#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int n, m;
vector<pair<int, int> > topLeft;
vector<pair<int, int> > bottomRight;
vector<vector<int> > board, oboard;
int prefSums[3000][3000];
bool works(int startx, int endx, int starty, int endy) {
if (startx > endx or starty > endy)
{
return false;
}
for (int x = startx; x <= endx; x++)
{
for (int y = starty; y <= endy; y++)
{
if (board[x][y] >= board[startx-1][y] or board[x][y] >= board[endx+1][y] or board[x][y] >= board[x][starty-1] or board[x][y] >= board[x][endy+1])
{
return false;
}
}
}
//cout << startx << "," << starty << " to " << endx << "," << endy << "\n";
return true;
}
ll count_rectangles(vector<vector<int> > a) {
n = a.size();
m = a[0].size();
board = a;
oboard = board;
prefSums[0][0] = board[0][0];
for (int i = 1; i < n; i++)
{
prefSums[i][0] = prefSums[i-1][0] + board[i][0];
}
for (int i = 1; i < m; i++)
{
prefSums[0][i] = prefSums[0][i-1] + board[0][i];
}
for (int i = 1; i < n; i++)
{
for (int j = 1; j < m; j++)
{
prefSums[i][j] = prefSums[i][j-1] + prefSums[i-1][j] - prefSums[i-1][j-1] + board[i][j];
}
}
ll totalCount = 0;
for (int i = 1; i < n-1; i++)
{
for (int j = 1; j < m-1; j++)
{
if (board[i][j] == 0)
{
int endx = i;
int endy = j;
while (endx < n-2 and board[endx+1][endy] == 0)
{
endx++;
}
while (endy < m-2 and prefSums[endx][endy+1] - prefSums[i-1][endy+1] - prefSums[endx][j-1] + prefSums[i-1][j-1] == 0)
{
endy++;
}
int totSum = prefSums[endx+1][endy+1];
if (i > 1)
{
totSum -= prefSums[i-2][endy+1];
}
if (j > 1)
{
totSum -= prefSums[endx+1][j-2];
}
if (i > 1 and j > 1)
{
totSum += prefSums[i-2][j-2];
}
if (totSum - oboard[i-1][j-1] - oboard[i-1][endy+1] - oboard[endx+1][j-1] - oboard[endx+1][endy+1] == 2 * (endx - i + 1 + endy - j + 1))
{
totalCount++;
}
for (int x = i; x <= endx; x++)
{
for (int y = j; y <= endy; y++)
{
board[x][y] = 1;
//cout << "Clearing " << x << " " << y << "\n";
}
}
//cout << "Total sum was " << prefSums[endx+1][endy+1]
//cout << "\n\n";
}
}
}
return totalCount;
}
