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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
fscanf(STDIN, "%d%d", $H, $W);
for($i = 0; $i < $H; $i++){
    $str = fgets(STDIN);
    for($j = 0; $j < $W; $j++){
        $map[$i][$j] = $str[$j];
    }
}
$sum = 0;
for($y = 0; $y < $H; $y++){
    for($x = 0; $x < $W; $x++){
        $ad = [];
        $black = dfs($y, $x);
        $white = count($ad, true) - count($ad);
        $sum += $black*$white;
    }
}
echo $sum,"\n";


function dfs($y, $x){
    global $map, $ad;
    if($map[$y][$x] != "#"){
        return 0;
    }else{
        $count = 1;
        $map[$y][$x] = "x"; 
    }
    foreach([[1,0],[-1,0],[0,1],[0,-1]] as list($dy, $dx)){
        if(isset($map[$y+$dy][$x+$dx]) && $map[$y+$dy][$x+$dx] == "."){
            $ad[$y+$dy][$x+$dx] = true;
            foreach([[1,0],[-1,0],[0,1],[0,-1]] as list($ddy, $ddx)){
                if(isset($map[$y+$dy+$ddy][$x+$dx+$ddx]) && $map[$y+$dy+$ddy][$x+$dx+$ddx] == "#"){
                    $count += dfs($y+$dy+$ddy, $x+$dx+$ddx);
                }
            }    
        }
    }
    return $count;
}