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 _ in range(h)]
visited=[[True]*w for _ in range(h)]
def bfs(sx,sy):
    q=deque([(sx,sy)])
    visited[sx][sy]=False
    black=1
    white=0
    while q:
        x,y=q.popleft()
        for dx,dy in [[0,1],[1,0],[0,-1],[-1,0]]:
            nx,ny=x+dx,y+dy
            if 0<=nx<h and 0<=ny<w:
                if visited[nx][ny]:
                    if s[x][y]=="#" and s[nx][ny]==".":
                        visited[nx][ny]=False
                        q.append((nx,ny))
                        white+=1
                    elif s[x][y]=="." and s[nx][ny]=="#":
                        visited[nx][ny]=False
                        q.append((nx,ny))
                        black+=1
    return black,white
ans=0
for sx in range(h):
    for sy in range(w):
        if s[sx][sy]=="#" and visited[sx][sy]:
            black,white=bfs(sx,sy)
            ans+=black*white
print(ans)