#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,l[N],r[N],T,ans;
int len[N],dp[N];
PII seg[N];
PII a[N];
vector<PII> upd[N];

const int inf=1<<30;
const int LOGN=12;
template<class T>
struct STTable {
    int n;
    T f[LOGN+1][N];
    void init(vector<T> a) { // 0-based
        n=SZ(a);
        assert(n < (1<<LOGN) && n < N);
        rep(i,0,n) f[0][i]=a[i];
        rep(j,1,LOGN) for (int i=0;i+(1<<j)-1<n;i++) {
            f[j][i]=min(f[j-1][i],f[j-1][i+(1<<(j-1))]);
        }
    }
    T query(int l,int r) {
        assert(l<=r);
        int len=31-__builtin_clz(r-l+1);
        return min(f[len][l],f[len][r-(1<<len)+1]);
    }
};
STTable<PII> t;

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);
    len[u]=R-L+1; seg[u]=mp(L,R);
    if (a[u].fi>T) {
        int w=a[u].fi-T;
        int v=len[u]*w;
        for (auto [val,l]:upd[u]) v=max(v,val+(len[u]-l)*w);
        if (l[u]) v=max(v,dp[l[u]]+(len[u]-len[l[u]])*w);
        if (r[u]) v=max(v,dp[r[u]]+(len[u]-len[r[u]])*w);
        ans=max(ans,v);
        dp[u]=v;
    } else dp[u]=-inf;
}

void build(VI v,int th) {
    int top=0;
    T=th;
    int n=SZ(v);
    rep(i,1,n+1) a[i]=mp(v[i-1],i);
    rep(i,1,n+1) upd[i].clear();
    t.init(vector<PII>(a+1,a+n+1));
    rep(i,1,n+1) if (dp[i]!=-inf) {
        auto v=t.query(seg[i].fi-1,seg[i].se-1);
        //printf("cnm %d %d %d\n",seg[i].fi-1,seg[i].se-1,v.se);
        upd[v.se].eb(dp[i],len[i]);
    }
    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(i,1,n+1) dp[i]=-inf;
    rep(L,0,n) build(nxt[L],L);
    return ans;
}