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 sys
c=0
b=0
wi=0
x=[-1,0,1,0]
y=[0,-1,0,1]
buf=[]
def count(h,w,S,table,H,W,index):
    global buf,x,y,b,wi
    if index==1:
        b+=1
    else:
        wi+=1
    if index==1:
        S[h][w]='6'
    for i in range(4):
        if h+y[i]>=0 and h+y[i]<H and w+x[i]>=0 and w+x[i]<W:
            if table[h+y[i]][w+x[i]]==-1:
                if index==0 and S[h+y[i]][w+x[i]]=='#':
                    table[h+y[i]][w+x[i]]=table[h][w]+1
                    buf.append([h+y[i],w+x[i],1])
                elif index==1 and S[h+y[i]][w+x[i]]=='.':
                    table[h+y[i]][w+x[i]]=table[h][w]+1
                    buf.append([h+y[i],w+x[i],0])
    if buf:
        a=buf.pop(0)
        count(a[0],a[1],S,table,H,W,a[2])
sys.setrecursionlimit(10000000)
H,W=map(int,input().split())
T=[]
for i in range(H):
    T.append(input())
S=[['' for j in range(W)]for i in range(H)]
for h in range(H):
    for w in range(W):
        S[h][w]=T[h][w]
for h in range(H):
    for w in range(W):
        if S[h][w]=='#':
            table=[[-1 for j in range(W)] for i in range(H)]
            table[h][w]=0
            p=0
            count(h,w,S,table,H,W,1)
            
            c+=b*wi
            b=0
            wi=0
print(c)