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 sys import setrecursionlimit
setrecursionlimit(200000)

H, W = map( int, input().split() )
S = [ list( input() ) for _ in range(H) ]


isVisited = [ [False]*W for _ in range(H) ]
dx = [1, -1, 0, 0]
dy = [0, 0, 1, -1]
# (i, j) から行けるペアの数
def dfs( x, y ):
    isVisited[x][y] = True
    numBlack, numWhite = 0, 0
    if S[x][y] == '#': numBlack = 1
    else:              numWhite = 1
    for i in range(4):
        nx = x + dx[i]
        ny = y + dy[i]
        if 0 <= nx and nx < H and 0 <= ny and ny < W and not isVisited[nx][ny]:
            if S[x][y] != S[nx][ny]:
                tmpB, tmpW = dfs( nx, ny )
                numBlack += tmpB
                numWhite += tmpW
    return numBlack, numWhite

ans = 0
for i in range(H):
    for j in range(W):
        if not isVisited[i][j]: 
            numBlack, numWhite = dfs( i, j )
            ans += numBlack * numWhite

print( ans )