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;
const int maxn = 444;
char g[maxn][maxn];
int h,w;
bool vis[maxn][maxn];
int64_t cntb,cntw;
int dx[] = {0,1,0,-1};
int dy[] = {1,0,-1,0};
int64_t ans;
void dfs(int x,int y) {
    vis[x][y] = 1;
    if(g[x][y] == '#') {
        cntb++;
    }else {
        cntw++;
    }
    for(int i=0;i<4;++i) {
        int nx = dx[i]+x;
        int ny = dy[i]+y;
        if(nx>=1 && nx<=h && ny>=1 && ny<=w && !vis[nx][ny] && g[nx][ny] != g[x][y]) {
            dfs(nx,ny);
        }
    }
}
int main() {
    cin>>h>>w;
    for(int i=1;i<=h;++i) {
        cin>>g[i]+1;
    }
    for(int i=1;i<=h;++i) {
        for(int j=1;j<=w;++j) {
            if(g[i][j] == '#' && !vis[i][j]) {
                cntb = cntw = 0;
                dfs(i,j);
                ans += cntb * cntw;
            }
        }
    }
    cout<<ans<<endl;
}