#pragma GCC optimize("O3")
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
#define pb push_back
#define ff first
#define ss second
#define MOD 1000000009
#define INF 1000000019
#define POT (1<<20)
#define INFL 1000000000000000099
ll toint(pair<pair<ll,ll>,pair<ll,ll>>a){
return ((a.ff.ff*2007LL+a.ff.ss)*2007LL+a.ss.ff)*2007LL+a.ss.ss;
}
pair<pair<ll,ll>,pair<ll,ll>>fromint(ll x){
return {{(x/(2007LL*2007LL*2007LL))%2007,(x/(2007LL*2007LL))%2007},{(x/2007)%2007,x%2007}};
}
ll inv(ll aa,ll n){
auto a=fromint(aa);
//swap(a.ff.ff,a.ff.ss);
swap(a.ss.ff,a.ss.ss);
//a.ff.ff=n-a.ff.ff+1;
//a.ff.ss=n-a.ff.ss+1;
a.ss.ff=n-a.ss.ff+1;
a.ss.ss=n-a.ss.ss+1;
return toint(a);
}
void wyp(ll x){
auto a= fromint(x);
cout<<a.ff.ff<<" "<<a.ff.ss<<" "<<a.ss.ff<<" "<<a.ss.ss<<" ";
}
pair<map<ll,vector<ll>>,vector<ll>>pomf(int n,vector<vector<int>>f){
map<ll,vector<ll>>mp;
vector<ll>v;
ll mx[n+7][n+7];
ll nxt[n+7][n+7][11];
for(ll i=1;i<=n;i++){mx[0][i]=0;nxt[n+1][i][0]=n+1;}
for(ll i=1;i<=n;i++){
mx[i][0]=10000;
mx[i][n+1]=10000;
for(ll j=1;j<=n;j++){
mx[i][j]=mx[i-1][j];
if(f[i-1][j-1])mx[i][j]=i;
}
mx[n+1][i]=n+1;
}
for(ll i=0;i<=n+1;i++)nxt[n+1][i][0]=n+1;
for(ll i=n;i>=1;i--){
nxt[i][n+1][0]=n+1;
for(ll j=n;j>=1;j--){
nxt[i][j][0]=nxt[i+1][j][0];
if(f[i-1][j-1])nxt[i][j][0]=i;
}
for(ll j=1;j<11;j++){
for(ll k=0;k+(1<<j)-1<=n+1;k++)nxt[i][k][j]=min(nxt[i][k][j-1],nxt[i][k+(1<<(j-1))-1][j-1]);
}
}
for(ll i=0;i<=n+1;i++){
for(ll j=0;j<=n+1;j++){
//cout<<nxt[i][j][0]<<" "<<mx[i][j]<<" ";
}
//cout<<"\n";
}
// cout<<"\n\n";
for(ll i=1;i<=n;i++){
ll lw[n+7],pw[n+7],lwp[n+7],pwp[n+7],pomlw[n+7];
lwp[0]=0;
pwp[n+1]=n+1;
for(ll j=1;j<=n;j++){
lwp[j]=lwp[j-1];
if(mx[i+1][j]==i+1)lwp[j]=j;
}
for(ll j=n;j>=1;j--){
pwp[j]=pwp[j+1];
if(mx[i+1][j]==i+1)pwp[j]=j;
}
for(ll i=1;i<=n;i++){
// cout<<lwp[i]<<" "<<pwp[i]<< " ";
}
// cout<<"\n";
stack<pair<ll,ll>>st;
st.push({10000,0});
//return {mp,v};
for(ll j=1;j<=n;j++){
while(mx[i][j]>st.top().ff)st.pop();
pomlw[j]=st.top().ss;
st.push({mx[i][j],j});
}
while(st.size())st.pop();
st.push({10000,0});
for(ll j=1;j<=n;j++){
while(mx[i][j]>=st.top().ff)st.pop();
lw[j]=st.top().ss;
st.push({mx[i][j],j});
}
while(st.size())st.pop();
st.push({10000,n+1});
for(ll j=n;j>=1;j--){
while(mx[i][j]>=st.top().ff)st.pop();
