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 fractions import gcd
# from datetime import date, timedelta
from heapq import*
import math
from collections import defaultdict, Counter, deque
import sys
from bisect import *
import itertools
import copy
sys.setrecursionlimit(10 ** 7)
MOD = 10 ** 9 + 7


def main():
    
    h, w = map(int, input().split())
    s = [list(input()) for i in range(h)]
    start = []
    d = {}
    for i in range(h):
        for j in range(w):
            if s[i][j] == "#": 
                start.append([i,j])
                d[(i, j)] = -1

    ans = [0,0]
    vis = [[-1 for i in range(w)] for j in range(h)]
    def f(x, y, pre):
        vis[x][y] = 1
        if s[x][y] == "#":
            ans[0] += 1
        else:
            ans[1]+=1
        for i, j in [[1, 0], [-1, 0], [0, 1], [0, -1]]:
            nx = i + x
            ny = j + y
            if nx >= 0 and ny >= 0 and nx < h and ny < w and vis[nx][ny] == -1:
                if pre == "B" and s[nx][ny] == ".":
                    f(nx,ny,"W")
                elif pre == "W" and s[nx][ny] == "#":
                    f(nx, ny, "B")
                
    
    ret = 0
    for i, j in start:
        if vis[i][j] == -1:
            f(i, j, "B")
        ret += ans[0] * ans[1]
        ans[0] = ans[1] = 0
    print(ret)


if __name__ == '__main__':
    main()