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(4100000)

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

C = [[1 for i in range(W)] for j in range(H)]
L = ['.', '#']
D = {'.':0, '#':1}
tx = [1, 0, -1, 0]
ty = [0, 1, 0, -1]

def dfs(x, y, c, l):
    C[x][y] = 0
    l[c] += 1
    for i in range(4):
        nx = x + tx[i]
        ny = y + ty[i]
        if 0 <= nx < H and 0 <= ny < W and C[nx][ny] and L[c] != S[nx][ny]:
            l = dfs(nx, ny, 1 - c, l)
    return l

ans = 0
for i in range(H):
    for j in range(W):
        l = dfs(i, j, D[S[i][j]], [0, 0])
        ans += l[0] * l[1]

print(ans)