvoid moveTo(int tr,int tc){\n if(curR==tr&&curC==tc)return;\n int nrow=abs(tr-curR),ncol=abs(tc-curC),rs=curR0?'D':'U',rs,0);while(curC!=tc)moveStep(cs>0?'R':'L',0,cs);return;}\n bool ld=(curLoad>0);\n auto cv=[&](int r,int c)->int{int ri=curR+r*rs,ci=curC+c*cs;if(!ld)return max(0,h[ri][ci]);if(g_dpv==1&&h[ri][ci]<0)return min(curLoad,-h[ri][ci])*2;return abs(h[ri][ci]);};\n int dp[21][21]={};bool fr[21][21]={};\n for(int r=1;r<=nrow;r++){dp[r][0]=dp[r-1][0]+cv(r,0);fr[r][0]=1;}\n for(int c=1;c<=ncol;c++)dp[0][c]=dp[0][c-1]+cv(0,c);\n for(int r=1;r<=nrow;r++)for(int c=1;c<=ncol;c++){int a=dp[r-1][c]+cv(r,c),b=dp[r][c-1]+cv(r,c);if(a>=b){dp[r][c]=a;fr[r][c]=1;}else dp[r][c]=b;}\n string path;int r=nrow,c=ncol;\n while(r||c){if(!r){path+='c';c--;}else if(!c){path+='r';r--;}else if(fr[r][c]){path+='r';r--;}else{path+='c';c--;}}\n reverse(path.begin(),path.end());\n for(char ch:path)if(ch=='r')moveStep(rs>0?'D':'U',rs,0);else moveStep(cs>0?'R':'L',0,cs);\n}\nbool allZero(){for(int i=0;i0)doLoad(h[0][0]);\n while(!allZero()&&(int)ops.size()<95000){\n auto md=[&](int i,int j){return abs(i-curR)+abs(j-curC);};\n int nD=INT_MAX,di=-1,dj=-1;double bDS=-1;int sdi=-1,sdj=-1;\n for(int i=0;i0){double sc=(double)min(curLoad,-h[i][j])/(d+1);if(sc>bDS){bDS=sc;sdi=i;sdj=j;}}}\n int dI=(sd&&sdi>=0)?sdi:di,dJ=(sd&&sdj>=0)?sdj:dj;\n if(curLoad==0){double bs=-1;int bi=-1,bj=-1;for(int i=0;i0){double sc=(double)h[i][j]/(md(i,j)+1);if(sc>bs){bs=sc;bi=i;bj=j;}}if(bi<0)break;moveTo(bi,bj);if(h[bi][bj]>0)doLoad(h[bi][bj]);}\n else{int fsi=-1,fsj=-1;if(th==-1){double bss=-1,bds=-1;int ssi=-1,ssj=-1;for(int i=0;i0){double sc=(double)h[i][j]*100/((double)(d+1)*max(curLoad,1));if(sc>bss){bss=sc;ssi=i;ssj=j;}}if(h[i][j]<0){double sc=(double)min(curLoad,-h[i][j])/(d+1);if(sc>bds)bds=sc;}}if(bss>bds&&ssi>=0){fsi=ssi;fsj=ssj;}}\n else{double bfs=-1;for(int i=0;i=(long long)nD*th)continue;double sc=nls?1.0/(d+1):(double)h[i][j]/(d+1);if(sc>bfs){bfs=sc;fsi=i;fsj=j;}}}\n if(fsi>=0){moveTo(fsi,fsj);if(h[fsi][fsj]>0)doLoad(h[fsi][fsj]);}else if(dI>=0){moveTo(dI,dJ);if(h[dI][dJ]<0&&curLoad>0)doUnload(min(curLoad,-h[dI][dJ]));}else break;}\n }\n for(int i=0;i0)totalS+=origH[i][j];\n if(h[0][0]>0)doLoad(h[0][0]);\n while(!allZero()&&(int)ops.size()<95000){\n auto md=[&](int i,int j){return abs(i-curR)+abs(j-curC);};\n int rem=0;for(int i=0;i0)rem+=h[i][j];\n int th=totalS>0?minT+(long long)(maxT-minT)*rem/totalS:minT;\n int nD=INT_MAX,di=-1,dj=-1;double bDS=-1;int sdi=-1,sdj=-1;\n for(int i=0;i0){double sc=(double)min(curLoad,-h[i][j])/(d+1);if(sc>bDS){bDS=sc;sdi=i;sdj=j;}}}\n int dI=(sd&&sdi>=0)?sdi:di,dJ=(sd&&sdj>=0)?sdj:dj;\n if(curLoad==0){double bs=-1;int bi=-1,bj=-1;for(int i=0;i0){double sc=(double)h[i][j]/(md(i,j)+1);if(sc>bs){bs=sc;bi=i;bj=j;}}if(bi<0)break;moveTo(bi,bj);if(h[bi][bj]>0)doLoad(h[bi][bj]);}\n else{double bfs=-1;int fsi=-1,fsj=-1;for(int i=0;i=(long long)nD*th)continue;double sc=(double)h[i][j]/(d+1);if(sc>bfs){bfs=sc;fsi=i;fsj=j;}}\n if(fsi>=0){moveTo(fsi,fsj);if(h[fsi][fsj]>0)doLoad(h[fsi][fsj]);}else if(dI>=0){moveTo(dI,dJ);if(h[dI][dJ]<0&&curLoad>0)doUnload(min(curLoad,-h[dI][dJ]));}else break;}\n }\n for(int i=0;i&t,vector>&c){int n=t.size();if(n<4)return;auto d=[&](int a,int b){return abs(c[a].first-c[b].first)+abs(c[a].second-c[b].second);};bool ip=true;int lm=0;while(ip&&lm++<50){ip=false;for(int i=0;ibg){bg=g;bj=j;}}if(bg>0){int e=t[i];t.erase(t.begin()+i);int p=(bj>=i)?bj:bj+1;t.insert(t.begin()+p,e);ip=true;break;}}}}\nvoid runTSP(int fb,bool opt=false){\n vector>cells;for(int i=0;ivis(n,false);vectortour;int cr=0,cc=0;\n for(int s=0;s=88000)break;auto[r,c]=cells[idx];moveTo(r,c);if(h[r][c]>0)doLoad(h[r][c]);else if(h[r][c]<0&&curLoad>0)doUnload(min(curLoad,-h[r][c]));}\n while(!allZero()&&(int)ops.size()<95000){auto md=[&](int i,int j){return abs(i-curR)+abs(j-curC);};int nD=INT_MAX,di=-1,dj=-1;for(int i=0;i0){double sc=(double)h[i][j]/(md(i,j)+1);if(sc>bs){bs=sc;bi=i;bj=j;}}if(bi<0)break;moveTo(bi,bj);if(h[bi][bj]>0)doLoad(h[bi][bj]);}else{double bfs=-1;int fsi=-1,fsj=-1;for(int i=0;i=(long long)nD*fb)continue;double sc=(double)h[i][j]/(d+1);if(sc>bfs){bfs=sc;fsi=i;fsj=j;}}if(fsi>=0){moveTo(fsi,fsj);if(h[fsi][fsj]>0)doLoad(h[fsi][fsj]);}else if(di>=0){moveTo(di,dj);if(h[di][dj]<0&&curLoad>0)doUnload(min(curLoad,-h[di][dj]));}else break;}}\n for(int i=0;i0)doLoad(h[curR][curC]);else if(h[curR][curC]<0&&curLoad>0)doUnload(min(curLoad,-h[curR][curC]));\n if(!col){for(int r=0;r0&&(int)ops.size()<88000)moveStep('L',0,-1);}}}\n else{for(int c=0;c0&&(int)ops.size()<88000)moveStep('U',-1,0);}}}\n while(!allZero()&&(int)ops.size()<95000){auto md=[&](int i,int j){return abs(i-curR)+abs(j-curC);};int nD=INT_MAX,di=-1,dj=-1;for(int i=0;i0){double sc=(double)h[i][j]/(md(i,j)+1);if(sc>bs){bs=sc;bi=i;bj=j;}}if(bi<0)break;moveTo(bi,bj);if(h[bi][bj]>0)doLoad(h[bi][bj]);}else{double bfs=-1;int fsi=-1,fsj=-1;for(int i=0;i=(long long)nD*fb)continue;double sc=(double)h[i][j]/(d+1);if(sc>bfs){bfs=sc;fsi=i;fsj=j;}}if(fsi>=0){moveTo(fsi,fsj);if(h[fsi][fsj]>0)doLoad(h[fsi][fsj]);}else