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())
S=[[int(c=='#') for c in input()] for i in range(H)]
v=[[0]*W for i in range(H)]
r=0
def bfs(p,x,y,c,b):
    while 1:
        c^=1
        q=set()
        for h,w in p:
            v[h][w]=1
            if h>0 and not v[h-1][w] and S[h-1][w]==c:
                q.add((h-1,w))
            if w>0 and not v[h][w-1] and S[h][w-1]==c:
                q.add((h,w-1))
            if h<H-1 and not v[h+1][w] and S[h+1][w]==c:
                q.add((h+1,w))
            if w<W-1 and not v[h][w+1] and S[h][w+1]==c:
                q.add((h,w+1))
        if not q:
            return x*y
        if b:
            x+=len(q)
        else:
            y+=len(q)
        b^=1
        p=q
for h in range(H):
    for w in range(W):
        if v[h][w]==0:
            r+=bfs([(h,w)],1,0,S[h][w],0)
print(r)