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:
from collections import deque
H,W = map(int,input().split())
S = [input() for i in range(H)]
ans = 0
flag = [[0]*W for i in range(H)]
for i in range(H*W):
    x,y = i%W,i//W
    if flag[y][x] == 1:
        continue
    flag[y][x] = 1
    bw = [0,0]
    bw[[".","#"].index(S[y][x])]+=1
    queue = deque([[x,y]])
    while queue:
        x,y = queue.popleft()
        for a,b in [[-1,0],[1,0],[0,1],[0,-1]]:
            if 0<=x+a<W and 0<=y+b<H and flag[y+b][x+a] == 0 and S[y][x] != S[y+b][x+a]:
                queue.append([x+a,y+b])
                flag[y+b][x+a] = 1
                bw[[".","#"].index(S[y+b][x+a])]+=1
    ans += bw[0]*bw[1]
print(ans)