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=[list(input()) for i in range(h)]

q=deque()
ans=0

def bfs(i,j):
    global ans
    white=0
    black=0
    q.append((i,j))
    while q:
        y,x=q.popleft()
        if s[y][x]=='#':
            black+=1
        if s[y][x]=='.':
            white+=1
        for dy,dx in ((1,0),(0,1),(-1,0),(0,-1)):
            ny = y+dy
            nx = x+dx
            if 0<=ny<h and 0<=nx<w and s[y][x]!=s[ny][nx] and field[ny][nx]==False:
                field[ny][nx]=True
                q.append((ny,nx))
    ans+=(black*white)

field=[[False]*w for j in range(h)]                         
for i in range(h):
    for j in range(w):
        if s[i][j]=='.' and field[i][j]==False:
            field[i][j]=True
            bfs(i,j)

print(ans)