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:
import sys
read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines

h,w = map(int,readline().split())
s = read().split()
color = [[0] * w for _ in range(h)]
for i in range(h):
    for j in range(w):
        if(s[i][j] =='#'):
            color[i][j] = 1

ans = 0
done = [[0] * w for _ in range(h)]
for i in range(h):
    for j in range(w):
        if(done[i][j]==1):
            continue

        cnt = [0]*2
        cnt[(i+j)%2] += 1
        done[i][j] = 1
        stack = [(i,j)]
        while(stack):
            x,y = stack.pop()
            for dx,dy in zip([-1,1,0,0],[0,0,-1,1]):
                dx += x
                dy += y
                if(0 <= dx < h)&(0 <= dy < w):
                    if(done[dx][dy] == 1):
                        continue
                    if(color[x][y] != color[dx][dy]):
                        done[dx][dy] = 1
                        stack.append((dx,dy))
                        cnt[(dx+dy)%2] += 1
        ans += cnt[0] * cnt[1]
        # print(i,j,cnt)

print(ans)