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)

def search(search_map, group, current_h, current_w, group_index):
    num = 0
    if current_h in search_map:
        search_map[current_h]
    else:
        search_map[current_h] = {}
        search_map[current_h][current_w] = True
    search_map[current_h][current_w] = True
    current = s_map[current_h][current_w]
    if (current == '.'):
        num += 1
    else:
        group[current_h][current_w] = group_index
    # 上
    if current_h > 0:
        next_h = current_h-1
        next_w = current_w
        isExist = False
        if next_h in search_map:
            if next_w in search_map[next_h]:
                isExist = True
        if s_map[next_h][next_w] != current and not(isExist):
            num += search(search_map, group, next_h, next_w, group_index)
    # 下
    if current_h < H-1:
        next_h = current_h+1
        next_w = current_w
        isExist = False
        if next_h in search_map:
            if next_w in search_map[next_h]:
                isExist = True
        if s_map[next_h][next_w] != current and not(isExist):
            num += search(search_map, group, next_h, next_w, group_index)
    # 左
    if current_w > 0:
        next_h = current_h
        next_w = current_w-1
        isExist = False
        if next_h in search_map:
            if next_w in search_map[next_h]:
                isExist = True
        if s_map[next_h][next_w] != current and not(isExist):
            num += search(search_map, group, next_h, next_w, group_index)
    # 右
    if current_w < W-1:
        next_h = current_h
        next_w = current_w+1
        isExist = False
        if next_h in search_map:
            if next_w in search_map[next_h]:
                isExist = True
        if s_map[next_h][next_w] != current and not(isExist):
            num += search(search_map, group, next_h, next_w, group_index)
    return num


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

s_map = {}
group = {}
searched_map = {}


for i in range(H):
    s_map[i] = {}
    group[i] = {}
    w = list(A[i])
    for j in range(W):
        s_map[i][j] = w[j]
        group[i][j] = 0

ans = 0
group_index = 1
group_cnt = {}
group_cnt[0] = 0
for i in range(H):
    for j in range(W):
        if s_map[i][j] == '#':
            if group[i][j] != 0:
                ans += group_cnt[group[i][j]]
            else:
                cnt = search({}, group, i, j, group_index)
                group_cnt[group_index] = cnt
                group_index += 1
                ans += cnt
print(ans)

'''
1 1
#
'''

'''
1 1
.
'''

'''
4 5
#####
#...#
#...#
#####
'''

'''
5 5
.....
.....
.###.
.###.
.....
'''


'''
3 1
#
.
#
'''


'''
3 3
###
#.#
###
'''

'''
5 5
##.##
#.###
####.
##.#.
####.
'''

'''
5 4
#.#.
####
####
#.##
##.#
'''

'''
5 4
#.#.
####
#.#.
####
####
'''

'''
5 4
....
.#..
..#.
...#
#.#.
'''