#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
using LL = long long;
#define UP 0
#define LEFT 1
#define DOWN 2
#define RIGHT 3
constexpr int INF = 1e9;
const vector<array<int, 2>> dd{{0,1},{0,-1},{1,0},{-1,0}};
int n, m;
struct comp {
int sz;
array<int, 4> ext;
comp() : sz(0), ext({INF, INF, -INF, -INF}) {}
comp(int i, int j) : sz(1), ext({i,j,i,j}) {}
bool good() {
if (ext[UP] == 0 || ext[DOWN] == n-1) return false;
if (ext[LEFT] == 0 || ext[RIGHT] == m-1) return false;
return sz == (ext[DOWN] - ext[UP] + 1) * (ext[RIGHT] - ext[LEFT] + 1);
}
};
comp join(const comp& a, const comp& b) {
comp ans;
ans.sz = a.sz + b.sz;
ans.ext[UP] = min(a.ext[UP], b.ext[UP]);
ans.ext[LEFT] = min(a.ext[LEFT], b.ext[LEFT]);
ans.ext[DOWN] = max(a.ext[DOWN], b.ext[DOWN]);
ans.ext[RIGHT] = max(a.ext[RIGHT], b.ext[RIGHT]);
return ans;
}
LL count_rectangles(vector<vector<int>> a) {
n = a.size();
m = a[0].size();
// subtask a[i][j] \in {0,1}
LL ans = 0;
vector<vector<bool>> vis(n, vector<bool>(m, false));
for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) {
if (vis[i][j] || a[i][j] == 1) continue;
comp cur(i, j);
queue<array<int, 2>> Q;
Q.push({i, j});
vis[i][j] = true;
while (!Q.empty()) {
auto [x, y] = Q.front();
Q.pop();
for (auto [dx, dy] : dd) {
int nx = x + dx;
int ny = y + dy;
if (nx < 0 || nx >= n || ny < 0 || ny >= m) continue;
if (vis[nx][ny] || a[nx][ny] == 1) continue;
vis[nx][ny] = true;
Q.push({nx, ny});
cur = join(cur, comp(nx, ny));
}
}
ans += cur.good();
}
return ans;
}
