#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
int n, m;
vector<vector<int>> a;
vector<int> dx = {0, 1, 0, -1}, dy = {1, 0, -1, 0};
bool visited[2502][2502];
int mnx, mny, mxx, mxy, ver = 0;
void dfs(int x, int y){
visited[x][y] = true;
ver++;
mnx = min(mnx, x);
mny = min(mny, y);
mxx = max(mxx, x);
mxy = max(mxy, y);
for (int i = 0; i < 4; i++){
int X = x + dx[i], Y = y + dy[i];
if (X > 0 && X < n - 1 && Y > 0 && Y < m - 1 && !visited[X][Y] && a[X][Y] == 0) dfs(X, Y);
}
}
const int MaxN = 702;
bool good[MaxN][MaxN][MaxN]; // i, l, r -> l..r subarray of i
vector<int> val[MaxN][MaxN];
int cnt[MaxN * MaxN];
long long count_rectangles(vector<vector<int>> A) {
a = A;
n = (int) A.size(), m = (int) A[0].size();
if (n == 3) {
int ans = 0;
for (int l = 1; l < m - 1; l++) {
int mx = 0;
for (int r = l; r < m - 1; r++) {
mx = max(mx, a[1][r]);
if (a[1][r] >= min(a[0][r], a[2][r])) break;
if (mx < min(a[1][l - 1], a[1][r + 1])) ans++;
}
}
return ans;
}
if (max(n, m) <= 700){
for (int i = 1; i + 1 < n; i++){
for (int l = 0; l + 2 < m; l++){
int mx = A[i][l + 1];
for (int r = l + 2; r < m; r++){
if (A[i][l] > mx && A[i][r] > mx){
good[i][l][r] = true;
}
mx = max(mx, A[i][r]);
}
}
}
for (int j = 0; j < m; j++){
for (int l = 0; l + 2 < n; l++){
int mx = A[l + 1][j];
for (int r = l + 2; r < n; r++){
if (A[l][j] > mx && A[r][j] > mx){
val[r][j].push_back(l * n + r);
}
mx = max(mx, A[r][j]);
}
}
}
int ans = 0;
for (int l = 0; l + 2 < m; l++) for (int r = l + 2; r < m; r++){
for (int x = 0; x + 2 < n; x++){
if (!good[x + 1][l][r] || good[x][l][r]) continue;
vector<int> used_values;
for (int y = x + 2; y < n; y++){
for (int j = l + 1; j < r; j++){
for (int v : val[y][j]){
if (v / n < x) continue;
cnt[v]++;
if (cnt[v] == r - l - 1) ans++;
used_values.push_back(v);
}
}
if (!good[y][l][r]) break;
}
for (int v : used_values){
cnt[v] = 0;
}
}
}
return ans;
}
int ans = 0;
for (int i = 1; i < n - 1; i++){
for (int j = 1; j < m - 1; j++){
if (visited[i][j] || a[i][j] == 1) continue;
mnx = mny = 1e9, mxx = mxy = ver = 0;
dfs(i, j);
if (ver != (mxx - mnx + 1) * (mxy - mny + 1)) continue;
bool ok = true;
for (int k = mnx; k <= mxx; k++){
if (a[k][mny - 1] == 0 || a[k][mxy + 1] == 0) ok = false;
}
for (int k = mny; k <= mxy; k++){
if (a[mnx - 1][k] == 0 || a[mxx + 1][k] == 0) ok = false;
}
if (ok) ans++;
}
}
return ans;
}
