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:
def aising19_c():
    from collections import deque

    h, w = (int(x) for x in input().split())
    color = [[s == '#' for s in str(input())] for _ in range(h)]
    used = [[False]*w for _ in range(h)]

    ans = 0
    for i in range(h):
        for j in range(w):
            if used[i][j]: continue
            bk, wt = 0, 0
            que = deque()
            used[i][j] = True
            que.append((i, j))
            while que:
                ci, cj = que.popleft()
                if color[ci][cj]: bk += 1
                else: wt += 1
                for di, dj in ((-1,0),(0,-1),(0,1),(1,0)):
                    ni, nj = ci+di, cj+dj
                    if ni < 0 or h <= ni or nj < 0 or w <= nj: continue
                    if color[ci][cj] == color[ni][nj]: continue
                    if used[ni][nj]: continue
                    used[ni][nj] = True
                    que.append((ni, nj))
            ans += bk * wt
    print(ans)

if __name__ == '__main__':
    aising19_c()