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: Time Limit Exceeded)

from collections import Counter,defaultdict,deque
import sys
import bisect
import math
import itertools
import string
import queue
import copy
# import numpy as np
# import scipy
from itertools import permutations, combinations
from heapq import heappop, heappush
input = sys.stdin.readline
sys.setrecursionlimit(10**8)
mod = 10**9+7

def inp(): # n=1
    return int(input())
def inpm(): # x=1,y=2
    return map(int,input().split())
def inpl(): # a=[1,2,3,4,5,...,n]
    return list(map(int, input().split()))
def inpls(): # a=['1','2','3',...,'n']
    return list(input().split())
def inplm(n): # x=[] 複数行
    return list(int(input()) for _ in range(n))
def inpll(n): # [[1,1,1,1],[2,2,2,2],[3,3,3,3]]
    return sorted([list(map(int, input().split())) for _ in range(n)])

def search(x,y,key):
    global wh,bl,s,done,h,w,que
    if x<0 or h<=x or y<0 or w<=y or  done[x][y]:
        return
    elif (key==0 and s[x][y]=='.') or (key==1 and s[x][y]=='#'):
        return
    elif key==0 and s[x][y]=='#':
        bl+=1
        key=1
        done[x][y]=True
        search(x-1,y,key)
        search(x,y-1,key)
        search(x+1,y,key)
        search(x,y+1,key)
    elif key==1 and s[x][y]=='.':
        wh+=1
        key=0
        done[x][y]=True
        search(x-1,y,key)
        search(x,y-1,key)
        search(x+1,y,key)
        search(x,y+1,key)

def main():
    global wh,bl,s,done,key,h,w,que
    h,w=inpm()
    s=[]
    for _ in range(h):
        s.append(tuple(input()))
    s=tuple(s)
    ans=0
    done = [[False for _ in range(w)] for _ in range(h)]
    que=deque([])
    for i in range(h):
        for j in range(w):
            if s[i][j]=='#':
                x0=i
                y0=j
                que.append((x0,y0))
    while len(que)>0:
        x,y=que.pop()
        key=0
        bl=0
        wh=0
        search(x,y,key)
        ans+=bl*wh
    print(ans)

if __name__ == "__main__":
    main()