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 Python (3.4.3) (judge verdict: Runtime Error)

# https://atcoder.jp/contests/aising2019/submissions/3986315
# 解説のように 連結成分を求めてから、bfsする

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

ans = 0

dx = [0, 0, 1, -1]
dy = [1, -1, 0, 0]

un_reached = [[True for i in range(W)] for j in range(H)]


def isIn(x, y):
    return 0 <= x < H and 0 <= y < W


def dfs(x, y):
    un_reached[x][y] = False
    if s[x][y] == '#':
        cc[1] += 1
    else:
        cc[0] += 1

    for i in range(4):
        nx = x+dx[i]
        ny = y+dy[i]
        if isIn(nx, ny) and s[nx][ny] != s[x][y] and un_reached[nx][ny]:
            dfs(nx, ny)


for i in range(H):
    for j in range(W):
        if un_reached[i][j]:
            cc = [0 for _ in range(2)]
            dfs(i, j)
            ans += cc[1]*cc[0]
print(ans)