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=[]
for i in range(H):
    S.append(input())

q=deque([])
T=[]
seen=[[0]*W for _ in range(H)]
step=[[0,1],[0,-1],[1,0],[-1,0]]
for h in range(H):
    for w in range(W):
        temp=[]
        if seen[h][w]==0:
            temp.append(S[h][w])
            seen[h][w]=1
            q.append([h,w,S[h][w]])
            while q:
                oh,ow,m=q.popleft()
                for dh,dw in step:
                    if 0<=oh+dh<H and 0<=ow+dw<W:
                        if seen[oh+dh][ow+dw]==0 and m!=S[oh+dh][ow+dw]:
                            temp.append(S[oh+dh][ow+dw])
                            seen[oh+dh][ow+dw]=1
                            q.append([oh+dh,ow+dw,S[oh+dh][ow+dw]])
            T.append(temp)

ans=0
for i in range(len(T)):
    black=0
    white=0
    for s in T[i]:
        if s=="#":
            black+=1
        else:
            white+=1
    ans+=black*white

print(ans)