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())
s = [list(input()) for i in range(h)]

used = [[0]*w for i in range(h)]
dx = [1,-1,0,0]
dy = [0,0,1,-1]
ans = 0

for i in range(h):
    for j in range(w):
        if used[i][j]:
            continue
        cw = 0
        cb = 0
        q = deque([])
        q.append([i,j])
        used[i][j] = 1
        while q:
            x,y = q.popleft()
            if s[x][y] == "#":
                cb += 1
            else:
                cw += 1
            for k in range(4):
                nx = x+dx[k]
                ny = y+dy[k]
                if 0 <= nx < h and 0 <= ny < w:
                    if (not used[nx][ny]) and s[x][y] != s[nx][ny]:
                        used[nx][ny] = 1
                        q.append([nx,ny])
        ans += cw*cb
print(ans)