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
def bfs(S,H,W,sh,sw):
    black,white=0,0
    d=deque()
    d.append([sh,sw])
    if S[sh][sw]=='#':
        black+=1
    elif S[sh][sw]=='.':
        white+=1
    seen[sh][sw]=1
    dx=[1,0,-1,0]
    dy=[0,1,0,-1]
    while(len(d)!=0):
        h=d[0][0]
        w=d[0][1]
        d.popleft()
        for dir in range(4):
            nh=h+dx[dir]
            nw=w+dy[dir]
            if(nh>H-1 or nh<0 or nw>W-1 or nw<0):
                continue
            if(seen[nh][nw] or S[nh][nw]==S[h][w]):
                continue
            if S[nh][nw]=='#':
                black+=1
            else:
                white+=1
            seen[nh][nw]=1
            d.append([nh,nw])
    return white,black

H,W=map(int,input().split())
G=[list(input()) for i in range(H)]
seen=[[0]*W for i in range(H)]
ans=0

for i in range(H):
    for j in range(W):
        if not seen[i][j]:
            w,b=bfs(G,H,W,i,j)
            ans+=w*b
print(ans)