#include <bits/stdc++.h>
#include "rect.h"
using namespace std;
typedef long long ll;
typedef vector<int> vi;
#define pb push_back
#define ff first
#define ss second
const int nax = 2505;
int n, m;
vector<vi> A;
ll ans = 0ll;
int LG[nax];
int spr[nax][nax][12];
int spc[nax][nax][12];
void init()
{
LG[1] = 0;
for(int i = 2; i < nax; i++)
LG[i] = LG[i/2] + 1;
for(int row = 0; row < n; row++)
{
for(int col = 0; col < m; col++)
spr[row][col][0] = spc[col][row][0] = A[row][col];
}
for(int j = 1; j < 12; j++)
{
for(int row = 0; row < n; row++)
{
for(int col = 0; col < m; col++)
{
spr[row][col][j] = max(spr[row][col][j - 1], spr[row][col + (1 << (j - 1))][j - 1]);
spc[col][row][j] = max(spc[col][row][j - 1], spc[col][row + (1 << (j - 1))][j - 1]);
}
}
}
}
int maxir(int row, int l, int r)
{
int j = LG[r - l + 1];
return max(spr[row][l][j], spr[row][r - (1 << j) + 1][j]);
}
int maxic(int col, int l, int r)
{
int j = LG[r - l + 1];
return max(spc[col][l][j], spc[col][r - (1 << j) + 1][j]);
}
ll count_rectangles(vector<vi> a)
{
n = a.size();
m = a[0].size();
A= a;
if(n <= 2 || m <= 2)
return 0ll;
init();
int pref[m + 1];
memset(pref, 0, sizeof(pref));
for(int i = 0; i < m; i ++)
{
pref[i + 1] = pref[i] + (min(A[0][i], A[2][i]) <= A[1][i]);
}
for(int i = 1; i < m - 1; i++)
{
for(int j = i; j < m - 1; j++)
{
if(pref[j + 1] - pref[i] == 0)
{
if(min(A[1][i - 1], A[1][j + 1]) > maxir(1, i, j))
ans++;
}
}
}
return ans;
}
