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: Time Limit Exceeded)

import queue
import copy

def solve(h, w, m, mm):
    t = copy.deepcopy(mm)
    d0 = [1,0,-1,0]
    d1 = [0,-1,0,1]
    comp=0
    c=0
    for i in range(1,h+1):
        for j in range(1,w+1):
            if (m[i][j]=='#' and t[i][j]=='#'):
                comp+=1
                bl, wh = 0, 0
                q = queue.Queue()
                q.put([i,j])
                while not q.empty():
                    cur = q.get()
                    for d in range(4):
                        nci, ncj = cur[0]+d0[d], cur[1]+d1[d]
                        if t[nci][ncj] == '#':
                            t[nci][ncj] = comp
                            if m[nci][ncj] == '#':
                                bl+=1
                            else:
                                wh+=1
                            q.put([nci,ncj])
                c += bl*wh
            elif (m[i][j]=='#' and t[i][j]=='.'):
                comp+=1
                bl, wh = 0, 0
                q = queue.Queue()
                q.put([i,j])
                while not q.empty():
                    cur = q.get()
                    for d in range(4):
                        nci, ncj = cur[0]+d0[d], cur[1]+d1[d]
                        if t[nci][ncj] == '.':
                            t[nci][ncj] = comp
                            if m[nci][ncj] == '.':
                                bl+=1
                            else:
                                wh+=1
                            q.put([nci,ncj])
                c += bl*wh
    return c

h, w = map(int,input().split())
m = [['*' for i in range(w+2)]]
for i in range(h):
    s = input()
    l = ['*']
    for j in range(w):
        l.append(s[j])
    l.append('*')
    m.append(l)
m.append(['*' for i in range(w+2)])
mm = copy.deepcopy(m)
for i in range(1,h+1):
    for j in range(1,w+1):
        if (i+j)%2==1:
            if m[i][j]=='#':
                mm[i][j]='.'
            else:
                mm[i][j]='#'
print(solve(h,w,m,mm))