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:
H,W = map(int,input().split())
S = [input() for _ in range(H)]

ans = 0
visited = [[0]*W for _ in range(H)]
stack = []
dx = [1,0,-1,0]
dy = [0,1,0,-1]

for i in range(H):
    for j in range(W):
        b,w = 0,0
        if not visited[i][j]:
            stack.append([i,j])
            visited[i][j] = 1
            while stack:
                x,y = stack.pop()
                if S[x][y]=='#':
                    b += 1
                else:
                    w += 1
                for k in range(4):
                    nx,ny = x+dx[k],y+dy[k]
                    if not(0<=nx<H and 0<=ny<W):
                        continue
                    if not visited[nx][ny] and S[x][y]!=S[nx][ny]:
                        visited[nx][ny] = 1
                        stack.append([nx,ny])
            ans += b*w

print(ans)