#include "soccer.h"
#include <bits/stdc++.h>
#define forsn(i, s, n) for (int i = int(s); i < int(n); i++)
#define forn(i, n) forsn(i, 0, n)
#define dforsn(i, s, n) for (int i = int(n) - 1; i >= int(s); i--)
#define dforn(i, n) dforsn(i, 0, n)
#define sz(x) int(x.size())
#define all(x) begin(x), end(x)
#define pb push_back
#define eb emplace_back
#define fst first
#define snd second
using namespace std;
using vi = vector<int>;
using ii = pair<int, int>;
using ll = long long;
const int MAX_N = 2005;
int pref[MAX_N][MAX_N], n;
vector<ii> ran[MAX_N];
int query(int i1, int i2, int j1, int j2) {
i2++, j2++;
return pref[i2][j2] - pref[i1][j2] - pref[i2][j1] + pref[i1][j1];
}
ii getMaximal(int i, int l, int r) {
int lo = i, hi = n;
while (hi - lo > 1) {
int mid = (lo + hi) / 2;
if (query(i, mid, l, r) == 0) lo = mid;
else hi = mid;
}
int i2 = lo;
lo = -1, hi = i;
while (hi - lo > 1) {
int mid = (lo + hi) / 2;
if (query(mid, i, l, r) == 0) hi = mid;
else lo = mid;
}
int i1 = hi;
return ii{i1, i2};
}
struct Rectangle {
int i1, i2, j1, j2;
ll val;
Rectangle(int i, int _j1, int _j2) {
j1 = _j1, j2 = _j2;
tie(i1, i2) = getMaximal(i, j1, j2);
val = 1LL * MAX_N * MAX_N * i + MAX_N * j1 + j2;
}
bool operator<(const Rectangle &o) const { return val < o.val; }
};
map<Rectangle, int> memo;
void aux(int i, const Rectangle &curr, vector<Rectangle> &v) {
int lo = -1, hi = sz(ran[i]);
while (hi - lo > 1) {
int mid = (lo + hi) / 2;
if (ran[i][mid].snd >= curr.j1) hi = mid;
else lo = mid;
}
int j = hi;
int &ret = memo[curr];
while (j < sz(ran[i]) && ran[i][j].fst <= curr.j2) {
v.eb(i, max(ran[i][j].fst, curr.j1), min(ran[i][j].snd, curr.j2));
j++;
}
}
int dp(const Rectangle &r) {
if (!memo.count(r)) {
vector<Rectangle> v;
if (r.i1 > 0) aux(r.i1 - 1, r, v);
if (r.i2 + 1 < n) aux(r.i2 + 1, r, v);
for (auto nxt : v) memo[r] = max(memo[r], dp(nxt) + (nxt.j2 - nxt.j1 + 1) * ((nxt.i2 - nxt.i1 + 1) - (r.i2 - r.i1 + 1)));
}
return memo[r];
}
int biggest_stadium(int N, vector<vi> F) {
n = N;
forn(i, n) forn(j, n) pref[i + 1][j + 1] = pref[i][j + 1] + pref[i + 1][j] - pref[i][j] + F[i][j];
forn(i, n) {
forn(j, n) {
if (F[i][j]) continue;
if (j == 0 || F[i][j - 1]) {
ran[i].eb(j, j);
} else {
ran[i].back().snd++;
}
}
}
int ret = 0;
forn(i, n) for (auto [j1, j2] : ran[i]) {
Rectangle r(i, j1, j2);
ret = max(ret, dp(r) + (r.j2 - r.j1 + 1) * (r.i2 - r.i1 + 1));
}
return ret;
}