if(di>=0){moveTo(di,dj);if(h[di][dj]<0&&curLoad>0)doUnload(min(curLoad,-h[di][dj]));}else break;}}\n for(int i=0;i>N;for(int i=0;i>h[i][j];origH[i][j]=h[i][j];}\n long long best=LLONG_MAX;vectorbestOps;\n auto go=[&](auto f){for(int i=0;i>{{-1,0,0},{-1,1,0},{0,0,0},{0,1,0},{30,0,0},{50,0,0},{70,0,0},{80,0,0},{90,0,0},{100,0,0},{110,0,0},{120,0,0},{130,0,0},{150,0,0},{175,0,0},{200,0,0},{250,0,0},{300,0,0},{400,0,0},{500,0,0},{750,0,0},{1000,0,0},{2000,0,0},{80,1,0},{100,1,0},{120,1,0},{150,1,0},{200,1,0},{300,1,0},{80,0,1},{100,0,1},{120,0,1},{150,0,1}})go([&]{runCore(t,sd,nls);});\n for(int fb:{80,100,150})go([&]{runTSP(fb,false);});\n for(int fb:{80,100,150})go([&]{runTSP(fb,true);});\n for(auto[fb,col]:vector>{{100,false},{150,false},{100,true},{150,true}})go([&]{runSerpentine(fb,col);});\n g_dpv=1;for(int t:{80,100,120,150,200})go([&]{runCore(t,false,false);});g_dpv=0;\n for(auto[mn,mx,sd]:vector>{\n {70,150,0},{80,200,0},{60,120,0},{50,100,0},{100,50,0},\n {200,80,0},{200,100,0},{150,60,0},{150,80,0},{120,60,0},\n {120,50,0},{100,40,0},{80,40,0},{70,200,0},{50,180,0},\n {40,200,0},{60,200,0},{80,160,0},{30,150,0},{160,70,0},\n {100,50,1},{80,200,1},{150,70,1},\n {200,50,0},{250,80,0},{300,100,0},{250,50,0},{300,70,0},\n {180,60,0},{130,40,0},{250,100,0},{200,60,0},{150,40,0},\n {40,250,0},{50,300,0},{60,250,0},{80,250,0},{30,200,0},\n {200,60,1},{150,50,1},{250,80,1},\n {300,50,0},{350,100,0},{250,60,0},{350,80,0},\n {40,350,0},{50,350,0},{70,300,0},{60,300,0},\n {150,30,0},{100,20,0},{250,150,0},{180,90,0}\n })go([&]{runDynamic(mn,mx,sd);});\n for(auto&op:bestOps)cout<\nusing namespace std;\nint main(){\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int N,M,T; cin>>N>>M>>T;\n const int SC=2*N*(N-1),nn=N*N;\n vector> X(SC,vector(M));\n for(int i=0;i>X[i][j];\n mt19937 rng(42);\n vector> nbr(nn); vector ndeg(nn,0);\n for(int p=0;p0)nbr[p][ndeg[p]++]=p-N;if(r0)nbr[p][ndeg[p]++]=p-1;if(c vals(SC,0);\n for(int k=0;k ins(SC,false); vector sel;\n for(int l=0;lX[bk][l])bk=k;if(!ins[bk]){ins[bk]=true;sel.push_back(bk);}}\n {vector ord(SC);iota(ord.begin(),ord.end(),0);sort(ord.begin(),ord.end(),[&](int a,int b){return vals[a]>vals[b];});for(int k:ord){if((int)sel.size()>=nn)break;if(!ins[k]){ins[k]=true;sel.push_back(k);}}}\n vector pst(nn*nn);\n for(int i=0;i psum(nn,0);\n for(int i=0;i&g,int p)->int{int v=0;for(int d=0;d&g)->int{int s=0;for(int p=0;p g)->vector{bool imp=true;while(imp){imp=false;for(int a=0;abef)imp=true;else swap(g[a],g[b]);}}return g;};\n auto grinit=[&]()->vector{vector g(nn,-1);vector used(nn,false);for(int pos=0;pos0)cv+=pst[s*nn+g[pos-N]];if(c>0)cv+=pst[s*nn+g[pos-1]];int64_t ev=(int64_t)cv*1000000LL+psum[s];if(ev>bv){bv=ev;bs=s;}}g[pos]=bs;used[bs]=true;}return g;};\n int gbest=-1; vector bg;\n for(int rest=0;rest<3;rest++){\n double rt0=chrono::duration(chrono::steady_clock::now()-ts).count();\n if(rt0>=0.185) break;\n double tl=(0.185-rt0)/(3-rest),tend=rt0+tl;\n vector g(nn); double T0;\n if(rest==0){g=grinit();T0=200.0;}else{iota(g.begin(),g.end(),0);shuffle(g.begin(),g.end(),rng);T0=1000.0;}\n int cur=totsc(g),lb=cur; vector lg=g; double temp=T0;\n for(int it=0;;it++){\n if((it&0x7FF)==0){double now=chrono::duration(chrono::steady_clock::now()-ts).count();if(now>=tend)break;temp=T0*pow(0.1/T0,(now-rt0)/tl);}\n int p1=rng()%nn,p2=rng()%nn; if(p1==p2)continue;\n int bef=ctrb(g,p1)+ctrb(g,p2); swap(g[p1],g[p2]); int aft=ctrb(g,p1)+ctrb(g,p2); int d=aft-bef;\n if(d>=0||(rng()%1000000)<(int)(1e6*exp((double)d/temp))){cur+=d;if(cur>lb){lb=cur;lg=g;}}else swap(g[p1],g[p2]);\n }\n lg=locsrch(lg); int sc=totsc(lg); if(sc>gbest){gbest=sc;bg=lg;}\n }\n for(int i=0;i>X[i][j];\n }\n return 0;\n}","ahc038":"#include \nusing namespace std;\nint N,M,V;\nconst int DR[]={0,1,0,-1},DC[]={1,0,-1,0};\nint rx,ry,nfp,Vp,rfp=-1;\nint fpd[16],hld[16],fpl[16];\nstruct Del{int sr,sc,tr,tc;bool done;};\nvectorP;int np;\nvector>g;\nmap,int>sm;\nvectorops;\nint fpr(int k){return rx+fpl[k]*DR[fpd[k]];}\nint fpc(int k){return ry+fpl[k]*DC[fpd[k]];}\nbool navto(int tr,int tc,int pk,int td){\n while((rx!=tr||ry!=tc||fpd[pk]!=td)&&(int)ops.size()<99990){\n char mv='.';\n if(rx!=tr||ry!=tc){if(rxtr)mv='U';else if(ry=N||fc<0||fc>=N)continue;\n if(hld[k]<0){if(k==rfp)continue;auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}}\n else{int di=hld[k];if(P[di].tr==fr&&P[di].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di].done=true;hld[k]=-1;op[Vp+1+k]='P';}}\n }\n ops.push_back(op);\n }\n return rx==tr&&ry==tc&&fpd[pk]==td;\n}\nint pickfp(int di,int r,int c){\n for(int k=0;k=0)continue;\n for(int d=0;d<4;d++){\n int ar=r-fpl[k]*DR[d],ac=c-fpl[k]*DC[d];if(ar<0||ar>=N||ac<0||ac>=N)continue;\n int md=abs(rx-ar)+abs(ry-ac),rot=min((d-fpd[k]+4)%4,(fpd[k]-d+4)%4),v=max(md,rot);\n if(v=99990){sm[{r,c}]=di;return -1;}\n string op(2*Vp,'.');bool picked=false;\n for(int k=0;k=N||fc<0||fc>=N)continue;\n if(k==bk&&fr==r&&fc==c&&g[r][c]==1&&hld[k]<0){hld[k]=di;g[r][c]=0;op[Vp+1+k]='P';picked=true;}\n else if(hld[k]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}}\n else if(hld[k]>=0){int di2=hld[k];if(P[di2].tr==fr&&P[di2].