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())
M=[list(input()) for _ in range(H)]

used=[[False for _ in range(W)] for __ in range(H)]
def dfs(sx,sy):
    global used
    if used[sy][sx]: return (0,0)
    black=white=0
    stack=[(sx,sy)]
    used[sy][sx]=True
    while stack:
        x,y=stack.pop()
        if M[y][x]=='#':
            black+=1
        else:
            white+=1
        for dx,dy in [(1,0),(-1,0),(0,1),(0,-1)]:
            nx,ny=x+dx,y+dy
            if 0<=nx<W and 0<=ny<H and not used[ny][nx]:
                if M[y][x]!=M[ny][nx]:
                    stack.append((nx,ny))
                    used[ny][nx]=True
    return (black,white)

ans=0
for y in range(H):
    for x in range(W):
        black,white=dfs(x,y)
        ans+=black*white
print(ans)