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():
    color=[["white" for _ in range(w)] for _ in range(h)]
    queue=deque([])
    ans=0

    for i in range(h):
        for j in range(w):
            if color[i][j]=="white" and S[i][j]=="#":
                queue.append([i,j])
                color[i][j]="gray"
                black,white=0,0

                while len(queue)>0:
                    c,d=queue.popleft()
                    if S[c][d]=="#":black +=1
                    else:white +=1

                    sign="." if S[c][d]=="#" else "#"
                    for a,b in [[1,0],[-1,0],[0,1],[0,-1]]:
                        X,Y=c+a,d+b
                        if 0<=X<h and 0<=Y<w:
                            if S[X][Y]==sign and color[X][Y]=="white":
                                color[X][Y]="gray"
                                queue.append([X,Y])
                    color[c][d]="black"
                ans +=black*white

    return ans


h,w=map(int,input().split())
S=[list(input()) for _ in range(h)]
print(BFS())