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di2].done=true;hld[k]=-1;op[Vp+1+k]='P';}}\n }\n ops.push_back(op);if(!picked){sm[{r,c}]=di;return -1;}return bk;\n}\nbool dropfp(int k,int di){\n if(hld[k]!=di)return true;\n int r=P[di].tr,c=P[di].tc;\n int bdir=-1,bar=-1,bac=-1,bv=INT_MAX;\n for(int d=0;d<4;d++){\n int ar=r-fpl[k]*DR[d],ac=c-fpl[k]*DC[d];if(ar<0||ar>=N||ac<0||ac>=N)continue;\n int md=abs(rx-ar)+abs(ry-ac),rot=min((d-fpd[k]+4)%4,(fpd[k]-d+4)%4),v=max(md,rot);\n if(v=99990)return false;\n string op(2*Vp,'.');bool ok=false;\n for(int k2=0;k2=N||fc<0||fc>=N)continue;\n if(k2==k&&fr==r&&fc==c&&g[r][c]==0&&hld[k2]==di){g[r][c]=1;P[di].done=true;hld[k2]=-1;op[Vp+1+k2]='P';ok=true;}\n else if(hld[k2]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k2]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k2]='P';}}\n else if(hld[k2]>=0){int di2=hld[k2];if(P[di2].tr==fr&&P[di2].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di2].done=true;hld[k2]=-1;op[Vp+1+k2]='P';}}\n }\n ops.push_back(op);return ok;\n}\nbool cbh(int bk){\n if(hld[bk]<0)return false;int di=hld[bk];\n pairtmp={-1,-1};\n {set>ts;for(auto&d:P)if(!d.done)ts.insert({d.tr,d.tc});\n int bdist=INT_MAX;\n for(int i=0;i>N>>M>>V;\n vectorsg(N),tg(N);for(auto&s:sg)cin>>s;for(auto&s:tg)cin>>s;\n vector>S,T;g.assign(N,vector(N,0));\n for(int i=0;imt(m,-1);\n {vectorsu(m,false),tu(m,false);\n for(int i=0;i=N||fc<0||fc>=N)continue;if(hld[k]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}}else{int di=hld[k];if(P[di].tr==fr&&P[di].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di].done=true;hld[k]=-1;op[Vp+1+k]='P';}}}};\n {string op(2*Vp,'.');\n for(int k=0;k=3){string op(2*Vp,'.');\n for(int k=0;ktsp(np);\n if(np>0){\n {vectorused(np,false);int cr=0,cc=0;for(int s=0;sint{if(b<0||b>=np)return 0;int r0=(a<0||a>=np)?0:P[tsp[a]].tr,c0=(a<0||a>=np)?0:P[tsp[a]].tc;return abs(r0-P[tsp[b]].sr)+abs(c0-P[tsp[b]].sc);};\n {bool imp=true;while(imp){imp=false;for(int i=0;i=0){imp=true;int val=tsp[bi];if(bj>bi){tsp.erase(tsp.begin()+bi);tsp.insert(tsp.begin()+bj,val);}else{tsp.erase(tsp.begin()+bi);tsp.insert(tsp.begin()+bj+1,val);}}}}\n }\n vectortsp_rank(np,np);for(int s=0;s=8)?0.005:0.03; // reduced TSP weight for large nfp\n int stall=0;\n while((int)ops.size()<97000){\n int tdone=0;for(auto&d:P)if(d.done)tdone++;if(tdone==np)break;\n bool prog=false;\n {bool any=true;\n while(any&&(int)ops.size()<97000){\n any=false;\n vector>dr;\n for(int k=0;kbest(n);iota(best.begin(),best.end(),0);\n if(n<=5){\n vectorperm(n);iota(perm.begin(),perm.end(),0);int bc=INT_MAX;\n do{int cost=0,cr=rx,cc=ry;for(int i:perm){int r=P[dr[i].second].tr,c=P[dr[i].second].tc;cost+=abs(cr-r)+abs(cc-c);cr=r;cc=c;}if(costused(n,false);int cr=rx,cc=ry;\n for(int step=0;stepint{int ra=(a<0)?rx:P[dr[best[a]].second].tr,ca=(a<0)?ry:P[dr[best[a]].second].tc;return abs(ra-P[dr[best[b]].second].tr)+abs(ca-P[dr[best[b]].second].tc);};\n bool imp2=true;while(imp2){imp2=false;for(int i=0;i=0){\n int k=pickfp(fi,P[fi].sr,P[fi].sc);\n if(k>=0){\n // Extras: global search with target proximity bonus\n for(int ex=0;ex=0){if(cbh(k))prog=true;break;}\n if(!prog){int ci=-1,bd=INT_MAX;for(auto&[src,di]:sm){int d=abs(rx-src.first)+abs(ry-src.second);if(d=0){int k=pickfp(ci,P[ci].sr,P[ci].sc);if(k>=0&&cbh(k))prog=true;}}}\n if(prog)stall=0;\n else{stall++;if(stall>300)break;\n string op(2*Vp,'.');for(int k=0;k=N||fc<0||fc>=N)continue;if(hld[k]<0){auto it=sm.find({fr,fc});if(it!=sm.end()&&g[fr][fc]==1){hld[k]=it->second;sm.erase(it);g[fr][fc]=0;op[Vp+1+k]='P';}}else{int di=hld[k];if(P[di].tr==fr&&P[di].tc==fc&&g[fr][fc]==0){g[fr][fc]=1;P[di].done=true;hld[k]=-1;op[Vp+1+k]='P';}}}ops.push_back(op);}\n }\n for(auto&op:ops)cout<\nusing namespace std;\nint main(){\n ios_base::sync_with_stdio(false);cin.tie(NULL);\n using Clock=chrono::steady_clock;auto t0=Clock::now();\n auto elMs=[&](){return(long long)chrono::duration_cast(Clock::now()-t0).count();};\n int N;cin>>N;int M=2*N;\n vectorX(M),Y(M),W(M);\n for(int i=0;i>X[i]>>Y[i];W[i]=(ix2)swap(x1,x2);if(y1>y2)swap(y1,y2);\n cout<<4<<\"\\n\"<bx(M),by(M);\n {vectoridx(M);iota(idx.begin(),idx.end(),0);\n sort(idx.begin(),idx.end(),[&](int a,int b){return X[a]&f,int lo,int hi)->pair{\n int cur=0,cs=-1,mx=0,blo=-1,bhi=-1;bool ir=false;\n for(int i=0,n=(int)f.size();i=lo&&f[i].other<=hi)gs+=f[i].w;i++;}\n if(!ir){if(gs>0){cs=xv;cur=gs;ir=true;if(cur>mx){mx=cur;blo=cs;bhi=xv;}}}\n else{cur+=gs;if(cur>mx){mx=cur;blo=cs;bhi=xv;}if(cur<0){cur=0;ir=false;}}}\n return{blo,bhi};};\n auto evalRect=[&](int x1,int x2,int y1,int y2){int s=0;\n for(int i=0;i=x1&&X[i]<=x2&&Y[i]>=y1&&Y[i]<=y2)s+=W[i];return s;};\n auto coordDescent=[&](int x1,int x2,int y1,int y2)->tuple{\n x1=max(0,min(CMAX,x1));x2=max(0,min(CMAX,x2));y1=max(0,min(CMAX,y1));y2=max(0,min(CMAX,y2));\n if(x1>x2)swap(x1,x2);if(y1>y2)swap(y1,y2);\n int px1=-1,px2=-1,py1=-1,py2=-1;\n for(int it=0;it<20;it++){if(x1==px1&&x2==px2&&y1==py1&&y2==py2)break;\n px1=x1;px2=x2;py1=y1;py2=y2;\n auto[nx1,nx2]=kadane(bx,y1,y2);if(nx1>=0){x1=nx1;x2=nx2;}\n auto[ny1,ny2]=kadane(by,x1,x2);if(ny1>=0){y1=ny1;y2=ny2;}}\n return make_tuple(evalRect(x1,x2,y1,y2),x1,x2,y1,y2);};\n const int G=200,step=CMAX/G;\n vector>grid(G,vector(G,0));\n for(int i=0;ics(G,0);\n for(int gx2=gx1;gx2mx){mx=cur;ms=cst;me=gy;}if(cur<0){cur=0;cst=gy+1;}}\n if(me>=0&&mx>bgs){bgs=mx;bgx1=gx1;bgx2=gx2;bgy1=ms;bgy2=me;}}}\n int ix1=bgx1*step,ix2=min((bgx2+1)*step,CMAX),iy1=bgy1*step,iy2=min((bgy2+1)*step,CMAX);\n int gscore=-1,rx1=0,rx2=1,ry1=0,ry2=1;\n struct BR{int s,x1,x2,y1,y2;};\n vector
