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:
#!/usr/bin/env python3
from itertools import product
import sys

sys.setrecursionlimit(200000)

H, W = map(int, input().split())
S = [input() for _ in range(H)]
color = [[None] * W for _ in range(H)]
memo = [[0, 0] for _ in range(H * W + 1)]
cnt = 1


def dfs(p, c):
    x, y = p
    color[x][y] = c
    memo[cnt][c] += 1
    for dx, dy in [[1, 0], [0, 1], [-1, 0], [0, -1]]:
        nx = x + dx
        ny = y + dy
        if 0 <= nx < H and 0 <= ny < W and color[nx][ny] is None and c != (S[nx][ny] == '#'):
            dfs([nx, ny], not c)


for i, j in product(range(H), range(W)):
    if color[i][j] is None:
        dfs([i, j], S[i][j] == '#')
        cnt += 1

ans = 0
for i in range(H * W):
    ans += memo[i][0] * memo[i][1]
print(ans)