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 PyPy3 (2.4.0) (judge verdict: Runtime Error)

H, W = map( int, input().split() )
S = [ list( input() ) for _ in range(H) ]

dx = [1, -1, 0, 0]
dy = [0, 0, 1, -1]
# (i, j) から行けるペアの数
def dfs( x, y, isVisited ):
    ans = 0
    isVisited[x][y] = True
    for i in range(4):
        nx = x + dx[i]
        ny = y + dy[i]
        if S[x][y] == '#':
            if 0 <= nx and nx < H and 0 <= ny and ny < W and not isVisited[nx][ny]:
                if S[nx][ny] == '.': ans += dfs( nx, ny, isVisited )+1
        else:
            if 0 <= nx and nx < H and 0 <= ny and ny < W and not isVisited[nx][ny]:
                if S[nx][ny] == '#': ans += dfs( nx, ny, isVisited )
    return ans


ans = 0
for i in range(H):
    for j in range(W):
        isVisited = [ [False]*W for _ in range(H) ]
        if S[i][j] == '#': ans += dfs( i, j, isVisited )

print( ans )