#include "soccer.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
struct block
{
int x1,x2,y1,y2,x3;
bool operator<(const block& other)
{
return (y2-y1) < (other.y2-other.y1);
}
};
int arr[2003][2003];
int pref[2003][2003];
vi ones[2003];
int nxt_one[2003][2003];
int one_cnt[2003][2003];
vector<block> blocks[2003];
int ans = 0;
unordered_map<int,int> ans_map[2003][2003];
unordered_map<ll,int> total_map;
ll hash_rect(ll x1, ll x2, ll y1, ll y2)
{
return x1 + x2*2005LL + y1*2005LL*2005LL + y2*2005LL*2005LL*2005LL;
}
int biggest_stadium(int n, vector<vi> F)
{
rep2(i,0,n+2)
{
rep2(j,0,n+2)
{
arr[i][j] = 1;
}
}
rep2(i,1,n)
{
rep2(j,1,n)
{
arr[i][j] = F[i-1][j-1];
}
}
rep2(i,1,n)
{
rep2(j,1,n)
{
pref[i][j] = pref[i][j-1] + pref[i-1][j] - pref[i-1][j-1] + arr[i][j];
}
}
rep2(i,0,n+1)
{
rep2(j,1,n)
{
if(arr[i][j] == 1)
{
int p = i-1;
int prev_l = -1;
int prev_r = -1;
while(p >= 0 && arr[p][j] == 0)
{
int lb = j;
int rb = j;
int l = 1;
int r = j;
while(l <= r)
{
int mid = (l+r)/2;
if(pref[i-1][j]-pref[i-1][mid-1]-pref[p-1][j]+pref[p-1][mid-1] == 0)
{
lb = mid;
r = mid-1;
}
else
{
l = mid+1;
}
}
l = j;
r = n;
while(l <= r)
{
int mid = (l+r)/2;
if(pref[i-1][mid]-pref[i-1][j-1]-pref[p-1][mid]+pref[p-1][j-1] == 0)
{
rb = mid;
l = mid+1;
}
else
{
r = mid-1;
}
}
if(prev_l != -1 && prev_r != -1 && (prev_l != lb || prev_r != rb))
{
blocks[(i-1)-(p+1)].pb({prev_l,prev_r,p+1,i-1,j});
}
prev_l = lb;
prev_r = rb;
p--;
}
if(prev_l != -1 && prev_r != -1) blocks[(i-1)-p+1].pb({prev_l,prev_r,p+1,i-1,j});
prev_l = -1;
prev_r = -1;
p = i+1;
while(p <= n && arr[p][j] == 0)
{
int lb = j;
int rb = j;
int l = 1;
int r = j;
while(l <= r)
{
int mid = (l+r)/2;
if(pref[p][j]-pref[p][mid-1]-pref[i][j]+pref[i][mid-1] == 0)
{
lb = mid;
r = mid-1;
}
else
{
l = mid+1;
}
}
l = j;
r = n;
while(l <= r)
{
int mid = (l+r)/2;
if(pref[p][mid]-pref[p][j-1]-pref[i][mid]+pref[i][j-1] == 0)
{
rb = mid;
l = mid+1;
}
else
{
r = mid-1;
}
}
if(prev_l != -1 && prev_r != -1 && (prev_l != lb || prev_r != rb))
{
blocks[p-(i+1)-1].pb({prev_l,prev_r,i+1,p-1,j});
}
prev_l = lb;
prev_r = rb;
p++;
}
if(prev_l != -1 && prev_r != -1) blocks[p-(i+1)-1].pb({prev_l,prev_r,i+1,p-1,j});
}
}
}
rep(j,n+2)
{
int cnt = 0;
rep(i,n+2)
{
if(arr[i][j] == 1)
{
ones[j].pb(i);
one_cnt[i][j] = cnt++;
}
}
}
rep(j,n+2)
{
nxt_one[j][siz(ones[j])] = siz(ones[j]);
ones[j].pb(n+2);
}
for(int i = n+1; i >= 0; i--)
{
rep(j,n+2)
{
if(arr[i][j] == 0)
{
continue;
}
else
{
if(i != 0 && arr[i-1][j] == 0) nxt_one[j][one_cnt[i][j]] = one_cnt[i][j];
else
{
nxt_one[j][one_cnt[i][j]] = nxt_one[j][one_cnt[i][j]+1];
}
}
}
}
rep(d,n)
{
forall(it,blocks[d])
{
ll h = hash_rect(it.x1,it.y1,it.x2,it.y2);
if(total_map.find(h) != total_map.end())
{
int best = total_map[h];
ans_map[it.x3][it.y1][it.y2] = max(ans_map[it.x3][it.y1][it.y2],best);
continue;
}
int best = (it.x2-it.x1+1)*(it.y2-it.y1+1);
int l = 0;
int r = siz(ones[it.x1-1])-1;
int a = 0;
while(l <= r)
{
int mid = (l+r)/2;
if(ones[it.x1-1][mid] >= it.y1)
{
a = mid;
r = mid-1;
}
else
{
l = mid+1;
}
}
while(ones[it.x1-1][a-1] < it.y2)
{
l = max(it.y1,ones[it.x1-1][a-1]+1);
r = min(it.y2,ones[it.x1-1][a]-1);
if(l <= r)
{
best = max(best,ans_map[it.x1-1][l][r]+(it.x2-it.x1+1)*(it.y2-it.y1+1)-(r-l+1)*(it.x2-it.x1+1));
}
a = nxt_one[it.x1-1][a+1];
// cerr << a << " " << it.x1-1 << " a\n";
}
l = 0;
r = siz(ones[it.x2+1])-1;
a = 0;
while(l <= r)
{
int mid = (l+r)/2;
if(ones[it.x2+1][mid] >= it.y1)
{
a = mid;
r = mid-1;
}
else
{
l = mid+1;
}
}
while(ones[it.x2+1][a-1] < it.y2)
{
l = max(it.y1,ones[it.x2+1][a-1]+1);
r = min(it.y2,ones[it.x2+1][a]-1);
if(l <= r)
{
best = max(best,ans_map[it.x2+1][l][r]+(it.x2-it.x1+1)*(it.y2-it.y1+1)-(r-l+1)*(it.x2-it.x1+1));
}
a = nxt_one[it.x2+1][a+1];
// cerr << a << " " << it.x2+1 << " " << ones[it.x2+1][a-1]<< " a2\n";
}
ans = max(ans,best);
ans_map[it.x3][it.y1][it.y2] = max(ans_map[it.x3][it.y1][it.y2],best);
total_map[h] = best;
}
}
return ans;
}
