#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
namespace binary_grid {
const int inf = 1e5;
const int maxn = 2501;
int dx[] = {+1, 0, -1, 0};
int dy[] = {0, -1, 0, +1};
int n, m;
int a[maxn][maxn];
int vis[maxn][maxn];
int cnt = 0;
int mnx, mxx, mny, mxy;
void dfs(int x, int y) {
cnt++;
vis[x][y] = 1;
mnx = min(mnx, x);
mxx = max(mxx, x);
mny = min(mny, y);
mxy = max(mxy, y);
for(int i = 0; i < 4; i++) {
int xx = dx[i] + x;
int yy = dy[i] + y;
if(1 <= xx and xx <= n and 1 <= yy and yy <= m and a[xx][yy] == 0 and !vis[xx][yy]) {
dfs(xx, yy);
}
}
}
int count_rectangles(vector<vector<int> > aa) {
n = aa.size(), m = aa[0].size();
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++) {
a[i + 1][j + 1] = aa[i][j];
}
}
int ans = 0;
for(int i = 1; i <= n; i++) {
for(int j = 1; j <= m; j++) {
if(!vis[i][j] and a[i][j] == 0) {
mnx = inf, mxx = -inf;
mny = inf, mxy = -inf;
cnt = 0;
dfs(i, j);
if((mxx - mnx + 1) * (mxy - mny + 1) == cnt and mnx != 1 and mxx != n and mny != 1 and mxy != m) {
ans++;
}
}
}
} return ans;
}
}
namespace slow_general {
using ii = pair<int, int>;
using ll = long long;
const int N = 2500;
const int inf = 1e9;
int n, m;
int g[N][N];
bitset<N> ls[N][N];
int mxx[N];
int count_rectangles(vector<vector<int> > a) {
n = a.size(), m = a[0].size();
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++) {
g[i][j] = a[i][j];
}
}
for(int i = 1; i < n - 1; i++) {
for(int j = 1; j < m - 1; j++) {
int mx = -inf;
for(int k = j; k > 0; k--) {
mx = max(mx, g[i][k]);
if(mx < g[i][j + 1]) {
if(mx < g[i][k - 1]) {
ls[i][j][k] = 1;
}
} else {
break;
}
}
}
}
int ans = 0;
for(int u = 1; u < n - 1; u++) {
for(int i = 1; i < m - 1; i++) {
mxx[i] = -inf;
}
for(int v = u; v < n - 1; v++) {
bitset<N> can;
for(int i = 1; i < m - 1; i++) {
mxx[i] = max(mxx[i], g[v][i]);
if(mxx[i] < g[u - 1][i] and mxx[i] < g[v + 1][i]) {
can[i] = 1;
}
}
int now = 0;
while(can._Find_next(now) < m - 1) {
int l = can._Find_next(now);
int r = l;
while(can[r + 1]) {
r++;
}
bitset<N> range;
for(int i = l; i <= r; i++) {
range[i] = 1;
}
for(int j = l; j <= r; j++) {
bitset<N> intersection = range;
for(int i = u; i <= v; i++) {
intersection &= ls[i][j];
if(intersection.count() == 0) {
break;
}
}
ans += intersection.count();
}
now = r;
}
}
move_u : ;
}
return ans;
}
}
long long count_rectangles(vector<vector<int> > a) {
int n = a.size(), m = a[0].size();
int mx = -1e9, mn = 1e9;
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++) {
mx = max(mx, a[i][j]);
mn = min(mn, a[i][j]);
}
}
if(0 <= mn and mx <= 1) {
return binary_grid::count_rectangles(a);
} else {
return slow_general::count_rectangles(a);
}
}