top_bases;const int NB=5;\n auto tryRun=[&](int x1,int x2,int y1,int y2){\n auto[s,a,b,c,d]=coordDescent(x1,x2,y1,y2);\n if(s>gscore){gscore=s;rx1=a;rx2=b;ry1=c;ry2=d;}\n if(s>0){\n bool dup=false;\n for(auto&br:top_bases){\n if(abs(br.x1-a)+abs(br.x2-b)+abs(br.y1-c)+abs(br.y2-d)<4000){\n if(s>br.s){br.s=s;br.x1=a;br.x2=b;br.y1=c;br.y2=d;}\n dup=true;break;\n }\n }\n if(!dup){\n top_bases.push_back({s,a,b,c,d});\n sort(top_bases.begin(),top_bases.end(),[](auto&a,auto&b){return a.s>b.s;});\n if((int)top_bases.size()>NB)top_bases.resize(NB);\n }\n }};\n tryRun(ix1,ix2,iy1,iy2);tryRun(0,CMAX,0,CMAX);\n {long long cx=0,cy=0;for(int i=0;i1700)break;\n int seed=rng()%N;int cx=X[seed],cy=Y[seed];int half;\n switch(rng()%4){case 0:half=200+rng()%800;break;case 1:half=1000+rng()%9000;break;\n case 2:half=10000+rng()%20000;break;default:half=30000+rng()%20000;break;}\n tryRun(cx-half,cx+half,cy-half,cy+half);}\n auto findArm=[&](const vector>&fish,int clo,int chi)->tuple{\n vectorxs;\n for(auto&[s,c,w]:fish)if(c>=clo&&c<=chi)xs.push_back(c);\n sort(xs.begin(),xs.end());xs.erase(unique(xs.begin(),xs.end()),xs.end());\n if(xs.empty())return{0,-1,-1,0};\n int kx=(int)xs.size();vectorcum(kx,0);int bsc=0,bc1=-1,bc2=-1,bsw=0;\n for(int i=0,n=(int)fish.size();i(fish[i]);\n while(i(fish[i])==csw){auto&[s2,c,w]=fish[i];++i;\n if(c>=clo&&c<=chi)cum[(int)(lower_bound(xs.begin(),xs.end(),c)-xs.begin())]+=w;}\n int cur=0,cs2=-1,mx=0,blo=-1,bhi=-1;bool ir=false;\n for(int j=0;j0){cs2=xs[j];cur=gs;ir=true;if(cur>mx){mx=cur;blo=cs2;bhi=xs[j];}}}\n else{cur+=gs;if(cur>mx){mx=cur;blo=cs2;bhi=xs[j];}if(cur<0){cur=0;ir=false;}}}\n if(mx>bsc){bsc=mx;bc1=blo;bc2=bhi;bsw=csw;}}\n return{bsc,bc1,bc2,bsw};};\n int global_best=-1;\n auto runPipeline=[&](int bx1,int bx2,int by1,int by2,int dep)->void{\n vector>ft,fb,fr,fl;\n for(int i=0;iby2&&X[i]>=bx1&&X[i]<=bx2)ft.emplace_back(Y[i],X[i],W[i]);\n if(Y[i]=bx1&&X[i]<=bx2)fb.emplace_back(-Y[i],X[i],W[i]);\n if(X[i]>bx2&&Y[i]>=by1&&Y[i]<=by2)fr.emplace_back(X[i],Y[i],W[i]);\n if(X[i]=by1&&Y[i]<=by2)fl.emplace_back(-X[i],Y[i],W[i]);}\n sort(ft.begin(),ft.end());sort(fb.begin(),fb.end());sort(fr.begin(),fr.end());sort(fl.begin(),fl.end());\n auto[ts,tax1,tax2,tay2]=findArm(ft,bx1,bx2);auto[bms,bax1,bax2,nb]=findArm(fb,bx1,bx2);int bay1=-nb;\n auto[rms,ray1,ray2,rax2]=findArm(fr,by1,by2);auto[ls,lay1,lay2,nl]=findArm(fl,by1,by2);int lax1=-nl;\n bool ht=ts>0&&tax1>=bx1&&tax2<=bx2&&tax1by2;\n bool hb=bms>0&&bax1>=bx1&&bax2<=bx2&&bax10&&ray1>=by1&&ray2<=by2&&ray1bx2;\n bool hl=ls>0&&lay1>=by1&&lay2<=by2&&lay1bud)continue;\n int sc=(mask&1?ts:0)+(mask&2?bms:0)+(mask&4?rms:0)+(mask&8?ls:0);\n if(sc>bsc){bsc=sc;bht=mask&1;bhb=mask&2;bhr=mask&4;bhl=mask&8;}\n }\n ht=ht&&bht;hb=hb&&bhb;hr=hr&&bhr;hl=hl&&bhl;\n }\n int tc=(ht?ct:0)+(hb?cb2:0)+(hr?cr2:0)+(hl?cl:0);\n struct AI{int c1,c2,sw,score,side;};\n vectorall_arms;\n if(ht)all_arms.push_back({tax1,tax2,tay2,ts,0});if(hb)all_arms.push_back({bax1,bax2,-bay1,bms,1});\n if(hr)all_arms.push_back({ray1,ray2,rax2,rms,2});if(hl)all_arms.push_back({lay1,lay2,-lax1,ls,3});\n int ub=tc,uv=4*(int)all_arms.size();\n auto acf=[&](const AI&a)->int{\n if(a.side==0)return 2*(a.sw-by2);if(a.side==1)return 2*(by1+a.sw);\n if(a.side==2)return 2*(a.sw-bx2);return 2*(bx1+a.sw);};\n vectorsc2;\n function>&,int,int,int,int)>far;\n far=[&](const vector>&fish,int clo,int chi,int side,int d){\n if(clo>chi||d<=0||elMs()>1950)return;\n auto[sc,c1,c2,sw]=findArm(fish,clo,chi);if(sc<=0||c1<0||c1>=c2)return;\n sc2.push_back({c1,c2,sw,sc,side});\n far(fish,clo,c1-1,side,d-1);far(fish,c2+1,chi,side,d-1);};\n if(ht){far(ft,bx1,tax1-1,0,dep);far(ft,tax2+1,bx2,0,dep);}\n if(hb){far(fb,bx1,bax1-1,1,dep);far(fb,bax2+1,bx2,1,dep);}\n if(hr){far(fr,by1,ray1-1,2,dep);far(fr,ray2+1,by2,2,dep);}\n if(hl){far(fl,by1,lay1-1,3,dep);far(fl,lay2+1,by2,3,dep);}\n sort(sc2.begin(),sc2.end(),[](const AI&a,const AI&b){return a.score>b.score;});\n {\n int ni=min((int)sc2.size(),60);\n int W=min((bud-ub)/2,100000);\n if(ni>0&&W>0){\n vector>dp(ni+1,vector(W+1,0));\n for(int i=0;i=wt)dp[i+1][w]=max(dp[i+1][w],dp[i][w-wt]+val);}\n }\n int cw=W;\n for(int i=ni-1;i>=0;i--){\n int wt=min(acf(sc2[i])/2,W),val=sc2[i].score;\n if(cw>=wt&&dp[i+1][cw]==dp[i][cw-wt]+val){\n int c=acf(sc2[i]);\n if(ub+c<=bud&&uv+4<=996){all_arms.push_back(sc2[i]);ub+=c;uv+=4;}\n cw-=wt;\n }\n }\n for(int i=ni;i<(int)sc2.size();i++){int c=acf(sc2[i]);if(c<=0||ub+c>bud||uv+4>996)continue;all_arms.push_back(sc2[i]);ub+=c;uv+=4;}\n }else{for(auto&arm:sc2){int