#include "soccer.h"
#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef basic_string<int> BI;
typedef long long ll;
typedef pair<int,int> PII;
typedef double db;
mt19937 mrand(random_device{}()); 
const ll mod=1000000007;
int rnd(int x) { return mrand() % x;}
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
// head

int bf(int N, std::vector<std::vector<int>> F) {
    vector<PII> rg;
    int cs=0;
    rep(i,0,N) rep(j,0,N) cs+=F[i][j];
    if (cs==0) return N*N;
    if (cs==1) {
        int x=0,y=0;
        rep(i,0,N) rep(j,0,N) if (F[i][j]) x=i,y=j;
        return N*N-min(x+1,N-x)*min(y+1,N-y);
    }
    rep(i,0,N) {
        int pl=N+1,pr=-1;
        rep(j,0,N) {
            if (F[i][j]==0) pl=min(pl,j),pr=max(pr,j);
        }
        if (pl<=pr) {
            rg.pb(mp(pl,pr));
            rep(j,pl,pr+1) if (F[i][j]==1) { return 0; }
        }
    }
    for (auto q1:rg) for (auto q2:rg) {
        auto p1=q1,p2=q2;
        if (p1>p2) swap(p1,p2);
        if (p1.fi<p2.fi&&p1.se<p2.se) return 0;
    }
    rg.clear();
    rep(j,0,N) {
        int pl=N+1,pr=-1;
        rep(i,0,N) {
            if (F[i][j]==0) pl=min(pl,i),pr=max(pr,i);
        }
        if (pl<=pr) {
            rg.pb(mp(pl,pr));
            rep(i,pl,pr+1) if (F[i][j]==1) { return 0; }
        }
    }
    for (auto q1:rg) for (auto q2:rg) {
        auto p1=q1,p2=q2;
        if (p1.fi<p2.fi&&p1.se<p2.se) return 0;
    }
    int r=0;
    rep(i,0,N) rep(j,0,N) {
        if (F[i][j]==0) ++r;
    }
    return r;
}

const int N=2010;
int stk[N],top,a[N],l[N],r[N],T,ans;
vector<array<int,3>> seg;
map<PII,int> dp,pd;
void dfs(int u,int L,int R) {
    if (l[u]) dfs(l[u],L,u-1);
    if (r[u]) dfs(r[u],u+1,R);
    if (a[u]>T) {
        int v=0;
        auto it=pd.lower_bound(mp(L,-1));
        vector<PII> er;
        while (it!=pd.end()&&it->fi.fi<=R) {
            if (it->fi.fi>=L&&it->fi.se<=R) {
                v=max(v,it->se+((R-L+1-(it->fi.se-it->fi.fi+1))*(a[u]-T)));
                er.pb(it->fi);
            }
            ++it;
        }
        for (auto x:er) pd.erase(x);
        if (pd.count(mp(L,R))) v=pd[mp(L,R)];
        v=max(v,(R-L+1)*(a[u]-T));
        if (dp.count(mp(L,u-1))) v=max(v,dp[mp(L,u-1)]+(R-L+1-((u-1)-L+1))*(a[u]-T));
        if (dp.count(mp(u+1,R))) v=max(v,dp[mp(u+1,R)]+(R-L+1-(R-(u+1)+1))*(a[u]-T));
        ans=max(ans,v);
        //printf("T %d L %d R %d v %d\n",T,L,R,v);
        dp[mp(L,R)]=v;
        //seg.pb({L-1,R-1,a[u]});
    }
}

void build(VI v,int th) {
    int top=0;
    T=th;
    int n=SZ(v);
    rep(i,1,n+1) a[i]=v[i-1];
    rep(i,1,n+1) l[i]=r[i]=0;
    rep(i,1,n+1) {
        int k=top;
        while (k>0&&a[stk[k-1]]>a[i]) --k;
        if (k) r[stk[k-1]]=i;
        if (k<top) l[i]=stk[k];
        stk[k++]=i;
        top=k;
    }
    dfs(stk[0],1,n);
    // rt is stk[0]
}

int biggest_stadium(int n, std::vector<std::vector<int>> F)
{
    //if (n>500) return bf(n,F);
    vector<vector<int>> nxt(n+1,VI(n));
    rep(i,0,n) {
        nxt[n][i]=n;
        per(L,0,n) {
            if (F[i][L]) nxt[L][i]=L;
            else nxt[L][i]=nxt[L+1][i];
        }
    }

    rep(L,0,n) {
        pd=dp; dp.clear();
        build(nxt[L],L);
    }
    return ans;
}