#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define fastIO cin.tie(0); ios::sync_with_stdio(false)
struct ST{
int l, r;
ST *lt, *rt;
int mx;
void comb() {
mx = max(lt->mx, rt->mx);
}
ST(int bl, int br, vector<int> &a) {
lt = rt = nullptr;
l = bl, r = br;
if(l == r) {
mx = a[l];
} else {
int m = (l+r)/2;
lt = new ST(l, m, a);
rt = new ST(m+1, r, a);
comb();
}
}
int qry(int ql, int qr) {
if(qr < l || r < ql) return -1;
if(ql <= l && r <= qr) return mx;
else return max(lt->qry(ql, qr), rt->qry(ql, qr));
}
};
ll count_rectangles(vector<vector<int>> arr) {
int r = size(arr);
int c = size(arr[0]);
vector<vector<int>> rotatedArr(c, vector<int>(r, 0));
for(int i = 0; i < r; i++) {
for(int j = 0; j < c; j++) {
rotatedArr[j][i] = arr[i][j];
}
}
vector<ST> rows, cols;
for(int i = 0; i < r; i++) {
rows.push_back(ST(0, c-1, arr[i]));
}
for(int i = 0; i < c; i++) {
cols.push_back(ST(0, r-1, rotatedArr[i]));
}
ll ans = 0;
for(int yl = 1; yl < r-1; yl++) {
for(int xl = 1; xl < c-1; xl++) {
for(int yr = yl; yr < r-1; yr++) {
for(int xr = xl; xr < c-1; xr++) {
bool valid = true;
for(int x = xl; x <= xr; x++) {
valid &= min(arr[yl-1][x], arr[yr+1][x]) > cols[x].qry(yl, yr);
}
for(int y = yl; y <= yr; y++) {
valid &= min(arr[y][xl-1], arr[y][xr+1]) > rows[y].qry(xl, xr);
}
ans += valid;
}
}
}
}
return ans;
}
