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: Runtime Error)

import numpy as np
from collections import deque

@np.vectorize
def trans(s):
    return True if s == "#" else False

def parse(inp):
    H, W = map(int, next(inp).split())
    return np.array([trans([w for w in next(inp).strip()]) for _ in range(H)])

def appender(i, j, H, W, C, S, Q):
    s = S[i, j]
    if i + 1 < H and not C[i+1, j] and np.logical_xor(s, S[i+1, j]):
        Q.append((i + 1, j))
    if i > 0 and not C[i-1, j] and np.logical_xor(s, S[i-1, j]):
        Q.append((i - 1, j))
    if j + 1 < W and not C[i, j+1] and np.logical_xor(s, S[i, j+1]):
        Q.append((i, j + 1))
    if j > 0 and not C[i, j-1] and np.logical_xor(s, S[i, j-1]):
        Q.append((i, j - 1))

def search(S, start, C):
    Q = deque([start])
    H, W = S.shape
    n0 = 0
    n1 = 0
    while Q:
        i, j = Q.popleft()
        if C[i, j]:
            continue
        else:
            C[i, j] = True
            if S[i, j] == 0:
                n0 += 1
            else:
                n1 += 1
            appender(i, j, H, W, C, S, Q)
    return n0, n1


def search_all(S):
    C = np.full_like(S, False).astype(np.bool)
    D = np.full_like(S, 0)
    ret = 0
    for i in range(S.shape[0]):
        for j in range(S.shape[1]):
            if D[i, j] == 0:
                n0, n1 = search(S, (i, j), C)
                D += C
                ret += n1 * n0
                if np.all(D):
                    return ret
                else:
                    C[:, :] = False




import sys
    
print(search_all(parse(sys.stdin)))