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 (3.8.2) (judge verdict: Time Limit Exceeded)

from sys import stdin
nii=lambda:map(int,stdin.readline().split())
lnii=lambda:list(map(int,stdin.readline().split()))
from collections import deque
from copy import deepcopy

h,w=nii()
s=[list(input()) for i in range(h)]

def BFS(sy,sx,ans):
  temp_s=deepcopy(s)

  que=deque()
  que.append((sy,sx))

  while que:
    y,x=que.popleft()
    for dy,dx in [[-1,0],[0,-1],[1,0],[0,1]]:
      ny=y+dy
      nx=x+dx
      if 0<=ny<h and 0<=nx<w:
        if (temp_s[y][x]=='#' and temp_s[ny][nx]=='.') or \
           (temp_s[y][x]=='.' and temp_s[ny][nx]=='#'):
          que.append((ny,nx))
          if temp_s[ny][nx]=='.':
            ans.add(((sy,sx),(ny,nx)))
            ans.add(((y,x),(ny,nx)))
          if temp_s[y][x]=='#':
            s[y][x]=='D'
    temp_s[y][x]='D'

  return ans

ans=set()
for i in range(h):
  for j in range(w):
    if s[i][j]=='#':
      ans=BFS(i,j,ans)

print(len(ans))