c=acf(arm);if(c<=0||ub+c>bud||uv+4>996)continue;all_arms.push_back(arm);ub+=c;uv+=4;}}\n }\n int bs=evalRect(bx1,bx2,by1,by2),combined=bs;\n for(auto&a:all_arms)combined+=a.score;\n if(combined<=global_best)return;\n if(all_arms.empty()){\n if(bs>global_best){global_best=bs;\n int x1=bx1,x2=bx2,y1=by1,y2=by2;\n if(x1>=x2){if(x2=y2){if(y2ta,ba3,ra,la3;\n for(auto&a:all_arms){if(a.side==0)ta.push_back(a);else if(a.side==1)ba3.push_back(a);\n else if(a.side==2)ra.push_back(a);else la3.push_back(a);}\n sort(ba3.begin(),ba3.end(),[](auto&a,auto&b){return a.c1b.c2;});\n sort(la3.begin(),la3.end(),[](auto&a,auto&b){return a.c2>b.c2;});\n vector>v;\n v.push_back({bx1,by1});\n {int cx=bx1;for(auto&a:ba3){int b1=-a.sw;if(a.c1>cx)v.push_back({a.c1,by1});\n v.push_back({a.c1,b1});v.push_back({a.c2,b1});v.push_back({a.c2,by1});cx=a.c2;}}\n v.push_back({bx2,by1});\n {int cy=by1;for(auto&a:ra){if(a.c1>cy)v.push_back({bx2,a.c1});\n v.push_back({a.sw,a.c1});v.push_back({a.sw,a.c2});v.push_back({bx2,a.c2});cy=a.c2;}}\n v.push_back({bx2,by2});\n {int cx=bx2;for(auto&a:ta){if(a.c2>res;\n for(auto&p:v){if(res.empty()||res.back()!=p)res.push_back(p);}\n while(res.size()>1&&res.front()==res.back())res.pop_back();\n if((int)res.size()<4)return;\n {set>vs(res.begin(),res.end());if((int)vs.size()!=(int)res.size())return;}\n global_best=combined;\n cout<<(int)res.size()<<\"\\n\";for(auto&[x,y]:res)cout<\nusing namespace std;\ntypedef long long ll;\n\nint N, T;\nvector W, H;\ndouble sW, sH, mxW, mxH, totA;\n\nstruct Op { int p, r; char d; int b; };\n\npair simulate(const vector& ops) {\n vector x0(N,0),y0(N,0),x1(N,0),y1(N,0);\n vector pl(N,false);\n for (const auto& o : ops) {\n int p = o.p;\n ll w = max(1LL, llround(o.r ? H[p] : W[p]));\n ll h = max(1LL, llround(o.r ? W[p] : H[p]));\n if (o.d == 'U') {\n ll xl = o.b >= 0 ? x1[o.b] : 0LL;\n ll yt = 0;\n for (int i = 0; i < N; i++)\n if (pl[i] && x0[i] < xl+w && x1[i] > xl)\n yt = max(yt, y1[i]);\n x0[p]=xl; y0[p]=yt; x1[p]=xl+w; y1[p]=yt+h;\n } else {\n ll yt = o.b >= 0 ? y1[o.b] : 0LL;\n ll xl = 0;\n for (int i = 0; i < N; i++)\n if (pl[i] && y0[i] < yt+h && y1[i] > yt)\n xl = max(xl, x1[i]);\n x0[p]=xl; y0[p]=yt; x1[p]=xl+w; y1[p]=yt+h;\n }\n pl[p] = true;\n }\n ll rW=0, rH=0;\n for (int i = 0; i < N; i++)\n if (pl[i]) { rW=max(rW,x1[i]); rH=max(rH,y1[i]); }\n return {rW, rH};\n}\n\n// col=false: shelf packing (rows); col=true: column packing\n// For col=false, line0 uses U, rest use L\n// For col=true, line0 uses L, rest use U\nvector make_pack(const vector& rot, double tgt, bool col) {\n vector ops; ops.reserve(N);\n int cl = -1; double cm = 0;\n vector lr; vector lc;\n int p0 = -1;\n for (int i = 0; i < N; i++) {\n double m = col ? (rot[i] ? W[i] : H[i]) : (rot[i] ? H[i] : W[i]);\n double c = col ? (rot[i] ? H[i] : W[i]) : (rot[i] ? W[i] : H[i]);\n if (cl < 0 || cm + m > tgt) {\n cl++; cm = m;\n lr.push_back(i); lc.push_back(c);\n if (cl == 0) {\n ops.push_back({i, rot[i], col?'L':'U', -1});\n p0 = i;\n } else {\n ops.push_back({i, rot[i], col?'U':'L', lr[cl-1]});\n }\n } else {\n cm += m;\n if (c > lc[cl]) { lc[cl]=c; lr[cl]=i; }\n if (cl == 0) {\n ops.push_back({i, rot[i], col?'L':'U', p0});\n p0 = i;\n } else {\n ops.push_back({i, rot[i], col?'U':'L', lr[cl-1]});\n }\n }\n }\n return ops;\n}\n\ndouble calc_score(const vector& rot, double tgt, bool col) {\n auto [a,b] = simulate(make_pack(rot, tgt, col));\n return (double)(a+b);\n}\n\nint main() {\n ios_base::sync_with_stdio(false);\n cin.tie(nullptr);\n\n double sigma;\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 sW=sH=mxW=mxH=totA=0;\n for (int i = 0; i < N; i++) {\n sW+=W[i]; sH+=H[i];\n mxW=max(mxW,W[i]); mxH=max(mxH,H[i]);\n totA+=W[i]*H[i];\n }\n\n const double BUDGET = 2600.0;\n auto t0 = chrono::steady_clock::now();\n auto now = [&]() {\n return chrono::duration(chrono::steady_clock::now()-t0).count();\n };\n\n vector g_rot;\n double g_tgt=0, g_score=1e18;\n bool g_col=false;\n\n for (int t = 0; t < T; t++) {\n double ts = now();\n double per = max(1.0, (BUDGET - ts) / (T - t));\n double dl = ts + per * 0.95;\n\n mt19937 rng(t * 1234567891u ^ 987654321u);\n uniform_real_distribution uni(0,1);\n\n bool col;\n double lo, hi, tgt;\n vector rot(N);\n\n if (t < (T+1)/2) {\n col = (t & 1);\n lo = col ? mxH : mxW;\n hi = col ? sH : sW;\n tgt = max(lo, min(hi, sqrt(totA)));\n // Init rotation: minimize cross-dim\n for (int i = 0; i < N; i++)\n rot[i] = col ? (H[i] br=rot;\n double bt=tgt;\n bool bc=col;\n double bs=cur;\n\n double Th = cur*0.05+1.0;\n double Tl = max(1.0, cur*1e-5);\n\n // Simulated Annealing\n for (int it=0; ; it++) {\n if ((it&63)==0 && now()>=dl) break;\n double frac = max(0.0, min(1.0, (now()-ts)/per));\n double Tc = max(Tl, Th * pow(Tl/Th, frac));\n\n int mv = rng()%10, fi=-1;\n double ot=tgt;\n bool oc=col;\n double olo=lo, ohi=hi;\n\n if (mv < 7) {\n fi = rng()%N;\n rot[fi] ^= 1;\n } else if (mv < 9) {\n tgt = max(lo, min(hi, tgt * exp((uni(rng)*2-1)*0.35)));\n } else {\n col ^= 1;\n lo = col ? mxH : mxW;\n hi = col ? sH : sW;\n tgt = max(lo, min(hi, ot));\n }\n\n