#include "rect.h"
#include<bits/stdc++.h>
using namespace std;
#define ll long long
ll count_rectangles(vector<vector<int>> a){
int n = a.size(), m = a[0].size();
vector<vector<int>> l(n, vector<int>(m, -1)), r(n, vector<int>(m, -1)), u(n, vector<int>(m, -1)), d(n, vector<int>(m, -1));
stack<pair<int,int>> st;
for (int i=0; i<n; i++){
while (!st.empty()) st.pop();
for (int j=0; j<m; j++){
while (!st.empty() && st.top().first <= a[i][j]){
r[i][st.top().second] = j;
st.pop();
}
if (!st.empty()) l[i][j] = st.top().second;
st.push({a[i][j], j});
}
}
for (int j=0; j<m; j++){
while (!st.empty()) st.pop();
for (int i=0; i<n; i++){
while (!st.empty() && st.top().first <= a[i][j]){
d[st.top().second][j] = i;
st.pop();
}
if (!st.empty()) u[i][j] = st.top().second;
st.push({a[i][j], i});
}
}
ll res = 0;
for (int t=1; t<n-1; t++){
for (int b=t; b<n-1; b++){
for (int i=1; i<m-1; i++){
for (int j=i; j<m-1; j++){
bool valid = true;
for (int row=t; row<=b; row++){
if (r[row][i-1] != j+1 && l[row][j+1] != i-1) valid = false;
}
for (int col=i; col<=j; col++){
if (d[t-1][col] != b+1 && u[b+1][col] != t-1) valid = false;
}
if (valid) res++;
}
}
}
}
return res;
}
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