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())
field=[["*" for i in range(w+2)]]+[["*"]+list(input())+["*"] for i in range(h)]+[["*"]*(w+2)]
dx=[-1,0,1,0]
dy=[0,-1,0,1]
visited=[[False for i in range(w+2)] for j in range(h+2)]
s={"#":0,".":1}
ans=0
def bfs(a,b):
    if visited[a][b] or field[a][b]=="*":return 0
    D=deque([(a,b)])
    visited[a][b]=True
    cnt=[0,0]
    while D:
        pos=D.popleft()
        cnt[s[field[pos[0]][pos[1]]]]+=1
        for i,j in zip(dx,dy):
            if field[pos[0]+i][pos[1]+j] == "*" or visited[pos[0]+i][pos[1]+j] or field[pos[0]+i][pos[1]+j]==field[pos[0]][pos[1]]:
                continue
            visited[pos[0]+i][pos[1]+j]=True
            D.append((pos[0]+i,pos[1]+j))
    return cnt[0]*cnt[1]
for i in range(h+2):
    for j in range(w+2):
        ans += bfs(i,j)
print(ans)