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 = [[c==".#"[(i+j)%2] for j,c in enumerate(input())] for i in range(H)]#(0,0)が黒のときFalse
V = [[-1]*W for _ in [0]*H]
ans = 0
for si in range(H):
    for sj in range(W):
        if V[si][sj] != -1:continue
        V[si][sj] = 0
        cnt = [0,0]
        cnt[(S[si][sj]+si+sj)%2]+=1
        q = [[si,sj]]
        while q:
            i,j = q.pop()
            for di,dj in ((1,0),(-1,0),(0,1),(0,-1)):
                if (not (0<=i+di<H)) or (not (0<=j+dj<W)):continue
                if V[i+di][j+dj] != -1:continue
                if S[i][j] != S[i+di][j+dj]:continue
                V[i+di][j+dj] = V[i][j]
                q.append([i+di,j+dj])
                cnt[(S[i][j]+i+di+j+dj)%2] += 1
        ans += cnt[0]*cnt[1]
print(ans)