pw[j]=st.top().ss;
st.push({mx[i][j],j});
}
lw[0]=0;
lw[n+1]=n+1;
pw[0]=0;
pw[n+1]=n+1;
for(ll j=1;j<=n;j++){
if(mx[i][pomlw[j]]==mx[i][j])continue;
//cout<<pw[j]<<"aa ";
ll lx=lw[j]+1;
ll px=pw[j]-1;
ll ly=mx[i][j]+1;
ll py=i;
//cout<<lx<<" "<<px<<" "<<ly<<" "<<py<<"\n\n";
if((lwp[j]>=lx || pwp[j]<=px) && lx<=px & ly<=py){
v.pb(toint({{lx,px},{ly,py}}));
}
if(lx==1 && px==n)continue;
ll lg=log2(px-lx+1);
ll py2=min(nxt[i][lx][lg],nxt[i][px-(1<<lg)+1][lg])-1;
ll ly2=min(mx[i][lx-1],mx[i][px+1])+1;
ll lx2,px2;
if(ly2==mx[i][lx-1]+1){
lx2=lw[lx-1]+1;
px2=pw[lx-1]-1;
}
else{
lx2=lw[px+1]+1;
px2=pw[px+1]-1;
}
//cout<<lx2<<" "<<px2<<" "<<ly2<<" "<<py2<<"\n\n\n";
mp[toint({{lx2,px2},{ly2,py}})].pb(toint({{lx,px},{ly,py2}}));
}
}
return {mp,v};
}
int biggest_stadium(int n,vector<vector<int>>f){
ll ans=0;
for(auto i :f){
// for(auto j : i)cout<<j<<" ";
// cout<<"\n";
}
// cout<<"\n";
auto pom=pomf(n,f);
//return 0;
vector<ll>states=pom.ss;
// cout<<"\n\n\n";
map<ll,vector<ll>>przej=pom.ff;
//for(ll i : states){wyp(i);/*cout<<": ";for(ll j : pom.ff[i])wyp(j);*/cout<<"\n";}//return 0;
for(auto it : przej){
//wyp(it.ff);
//cout<<": ";
//for(ll i : it.ss)wyp(i);
//cout<<"\n";
}
map<ll,ll>bst;
for(ll i=0;i<n/2;i++){
for(ll j=0;j<n;j++)swap(f[i][j],f[n-i-1][j]);
}//return 0;
for(auto i :f){
// for(auto j : i)cout<<j<<" ";
// cout<<"\n";
}
// cout<<"\n";
auto pom2=pomf(n,f);
for(ll i : pom2.ss)states.pb(inv(i,n));
for(auto it : pom2.ff){
for(ll i : (it).ss)przej[inv((it).ff,n)].pb(inv(i,n));
}
//cout<<"\n\n\n";
for(ll i : states){//wyp(i);/*cout<<": ";for(ll j : pom.ff[i])wyp(j);*/cout<<"\n";
}//return 0;
for(auto it : przej){
//wyp(it.ff);
//cout<<": ";
//for(ll i : it.ss)wyp(i);
//cout<<"\n";
}
sort(states.begin(),states.end(),[](const ll & a,const ll & b){
auto poma=fromint(a);
auto pomb=fromint(b);
return poma.ff.ss-poma.ff.ff>pomb.ff.ss-pomb.ff.ff;
});
for(ll i : states){
//wyp(i);
auto pomi=fromint(i);
bst[i]=max(bst[i],(pomi.ff.ss-pomi.ff.ff+1)*(pomi.ss.ss-pomi.ss.ff+1));
//cout<<bst[i]<<"\n";
ans=max(ans,bst[i]);
for(ll j : przej[i]){
auto pomj=fromint(j);
bst[j]=max(bst[j],bst[i]+(pomj.ss.ss-pomj.ss.ff-pomi.ss.ss+pomi.ss.ff)*(pomj.ff.ss-pomj.ff.ff+1));
}
}
return ans;
}
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