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())
X = [[[0, 1][a=="#"] for a in input()] for i in range(H)]

ch = [[0] * W for _ in range(H)]
move = [[-1,0], [1,0], [0,-1], [0,1]]
ans = 0
for i in range(H):
    for j in range(W):
        if ch[i][j]:
            continue
            
        q = deque([[i,j]])
        a = [0, 0]
        while q:
            t = q.popleft()
            x = t[0]
            y = t[1]
            ch[x][y] = 1
            a[(x+y)%2] += 1
            for m in move:
                nx = x + m[0]
                ny = y + m[1]
                if nx >= 0 and nx < H and ny >= 0 and ny < W and X[x][y] != X[nx][ny]:
                    if ch[nx][ny] == 0:
                        q.append([nx,ny])
                        ch[nx][ny] = 1
        ans += a[0] * a[1]

print(ans)