Problem: 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.

Examples

Input

3 3
.#.
..#
#..


Output

10


Input

3 3
.#.
..#
..


Output

10


Input

2 4
....
....


Output

0


Input

4 3


...


Output

6

Solution (in PYTHON3):

Solution:
from collections import deque
H,W=map(int, input().split())
inl=[input() for _ in range(H)]

checked = set([])
lis = [(1,0),(0,1),(-1,0),(0,-1)]

def bfs(i,j):
    fifo = deque([])
    fifo.append((i,j))
    checked.add((i,j))
    cntBlack = 0
    cntWhite = 0
    while fifo:
        i,j = fifo.popleft()
        if inl[i][j] == '.':
            cntWhite += 1
        else:
            cntBlack += 1

        for di,dj in lis:
            if i+di >= 0 and i+di < H and j+dj >= 0 and j+dj < W and \
                not (i+di, j+dj) in checked \
                and inl[i][j] != inl[i+di][j+dj]:

                checked.add((i+di, j+dj))
                fifo.append((i+di, j+dj))
    return cntBlack*cntWhite

res = 0
for i in range(H):
    for j in range(W):
        if not (i,j) in checked:
            res += bfs(i,j)
print(res)