Problem: There is a grid with H rows and W columns, where each square is painted black or white.

You are given H strings S_1, S_2, ..., S_H, each of length W. If the square at the i-th row from the top and the j-th column from the left is painted black, the j-th character in the string S_i is `#`; if that square is painted white, the j-th character in the string S_i is `.`.

Find the number of pairs of a black square c_1 and a white square c_2 that satisfy the following condition:

* There is a path from the square c_1 to the square c_2 where we repeatedly move to a vertically or horizontally adjacent square through an alternating sequence of black and white squares: black, white, black, white...

Constraints

* 1 \leq H, W \leq 400
* |S_i| = W (1 \leq i \leq H)
* For each i (1 \leq i \leq H), the string S_i consists of characters `#` and `.`.

Input

Input is given from Standard Input in the following format:


H W
S_1
S_2
:
S_H


Output

Print the answer.

Examples

Input

3 3
.#.
..#
#..


Output

10


Input

3 3
.#.
..#
..


Output

10


Input

2 4
....
....


Output

0


Input

4 3


...


Output

6

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

int dx[] = {0, 1, 0, -1};
int dy[] = {1, 0, -1, 0};

int h, w;
vector<string> s;
vector<vector<bool>> v;

array<int, 2> dfs(int y, int x) {
  array<int, 2> r = {0, 0};
  r[s[y][x] == '#']++;
  for (int i = 0; i < 4; i++) {
    int ny = y + dy[i], nx = x + dx[i];
    if (!(0 <= ny && ny < h && 0 <= nx && nx < w) || v[ny][nx] || s[ny][nx] == s[y][x]) continue;
    v[ny][nx] = true;
    auto t = dfs(ny, nx);
    r[0] += t[0];
    r[1] += t[1];
  }
  return r;
}

int main() {
  cin >> h >> w;
  s = vector<string>(h);
  v = vector<vector<bool>>(h, vector<bool>(w));
  for (auto &e : s) {
    cin >> e;
  }
  ll r = 0;
  for (int i = 0; i < h; i++) {
    for (int j = 0; j < w; j++) {
      if (v[i][j]) continue;
      v[i][j] = true;
      auto t = dfs(i, j);
      r += (ll)t[0] * t[1];
    }
  }
  cout << r << endl;
}