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:
import sys
sys.setrecursionlimit(200000)
H,W=map(int,input().split())
S=[]
for i in range(H):
    S.append(input())

ans=0
dx=[0,0,1,-1]
dy=[1,-1,0,0]

was=[[0 for i in range(W)] for j in range(H)]

def dfs(x,y):
    global cc
    global was
    was[x][y]=1
    if S[x][y]=="#":
        cc[1]+=1
    else:
        cc[0]+=1
    for i in range(4):
        nx=x+dx[i]
        ny=y+dy[i]
        if nx>=0 and ny>=0 and nx<H and ny<W and S[nx][ny]!=S[x][y] and not was[nx][ny]:
            dfs(nx,ny)

for i in range(H):
    for j in range(W):
        if not was[i][j]:
            cc=[0]*2
            dfs(i,j)
            ans+= cc[1]*cc[0]

print(ans)