double ns = calc_score(rot, tgt, col);\n double d = ns - cur;\n if (d <= 0 || uni(rng) < exp(-d/Tc)) {\n cur = ns;\n if (ns < bs) { bs=ns; br=rot; bt=tgt; bc=col; }\n } else {\n if (fi >= 0) rot[fi] ^= 1;\n else if (mv < 9) tgt = ot;\n else { col=oc; lo=olo; hi=ohi; tgt=ot; }\n }\n }\n\n // Final greedy passes\n for (int pass=0; pass<3; pass++) {\n bool imp=false;\n for (int i=0; i> Wf >> Hf;\n }\n\n return 0;\n}","ahc041":"#include \nusing namespace std;\ntypedef long long ll;\nint N,M,H,A[1000];\nvectorG[1000];\nint par[1000],dep[1000],ssm[1000],mdn[1000];\nvectorch[1000];\nvoid dfs_init(int v){ssm[v]=A[v];mdn[v]=0;for(int c:ch[v]){dfs_init(c);ssm[v]+=ssm[c];mdn[v]=max(mdn[v],mdn[c]+1);}}\nvoid push_dep(int v,int d){dep[v]=d;for(int c:ch[v])push_dep(c,d+1);}\nbool in_sub(int w,int v){for(;w!=-1;w=par[w])if(w==v)return true;return false;}\nvoid pull_ssm(int v){for(;v!=-1;v=par[v]){int s=A[v];for(int c:ch[v])s+=ssm[c];ssm[v]=s;}}\nvoid pull_mdn(int v){for(;v!=-1;v=par[v]){int m=0;for(int c:ch[v])m=max(m,mdn[c]+1);mdn[v]=m;}}\nvoid do_move(int v,int np){int op=par[v];if(op!=-1){auto&c=ch[op];c.erase(find(c.begin(),c.end(),v));}par[v]=np;if(np!=-1){ch[np].push_back(v);push_dep(v,dep[np]+1);}else push_dep(v,0);if(op!=-1){pull_ssm(op);pull_mdn(op);}if(np!=-1){pull_ssm(np);pull_mdn(np);}}\nvoid rebuild(){for(int i=0;iq;q.push(v);while(!q.empty()){int u=q.front();q.pop();for(int c:ch[u]){dep[c]=dep[u]+1;q.push(c);}}}for(int v=0;vp(N);iota(p.begin(),p.end(),0);if(iter==0)sort(p.begin(),p.end(),[](int a,int b){return A[a]>A[b];});else shuffle(p.begin(),p.end(),rng);for(int v:p){int lim=H-1-mdn[v];if(lim<0)continue;int bp=par[v];ll bg=0;for(int w:G[v]){if(dep[w]>lim||in_sub(w,v))continue;ll g=(ll)(dep[w]+1-dep[v])*ssm[v];if(g>bg){bg=g;bp=w;}}if(bg>0){do_move(v,bp);ok=true;}}if(!ok)break;}}\nvoid build_bfs(vector&ord){fill(par,par+N,-1);fill(dep,dep+N,0);for(int i=0;ivis(N,false);for(int s:ord){if(vis[s])continue;queueq;q.push(s);vis[s]=true;while(!q.empty()){int v=q.front();q.pop();if(dep[v]>=H)continue;for(int u:G[v])if(!vis[u]){vis[u]=true;par[u]=v;dep[u]=dep[v]+1;ch[v].push_back(u);q.push(u);}}}for(int v=0;v=H)return;int lim=H-1-mdn[v];int bp=par[v];ll bg=0;for(int w:G[v]){if(dep[w]>lim||in_sub(w,v))continue;ll g=(ll)(dep[w]+1-dep[v])*ssm[v];if(g>bg){bg=g;bp=w;}}if(bg>0){do_move(v,bp);cur+=bg;}}\nint main(){\n ios::sync_with_stdio(false);cin.tie(0);\n cin>>N>>M>>H;for(int i=0;i>A[i];\n for(int i=0;i>u>>v;G[u].push_back(v);G[v].push_back(u);}\n for(int i=0;i>x>>y;}\n auto t0=chrono::steady_clock::now();\n mt19937 rng(42);\n ll best_sc=-1;vectorbest_par(N);\n for(int trial=0;;trial++){\n if(chrono::duration(chrono::steady_clock::now()-t0).count()>0.30)break;\n vectorord(N);iota(ord.begin(),ord.end(),0);\n if(trial==0)sort(ord.begin(),ord.end(),[](int a,int b){return A[a]best_sc){best_sc=sc;copy(par,par+N,best_par.begin());}\n }\n copy(best_par.begin(),best_par.end(),par);rebuild();ll cur=best_sc;\n uniform_real_distributionuni(0,1);\n auto ts=chrono::steady_clock::now();\n double sa_t=max(0.05,1.97-chrono::duration(ts-t0).count());\n double T=1000.0;\n for(long long step=0;;step++){\n if(step%10000==0){double t=chrono::duration(chrono::steady_clock::now()-ts).count();if(t>=sa_t)break;T=1000.0*pow(0.001,t/sa_t);}\n int v=rng()%N;int lim=H-1-mdn[v];if(lim<0)continue;\n if(G[v].empty())continue;int w=G[v][rng()%G[v].size()];\n if(w==par[v]||dep[w]>lim||in_sub(w,v))continue;\n ll gain=(ll)(dep[w]+1-dep[v])*ssm[v];\n if(gain>0||(T>0.01&&uni(rng)0)greedy_one(v,cur);\n if(cur>best_sc){best_sc=cur;copy(par,par+N,best_par.begin());}\n }\n }\n if(chrono::duration(chrono::steady_clock::now()-t0).count()<1.98){\n copy(best_par.begin(),best_par.end(),par);rebuild();\n run_greedy(rng);\n ll sc=compute_score();if(sc>best_sc)copy(par,par+N,best_par.begin());\n }\n for(int v=0;v\nusing namespace std;\nint N,M,R_[42],C_[42],ctop[21],cbot[21],rlef[21],rrig[21];\nint gc_mode;\nint gc(int d,int v){if(gc_mode==0){if(d==0)return v+1;if(d==1)return N-v;if(d==2)return 2*(v+1);return 2*(N-v);}if(d==0)return 2*(v+1);if(d==1)return 2*(N-v);if(d==2)return v+1;return N-v;}\nint od(int k,int d){return(d<=1)?R_[k]:C_[k];}\nint ad_[42],ax_[42];\nvectorgv[4][21];\nvoid ins(int d,int a,int v){auto&vec=gv[d][a];vec.insert(lower_bound(vec.begin(),vec.end(),v),v);}\nvoid del(int d,int a,int v){auto&vec=gv[d][a];vec.erase(lower_bound(vec.begin(),vec.end(),v));}\nint gcv(int d,int a){if(gv[d][a].empty())return 0;return gc(d,(d==0||d==2)?gv[d][a].back():gv[d][a].front());}\nbool vg(int k,int d,int a){int r=R_[k],c=C_[k],kd=(d<=1)?r:c;if(d==0)return a==c&&kdcbot[a];if(d==2)return a==r&&kdrrig[a];}\nint bpc(int j){if(gc_mode==1)return 0;if(!gv[0][j].empty()&&!gv[1][j].empty())return min(gcv(0,j),gcv(1,j));return 0;}\nint bpr(int i){if(gc_mode==0)return 0;if(!gv[2][i].empty()&&!gv[3][i].empty())return min(gcv(2,i),gcv(3,i));return 0;}\nint TC(){int t=0;for(int d=0;d<4;d++)for(int i=0;iint{return(eint{return(eco[21],ro[21];\nvoid ls(){bool imp=true;while(imp){imp=false;int bg=0,bt=-1,bk=-1,ba=-1,bb=-1,bd=-1,bx=-1;for(int