#include <bits/stdc++.h>
using namespace std;
const int N = 2525;
int m, n, sum[N][N], isGood[N][N], a[N][N];
vector<pair<int, int>> intervals;
int maxRow[777][777][11], maxCol[777][777][11], lg2[N];
void init()
{
for (int i = 1; i <= m; i++)
{
for (int j = 1; j <= n; j++)
maxRow[i][j][0] = a[i][j];
for (int lg = 0; lg < 9; lg++)
for (int j = 1; j + (1 << lg) - 1 <= n; j++)
maxRow[i][j][lg + 1] = max(maxRow[i][j][lg], maxRow[i][j + (1 << lg) - 1][lg]);
}
for (int i = 1; i <= n; i++)
{
for (int j = 1; j <= m; j++)
maxCol[i][j][0] = a[j][i];
for (int lg = 0; lg < 9; lg++)
for (int j = 1; j + (1 << lg) - 1 <= m; j++)
maxCol[i][j][lg + 1] = max(maxCol[i][j][lg], maxCol[i][j + (1 << lg) - 1][lg]);
}
for (int j = 0; j < 10; j++)
for (int i = 1 << j; i < 1 << j + 1; i++)
lg2[i] = j;
}
int getMax(int arr[777][11], int l, int r)
{
int curLg2 = lg2[r - l + 1];
return max(arr[l][curLg2], arr[r - (1 << curLg2) + 1][curLg2]);
}
void populateIntervals(int row, int l, int r)
{
if (l >= r - 1)
return;
intervals.push_back({l, r});
int id = l + 1;
for (int i = l + 2; i < r; i++)
if (a[row][i] > a[row][id])
id = i;
populateIntervals(row, l, id);
populateIntervals(row, id, r);
}
long long subtask4()
{
init();
long long ans = 0;
for (int i = 2; i < m; i++)
{
intervals.clear();
populateIntervals(i, 1, n);
int numIntervals = intervals.size();
vector<int> isGoodInterval(numIntervals, 1);
vector<int> isGoodCol(n + 1, 0);
for (int ii = i; ii < m; ii++)
{
// check col
for (int j = 2; j < n; j++)
{
int curMaxCol = getMax(maxCol[j], i, ii);
isGoodCol[j] = isGoodCol[j - 1] + (curMaxCol < min(a[i - 1][j], a[ii + 1][j]));
}
// check row
for (int j = 0; j < numIntervals; j++)
{
int l = intervals[j].first, r = intervals[j].second;
int maxInterval = getMax(maxRow[ii], l + 1, r - 1);
isGoodInterval[j] &= maxInterval < min(a[ii][l], a[ii][r]);
ans += isGoodInterval[j] && isGoodCol[r - 1] - isGoodCol[l] == r - 1 - l;
}
}
}
return ans;
}
int calc(int l, int r)
{
if (l >= r - 1)
return 0;
int id = l + 1;
for (int i = l + 2; i < r; i++)
if (a[2][i] > a[2][id])
id = i;
int isGoodInterval = a[2][id] < min(a[2][l], a[2][r]) && isGood[2][r - 1] - isGood[2][l] == r - 1 - l;
return calc(l, id) + calc(id, r) + isGoodInterval;
}
long long subtask5()
{
for (int i = 2; i < m; i++)
for (int j = 2; j < n; j++)
isGood[i][j] = isGood[i][j - 1] + (a[i][j] < min(a[i - 1][j], a[i + 1][j]));
return calc(1, n);
}
int getSum(int x, int y, int xx, int yy)
{
return sum[xx][yy] + sum[x][y] - sum[xx][y] - sum[x][yy];
}
long long subtask6()
{
for (int i = 1; i <= m; i++)
for (int j = 1; j <= n; j++)
sum[i][j] = sum[i - 1][j] + sum[i][j - 1] - sum[i - 1][j - 1] + a[i][j];
vector<int> maxCol(n + 1, 0);
long long ans = 0;
for (int i = 2; i < m; i++)
{
int maxRow = 0;
for (int j = 2; j < n; j++)
if (!a[i][j])
{
maxRow++;
maxCol[j]++;
int ii = i - maxCol[j] + 1, jj = j - maxRow + 1;
ans += getSum(ii - 1, jj - 1, i, j) == 0 &&
getSum(ii - 2, jj - 1, ii - 1, j) == maxRow &&
getSum(i, jj - 1, i + 1, j) == maxRow &&
getSum(ii - 1, jj - 2, i, jj - 1) == maxCol[j] &&
getSum(ii - 1, j, i, j + 1) == maxCol[j];
}
else maxRow = maxCol[j] = 0;
}
return ans;
}
long long count_rectangles(vector<vector<int>> _a)
{
m = _a.size();
n = _a[0].size();
for (int i = 1; i <= m; i++)
for (int j = 1; j <= n; j++)
a[i][j] = _a[i - 1][j - 1];
if (m == 3)
return subtask5();
if (max(m, n) <= 700)
return subtask4();
for (int i = 1; i <= m; i++)
for (int j = 1; j <= n; j++)
if (a[i][j] > 1)
return 0;
return subtask6();
}
