#include "rect.h"
#ifdef NYAOWO
#include "grader.cpp"
#endif
#include <bits/stdc++.h>
#define For(i, a, b) for(int i = a; i <= b; i++)
#define Forr(i, a, b) for(int i = a; i >= b; i--)
#define F first
#define S second
#define eb emplace_back
#define sz(x) ((int)x.size())
#define all(x) x.begin(), x.end()
#define int LL
using namespace std;
using LL = long long;
using pii = pair<int, int>;
const int MAXN = 2510;
int a[MAXN][MAXN];
int n, m;
int mx[MAXN];
int fail[MAXN];
int ok[MAXN][MAXN];
long long count_rectangles(std::vector<std::vector<int32_t> > A) {
n = sz(A);
m = sz(A[0]);
if(min(n, m) <= 2) return 0;
assert(n <= 200);
For(i, 0, n - 1) For(j, 0, m - 1) a[i][j] = A[i][j];
long long ans = 0;
For(u, 1, n - 2) {
For(i, 1, m - 2) For(j, i, m - 2) {
ok[i][j] = 1;
}
For(i, 0, m - 1) {
mx[i] = a[u][i];
}
For(d, u, n - 2) {
For(i, 0, m - 1) {
mx[i] = a[d][i];
fail[i] = mx[i] >= min(a[u - 1][i], a[d + 1][i]);
}
For(l, 1, m - 2) {
bool ac = true;
int cur = a[d][l];
For(r, l, m - 2) {
if(fail[r]) ac = false;
cur = max(cur, a[d][r]);
if(cur >= min(a[d][l - 1], a[d][r + 1])) ok[l][r] = 0;
if(ok[l][r] && ac) {
ans++;
// cout << u << " " << d << " " << l << " " << r << "\n";
}
}
}
}
}
return ans;
}
