#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];
}
bool isMaximal(int i1, int i2, int j1, int j2) {
if (query(i1, i2, j1, j2) > 0) return false;
if (i1 > 0 && query(i1 - 1, i2, j1, j2) == 0) return false;
if (i2 + 1 < n && query(i1, i2 + 1, j1, j2) == 0) return false;
if (j1 > 0 && query(i1, i2, j1 - 1, j2) == 0) return false;
if (j2 + 1 < n && query(i1, i2, j1, j2 + 1) == 0) return false;
return true;
}
ii getMaximal(int i, int l, int r) {
assert(query(i, i, l, r) == 0);
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;
assert(isMaximal(i1, i2, l, r));
return ii{i1, i2};
}
vector<ii> getRanges(int i, int l, int r) {
int lo = -1, hi = sz(ran[i]);
while (hi - lo > 1) {
int mid = (lo + hi) / 2;
if (ran[i][mid].snd >= l) hi = mid;
else lo = mid;
}
int j = hi;
if (j == sz(ran[i])) return {};
vector<ii> ret;
ret.eb(max(ran[i][j].fst, l), min(ran[i][j].snd, r));
j++;
while (j < sz(ran[i]) && ran[i][j].fst <= r) {
ret.eb(ran[i][j].fst, min(ran[i][j].snd, r));
j++;
}
return ret;
}
struct Rectangle {
int i1, i2, j1, j2;
bool operator<(const Rectangle &o) const {
return make_tuple(i1, i2, j1, j2) < make_tuple(o.i1, o.i2, o.j1, o.j2);
}
};
map<Rectangle, int> memo;
void expand(Rectangle r, int i, vector<Rectangle> &v) {
for (auto [j1, j2] : getRanges(i, r.j1, r.j2)) {
auto [i1, i2] = getMaximal(i, j1, j2);
v.eb(i1, i2, j1, j2);
}
}
int dp(Rectangle r) {
if (memo.count(r)) return memo[r];
vector<Rectangle> v;
if (r.i1 > 0) expand(r, r.i1 - 1, v);
if (r.i2 + 1 < n) expand(r, r.i2 + 1, v);
int &ret = memo[r];
for (auto nxt : v) ret = max(ret, dp(nxt) + (nxt.j2 - nxt.j1 + 1) * ((nxt.i2 - nxt.i1 + 1) - (r.i2 - r.i1 + 1)));
return ret;
}
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]) {
auto [i1, i2] = getMaximal(i, j1, j2);
Rectangle r = {i1, i2, j1, j2};
ret = max(ret, dp(r) + (j2 - j1 + 1) * (i2 - i1 + 1));
}
return ret;
}
