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 PYTHON):

Solution:
def main():
    from collections import defaultdict
    import sys
    sys.setrecursionlimit(10 ** 9)
    
    H, W = list(map(int, raw_input().split()))
    G = [list(raw_input()) for i in range(H)]
    
    Visited = [[0] * W for i in range(H)]
    direction = [[0, 1], [0, -1], [1, 0], [-1, 0]]
    
    
    def dfs(ny, nx, color):
        for dy, dx in direction:
            if not ((0 <= ny + dy < H) and (0 <= nx + dx < W)):
                continue
    
            if G[ny + dy][nx + dx] == G[ny][nx]:
                continue
    
            if Visited[ny + dy][nx + dx] != 0:
                continue
    
            if G[ny + dy][nx + dx] == '#':
                Visited[ny + dy][nx + dx] = color
            else:
                Visited[ny + dy][nx + dx] = -color
    
            dfs(ny + dy, nx + dx, color)
    
    
    Color = 1
    for y in range(H):
        for x in range(W):
            if Visited[y][x] == 0:
                if G[y][x] == '#':
                    Visited[y][x] = Color
                else:
                    Visited[y][x] = -Color
                dfs(y, x, Color)
                Color += 1
    
    D = defaultdict(int)
    for i in range(1, Color + 1):
        D[i] = 0
        D[-i] = 0
    
    for row in Visited:
        for data in row:
            D[data] += 1
    
    ans = 0
    for key in D.keys():
        ans += D[key] * D[-key]
    
    print(ans // 2)
    
main()