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
sys.setrecursionlimit(1000000)

move=((1,0),(0,1),(-1,0),(0,-1))

#深さ優先探索
def dfs(used,mat,node,nums):
    y,x=node
    color=mat[y][x]
    if used[y][x]==1 or color=='!':
        return
    
    used[y][x]=1
    nums[color]+=1
    for i,j in move:
        if mat[y+i][x+j]!=color and mat[y+i][x+j] != '!':
            dfs(used,mat,(y+i,x+j),nums)


H,W=list(map(int,input().split()))

grid=['!'*(W+2)]
used=[[0 for _ in range(W+2)] for _ in range(H+2)]

for i in range(H):
    grid.append('!'+input()+'!')
grid.append('!'*(W+2))

ans=0
for i in range(H+2):
    for j in range(W+2):
        nums={'#':0,'.':0}
        dfs(used,grid,(i,j),nums)
        ans+=nums['#']*nums['.']
print(ans)