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)]

check = [[False for _ in range(w)]for __ in range(h)]

import queue
q=queue.Queue()
nh = [1,0,-1,0]
nw = [0,1,0,-1]

ans = 0
for i in range(h):
    for j in range(w):
        if check[i][j]:continue
        check[i][j] =True
        cnt = [0]*2
        cnt[s[i][j] == '#']+=1
        q.put([i,j])
        while not q.empty():
            nowi,nowj = q.get()
            for ne in range(4):
                ni = nowi + nh[ne]
                nj = nowj + nw[ne]
                if ni<0 or h <=ni or nj<0 or w<=nj:continue
                if s[nowi][nowj] == s[ni][nj]:continue
                if check[ni][nj]:continue
                check[ni][nj]=True
                cnt[s[ni][nj]=='#']+=1
                q.put([ni,nj])
        ans += cnt[0]*cnt[1]
print(ans)