Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3 3
.#.
..#
#..

Sample Output 1

10

Some of the pairs satisfying the condition are ((1, 2), (3, 3)) and ((3, 1), (3, 2)), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

Sample Input 2

2 4
....
....

Sample Output 2

0

Sample Input 3

4 3
###
###
...
###

Sample Output 3

6

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

console.log((args=>{
  const [HW,...S] = args.trim().split('\n');
  const [H,W] = HW.split(' ').map(v=>parseInt(v));
  const trail = Array.from({length:H},_=>Array(W).fill(false));
  const dir = [[-1,0],[0,-1],[1,0],[0,1]];
  let p = 0;
  for ( let i = 0; i < H; i++ ) {
    for ( let j = 0; j < W; j++ ) {
      if ( trail[i][j] ) continue;
      const stack = [[i,j]];
      trail[i][j] = true;
      let w = S[i][j]==='.'|0, b = w^1;
      while ( stack.length ) {
        const [x,y] = stack.pop();
        for ( const [dx,dy] of dir ) {
          const nx = x+dx, ny = y+dy;
          if ( nx < 0 || H <= nx || ny < 0 || W <= ny
            || trail[nx][ny] || S[x][y] === S[nx][ny] ) continue;
          trail[nx][ny] = true;
          if ( S[nx][ny] === '#' ) b++; else w++;
          stack.push([nx,ny]);
        }
      }
      p += w * b;
    }
  }
  return `${p}`;
})(require('fs').readFileSync('/dev/stdin', 'utf8')));