k=0;kbg){bg=g;bt=1;bk=k;bd=d;bx=a;}};if(rcbot[c])t1(1,c);if(crrig[r])t1(3,r);}for(int j=0;jbg){bg=g;bt=2;ba=a;bb=b;bd=d;bx=x;}};t(0,j);t(1,j);}}for(int i=0;ibg){bg=g;bt=2;ba=a;bb=b;bd=d;bx=x;}};t(2,i);t(3,i);}}if(bg>0){if(bt==1)mv1(bk,bd,bx);else mv2(ba,bb,bd,bx);imp=true;}}}\nint bc=INT_MAX,bad_[42],bax_[42];\nvoid sb(){bc=TC();for(int k=0;kops[4];int n=0;if(rcbot[c])ops[n++]={1,c};if(crrig[r])ops[n++]={3,r};int gd,ga;if(det){int best=INT_MAX;gd=ops[0].first;ga=ops[0].second;for(int i=0;i>N;vectorbrd(N);for(int i=0;i>brd[i];M=0;for(int i=0;i\nusing namespace std;\nconst int MAXN=100;\nint N,L,T[MAXN],a[MAXN],b[MAXN],cv[MAXN],fv[MAXN],flow[MAXN];\nvoid computeFlow(){fill(flow,flow+N,0);for(int i=0;i0&&!vis[j])return false;return true;}\nbool checkBwd(){if(T[0]==0)return true;static int rl[MAXN][2*MAXN],rc[MAXN];static bool vis[MAXN];int q[MAXN],qh=0,qt=0;fill(rc,rc+N,0);for(int i=0;i0&&!vis[j])return false;return true;}\nvoid fixFwdConn(){for(int pass=0;pass0&&!vis[j]){u=j;break;}if(u<0)break;long long bd=(long long)4e18;int bi=-1;bool bA=false;for(int i=0;i0)?((long long)(abs(flow[oa]-w-T[oa])-abs(flow[oa]-T[oa]))+(long long)(abs(flow[u]+w-T[u])-abs(flow[u]-T[u]))):0LL;if(d0)?((long long)(abs(flow[ob]-w-T[ob])-abs(flow[ob]-T[ob]))+(long long)(abs(flow[u]+w-T[u])-abs(flow[u]-T[u]))):0LL;if(d0){flow[a[bi]]-=cv[bi];flow[u]+=cv[bi];}a[bi]=u;}else{if(fv[bi]>0){flow[b[bi]]-=fv[bi];flow[u]+=fv[bi];}b[bi]=u;}}}\nvoid fixBwdConn(){if(T[0]==0)return;for(int pass=0;pass0&&!vis[j]){u=j;break;}if(u<0)break;long long bd=(long long)4e18;int bk=-1;bool bA=false;for(int k=0;k0)?((long long)(abs(flow[oa]-w-T[oa])-abs(flow[oa]-T[oa]))+(long long)(abs(flow[k]+w-T[k])-abs(flow[k]-T[k]))):0LL;if(d0)?((long long)(abs(flow[ob]-w-T[ob])-abs(flow[ob]-T[ob]))+(long long)(abs(flow[k]+w-T[k])-abs(flow[k]-T[k]))):0LL;if(d0){flow[a[u]]-=cv[u];flow[bk]+=cv[u];}a[u]=bk;}else{if(fv[u]>0){flow[b[u]]-=fv[u];flow[bk]+=fv[u];}b[u]=bk;}}}\nvoid flowSearch(){long long ce=flowErr();bool imp=true;while(imp){imp=false;for(int i=0;i0)?((long long)(abs(flow[old]-w-T[old])-abs(flow[old]-T[old]))+(long long)(abs(flow[j]+w-T[j])-abs(flow[j]-T[j]))):0LL;if(d=0){if(w>0){flow[old]-=w;flow[bj]+=w;}ce+=bd;if(t2)b[i]=bj;else a[i]=bj;imp=true;}}}}\nlong long simulateFull(int co[],int od[],int ed[]){int cnt[MAXN]={},vc[MAXN]={};fill(od,od+N,0);fill(ed,ed+N,0);int cur=0;cnt[0]=vc[0]=1;for(int w=2;w<=L;w++){if(vc[cur]&1){od[cur]++;cur=a[cur];}else{ed[cur]++;cur=b[cur];}cnt[cur]++;vc[cur]++;}long long e=0;for(int j=0;j>N>>L;for(int i=0;i>T[i];\n for(int i=0;i>items;\n for(int i=0;i0)rem[0]--;\n priority_queue>pq;for(int j=0;j(chrono::steady_clock::now()-t0).count();};\n struct Cand{long long d;int i,t,j;bool operator<(const Cand&o)const{return dcands;cands.reserve(20001);\n int noImp=0;\n // PHASE 1: EXACT 49,136,088 proxy search (1750ms)\n while(el()<1750000LL){\n cands.clear();\n for(int i=0;i0){int oj=a[i];for(int j=0;j0){int oj=b[i];for(int j=0;j0)partial_sort(cands.begin(),cands.begin()+K,cands.end());\n bool found=false;\n for(int k=0;k=15){\n bool pittBetter=false;\n for(int ptry=0;ptry<3&&!pittBetter;ptry++){\n copy(ba,ba+N,a);copy(bb,bb+N,b);\n for(int p=0;p<8;p++){int i=rng()%N,t=rng()%2,j=(int)(rng()%N);if(t)b[i]=j;else a[i]=j;}\n computeFlow();flowSearch();fixFwdConn();\n long long err=simulate();\n if(err\nusing namespace std;\nint main() {\n ios_base::sync_with_stdio(false); cin.tie(NULL);\n int N,M,Q,L,W; cin>>N>>M>>Q>>L>>W;\n vectorG(M);for(int&g:G)cin>>g;\n vectorcx(N),cy(N);\n for(int i=0;i>lx>>rx>>ly>>ry;cx[i]=(lx+rx)/2.0;cy[i]=(ly+ry)/2.0;}\n auto ed2=[&](int a,int b)->double{double dx=cx[a]-cx[b],dy=cy[a]-cy[b];return dx*dx+dy*dy;};\n vectormpar(N,-1);vectormkey(N,0);\n {vectorvis(N,false);vectorkey(N,1e18);key[0]=0;\n for(int it=0;it>mch(N);for(int v=1;vpost,preord;\n {stack>s;s.push({0,0});while(!s.empty()){auto&[v,ci]=s.top();if(ci<(int)mch[v].size())s.push({mch[v][ci++],0});else{post.push_back(v);s.pop();}}}\n {stacks;s.push(0);while(!s.empty()){int v=s.top();s.pop();preord.push_back(v);for(int i=(int)mch[v].size()-1;i>=0;i--)s.push(mch[v][i]);}}\n vectoresz(N,1);for(int v:post)for(int c:mch[v])esz[v]+=esz[c];\n vector>elist;for(int v=1;v());\n multisetremG(G.begin(),G.end());map>szg;for(int i=0;iscut(N,false),asgn(N,false);vector>groups(M);\n for(auto&[w,v]:elist){if(asgn[v])continue;int s=esz[v];if(s<=0||!remG.count(s))continue;\n remG.erase(remG.find(s));int u=mpar[v];while(u!