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(10**6)

H, W = map(int, input().split())
S = [input() for i in range(H)]
visited = [[0] * W for i in range(H)]

def dfs(y, x):
    b, w = 0, 0
    if S[y][x] == '#': b += 1
    else: w += 1
    for dy, dx in ((0,1), (1,0), (0,-1), (-1,0)):
        ny, nx = y + dy, x + dx
        if ny < 0 or ny >= H or nx < 0 or nx >= W: continue
        if S[y][x] == S[ny][nx] or visited[ny][nx]: continue
        visited[ny][nx] = 1
        n, m = dfs(ny, nx)
        b += n
        w += m
    return (b, w)

ans = 0
for i in range(H):
    for j in range(W):
        if not visited[i][j]:
            visited[i][j] = 1
            b, w = dfs(i, j)
            ans += b * w
print(ans)