#include <bits/stdc++.h>
using namespace std;
struct vCount {
  int horiz, vert;
};
const int maxn = 1005;
int n, m;
bool grid[maxn][maxn];
vCount counts[maxn][maxn];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> m;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      char c;
      cin >> c;
      grid[i][j] = (c == '*');
    }
  }
  for (int i = 0; i < n; i++) {
    int num = 0;
    for (int j = 0; j < m; j++) {
      if (grid[i][j]) {
        num++;
      }
    }
    num--;
    for (int j = 0; j < m; j++) {
      counts[i][j].horiz = num;
    }
  }
  for (int i = 0; i < m; i++) {
    int num = 0;
    for (int j = 0; j < n; j++) {
      if (grid[j][i]) {
        num++;
      }
    }
    num--;
    for (int j = 0; j < n; j++) {
      counts[j][i].vert = num;
    }
  }
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      if (grid[i][j]) {
        vCount c = counts[i][j];
        long long plus = c.vert * c.horiz;
        ans += plus;
      }
    }
  }
  cout << ans << '\n';
  return 0;
}

### Prompt

Please create a solution in CPP to the following problem:

You are given a n × m field consisting only of periods ('.') and asterisks ('*'). Your task is to count all right triangles with two sides parallel to the square sides, whose vertices are in the centers of '*'-cells. A right triangle is a triangle in which one angle is a right angle (that is, a 90 degree angle).

Input

The first line contains two positive integer numbers n and m (1 ≤ n, m ≤ 1000). The following n lines consist of m characters each, describing the field. Only '.' and '*' are allowed.

Output

Output a single number — total number of square triangles in the field. Please, do not use %lld specificator to read or write 64-bit integers in C++. It is preffered to use cout (also you may use %I64d).

Examples

Input

2 2
**
*.


Output

1


Input

3 4
*..*
.**.
*.**


Output

9

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
struct vCount {
  int horiz, vert;
};
const int maxn = 1005;
int n, m;
bool grid[maxn][maxn];
vCount counts[maxn][maxn];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> m;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      char c;
      cin >> c;
      grid[i][j] = (c == '*');
    }
  }
  for (int i = 0; i < n; i++) {
    int num = 0;
    for (int j = 0; j < m; j++) {
      if (grid[i][j]) {
        num++;
      }
    }
    num--;
    for (int j = 0; j < m; j++) {
      counts[i][j].horiz = num;
    }
  }
  for (int i = 0; i < m; i++) {
    int num = 0;
    for (int j = 0; j < n; j++) {
      if (grid[j][i]) {
        num++;
      }
    }
    num--;
    for (int j = 0; j < n; j++) {
      counts[j][i].vert = num;
    }
  }
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      if (grid[i][j]) {
        vCount c = counts[i][j];
        long long plus = c.vert * c.horiz;
        ans += plus;
      }
    }
  }
  cout << ans << '\n';
  return 0;
}

```