=-1&&!scut[u]){esz[u]-=s;u=mpar[u];}scut[v]=true;\n int gid=szg[s].front();szg[s].pop();queueq;q.push(v);\n while(!q.empty()){int nu=q.front();q.pop();if(asgn[nu])continue;groups[gid].push_back(nu);asgn[nu]=true;for(int c:mch[nu])if(!asgn[c])q.push(c);}}\n {vectorrem;for(int v:preord)if(!asgn[v])rem.push_back(v);\n int pos=0;for(int i=0;i>sc(M);\n for(int i=0;icx[v[rxi]])rxi=k;\n if(cy[v[k]]cy[v[ryi]])ryi=k;\n if(cx[v[k]]+cy[v[k]]>cx[v[d1i]]+cy[v[d1i]])d1i=k;\n if(cy[v[k]]-cx[v[k]]>cy[v[d2i]]-cx[v[d2i]])d2i=k;\n if(cx[v[k]]+cy[v[k]]vector{\n vectorused(g,false);vectorp;p.reserve(g);p.push_back(v[s0]);used[s0]=true;\n for(int k=1;k&p)->double{double l=0;for(int k=1;k&p){\n for(int it=0;it<30;it++){bool imp=false;\n for(int a=0;a&p){\n if(g<4)return;\n for(int it=0;it<10;it++){\n double bg=1e-9;int ba=-1,bj=-1;\n for(int a=1;abg){bg=rg-ic;ba=a;bj=j;}}}\n if(ba<0)break;\n int moved=p[ba];\n if(bjbj;kk--)p[kk]=p[kk-1];p[bj]=moved;}\n else{for(int kk=ba;kk&p){\n if(g<5)return;\n for(int it=0;it<5;it++){\n double bg=1e-9;int ba=-1,bj=-1,bdir=0;\n for(int a=1;a=a-1&&j<=a+3)continue;\n double base=ed2(p[j-1],p[j]);\n double fwd=ed2(p[j-1],p[a])+ed2(p[a+1],p[j])-base;\n double bwd=ed2(p[j-1],p[a+1])+ed2(p[a],p[j])-base;\n double best=min(fwd,bwd);\n if(rg-best>bg){bg=rg-best;ba=a;bj=j;bdir=(bwdba+1)?(bj-2):bj;\n vectornp;np.reserve(g);int cnt=0;\n for(int k=0;kv7orig({lxi,rxi,lyi,ryi,ceni});\n vectorstarts={lxi,rxi,lyi,ryi,d1i,d2i,d3i,d4i,ceni};\n sort(starts.begin(),starts.end());starts.erase(unique(starts.begin(),starts.end()),starts.end());\n double bestl=1e18,bestl2=1e18,bestl_v7=1e18;\n vectorsc2,sc_v7;\n auto upd=[&](vector&p,double l,bool isv7){\n if(l0);}\n {vectorp(v);topt(p);double l=plen(p);upd(p,l,true);}\n auto do_opt=[&](vector&p){run_oropt(p);if(use_o2)run_oropt2(p);topt(p);};\n {auto p=sc[i];do_opt(p);sc[i]=p;}\n double best=plen(sc[i]);\n if((int)sc2.size()==g){auto p=sc2;do_opt(p);double l=plen(p);if(l>>>ae(M);\n auto dq=[&](const vector&qc,int gi){if((int)qc.size()<2||qrem<=0)return;qrem--;\n cout<<\"? \"<>a>>b;ae[gi].push_back({ed2(a,b),{a,b}});}};\n auto nw=[&](int g)->int{if(g<=1)return 0;if(g<=L)return 1;return(g-2)/(L-1)+1;};\n int tmand=0;for(int i=0;i=g);if(last&&en-st(sc[i].begin()+st,sc[i].begin()+en),i);if(last)break;st+=L-1;}}\n {vectorlg;for(int i=0;iL)lg.push_back(i);\n if(!lg.empty()&&xtra>0)for(int qi=0;qi0;qi++){int gi=lg[qi%(int)lg.size()];int g=G[gi];\n int stride=max(1,g/L),off=(qi/(int)lg.size())%stride;\n vectorwin;for(int k=off;k=2)dq(win,gi);}}\n vectorpar(N);auto fu=[&](int x)->int{while(par[x]!=x){par[x]=par[par[x]];x=par[x];}return x;};\n vector>>ans(M);\n for(int i=0;i0)cout<<\" \";cout<\nusing namespace std;\nconst int N=20;bool grid[N][N];\nconst int DR[]={-1,1,0,0},DC[]={0,0,-1,1};\ninline bool inB(int r,int c){return(unsigned)r<(unsigned)N&&(unsigned)c<(unsigned)N;}\ninline void slE(int r,int c,int d,int er,int ec,int &sr,int &sc){\n switch(d){case 0:sr=(ec==c&&er>=0&&err&&er=0&&ecc&&ec> fp1(int r0,int c0,int tr,int tc){\n memset(d1,-1,sizeof(d1));int S=(r0*N+c0)*441,G=(tr*N+tc)*441;if(S==G)return{};\n d1[S]=0;int qh=0,qt=0;q1[qt++]=S;\n while(qh> res;int r=r0,c=c0;while(r!=tr){res.push_back({'M',r> path;for(int cur=G;cur!=S;cur=p1[cur])path.push_back({\"MSA\"[a1[cur]>>2],\"UDLR\"[a1[cur]&3]});reverse(path.begin(),path.end());return path;}\n#define MAKEFPN(NM,NS,DP,PP,QP,AP,NPH,FALLSZ) \\\nconst int NS=N*N*NPH*21*21;static int DP[NS],PP[NS],QP[NS];static uint8_t AP[NS];\nMAKEFPN(fp2,NS2,d2,p2,q2,a2,2,2)\nMAKEFPN(fp3,NS3,d3,p3,q3,a3,3,3)\nMAKEFPN(fp4,NS4,d4,p4,q4,a4,4,4)\nMAKEFPN(fp5,NS5,d5,p5,q5,a5,5,5)\nMAKEFPN(fp6,NS6,d6,p6,q6,a6,6,6)\nMAKEFPN(fp7,NS7,d7,p7,q7,a7,7,7)\nMAKEFPN(fp8,NS8,d8,p8,q8,a8,8,8)\n#undef MAKEFPN\ntemplate\nvector> fpNimpl(int r0,int c0,const int*trs,const int*tcs){\n memset(DP,-1,NSZ*sizeof(int));\n auto E=[&](int r,int c,int ph,int er,int ec){return (r*N+c)*NPH*441+ph*441+(er+1)*21+(ec+1);};\n int S=E(r0,c0,0,-1,-1),G=E(trs[NPH-1],tcs[NPH-1],NPH-1,-1,-1);\n DP[S]=0;int qh=0,qt=0;QP[qt++]=S;\n while(qh> res;for(int i=0,pr=r0,pc=c0;i> path;for(int cur=G;cur!=S;cur=PP[cur])path.push_back({\"MSA\"[AP[cur]>>2],\"UDLR\"[AP[cur]&3]});reverse(path.begin(),path.end());return path;}\nvector> fp2(int r0,int c0,int a,int b,int c,int d){int tr[]={a,c},tc[]={b,d};return fpNimpl<2,NS2,d2,p2,q2,a2>(r0,c0,tr,tc);}\nvector> fp3(int r0,int c0,int a,int b,int c,int d,int e,int f){int tr[]={a,c,e},tc[]={b,d,f};return fpNimpl<3,NS3,d3,p3,q3,a3>(r0,c0,tr,tc);}\nvector> fp4(int r0,int c0,int a,int b,int c,int d,int e,int f,int g,int h){int tr[]={a,c,e,g},tc[]={b,d,f,h};return fpNimpl<4,NS4,d4,p4,q4,a4>(r0,c0,tr,tc);}\nvector> fp5(int r0,int c0,int a,int b,int c,int d,int e,int f,int g,int h,int i,int j){int tr[]={a,c,e,g,i},tc[]={b,d,f,h,j};return fpNimpl<5,NS5,d5,p5,q5,a5>(r0,c0,tr,tc);}\nvector> fp6(int r0,int c0,int a,int b,int c,int d,int e,int f,int g,int h,int i,int j,int k,int l){int tr[]={a,c,e,g,i,k},tc[]={b,d,f,h,j,l};return fpNimpl<6,NS6,d6,p6,q6,a6>(r0,c0,tr,tc);}\nvector> fp7(int r0,int c0,int a,int b,int c,int d,int e,int f,int g,int h,int i,int j,int k,int l,int m,int n){int tr[]={a,c,e,g,i,k,m},tc[]={b,d,f,h,j,l,n};return fpNimpl<7,NS7,d7,p7,q7,a7>(r0,c0,tr,tc);}\nvector> fp8(int r0,int c0,int a,int b,int c,int d,int e,int f,int g,int h,int i,int j,int k,int l,int m,int n,int o,int p){int tr[]={a,c,e,g,i,k,m,o},tc[]={b,d,f,h,j,l,n,p};return fpNimpl<8,NS8,d8,p8,q8,a8>(r0,c0,tr,tc);}\nint cr,cc,eebr=-1,eebc=-1;\nvoid execPath(const vector>&path){\n for(auto[a,d]:path){cout<>Nin>>M;vector> pts(M);\n for(int i=0;i>pts[i].first>>pts[i].second;\n memset(grid,0,sizeof(grid));cr=pts[0].first;cc=pts[0].second;eebr=eebc=-1;\n int k=1;\n while(k