#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
#define sig signed
#define int long long
#define arr array
#define vec vector
#define pii pair<int, int>
#define fir first
#define sec second
const int N = 2e2 + 5, M = 2e2 + 5;
int n, m;
arr<arr<int, M>, N> a;
arr<arr<arr<int, M>, M>, N> mx, vld, up, dwn, fr;
void prcmp() {
for (int i = 1; i <= n; i++) {
for (int l = 1; l <= m; l++) {
for (int r = l; r <= m; r++) {
mx[i][l][r] = max(mx[i][l][r - 1], a[i][r]);
vld[i][l][r] = (l != 1 && r != m && mx[i][l][r] < a[i][l - 1] && mx[i][l][r] < a[i][r + 1]);
}
}
}
for (int i = 1; i <= n; i++) {
for (int l = 1; l <= m; l++) {
for (int r = l; r <= m; r++) {
up[i][l][r] = 0, dwn[i][l][r] = n + 1, fr[i][l][r] = n + 1;
for (int j = i - 1; j >= 1; j--) {
if (mx[j][l][r] >= mx[i][l][r]) {
up[i][l][r] = j;
break;
}
}
for (int j = i + 1; j <= n; j++) {
if (mx[j][l][r] >= mx[i][l][r]) {
dwn[i][l][r] = j;
break;
}
}
for (int j = i + 1; j <= n; j++) {
if (!vld[j][l][r]) {
fr[i][l][r] = j;
break;
}
}
// cout << i << " " << l << " " << r << ": " << mx[i][l][r] << endl;
// cout << i << " " << l << " " << r << ": " << up[i][l][r] << endl;
}
}
}
}
int cmp() {
int ans = 0;
for (int i = 1; i <= n - 2; i++) {
for (int l = 2; l <= m - 1; l++) {
for (int r = l; r <= m - 1; r++) {
int j = min({fr[i][l][r], dwn[i][l][r], n});
if (i + 2 > j) continue;
int nw_ans = 0;
for (int k = i + 2; k <= j; k++)
nw_ans += (up[k][l][r] <= i);
// cout << i << " " << l << " " << r << "; " << nw_ans << endl;
ans += nw_ans;
}
}
}
return ans;
}
int count_rectangles(vec<vec<sig>> _a) {
n = _a.size(), m = _a[0].size();
for (int i = 1; i <= n; i++)
for (int j = 1; j <= m; j++)
a[i][j] = _a[i - 1][j - 1];
prcmp();
int ans = cmp();
return ans;
}
