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(10 ** 9)

H, W = [int(i) for i in input().split()]
S = [[j for j in input()]for i in range(H)]

INF = int(1e12)

def dfs(h, w, p):
    b_cnt = 0
    w_cnt = 0
    if h < 0 or h >= H or w < 0 or w >= W:
        return 0, 0
    if S[h][w] == p or S[h][w] == 'x':
        return 0, 0
    if S[h][w] == '#':
        b_cnt += 1
    elif S[h][w] == '.':
        w_cnt += 1
    t = S[h][w]
    S[h][w] = 'x'

    for dh, dw in ((0, 1), (0, -1), (1, 0), (-1, 0)):
        res = dfs(h + dh, w + dw, t)
        b_cnt += res[0]
        w_cnt += res[1]

    return (b_cnt, w_cnt)

ans = 0

for h in range(H):
    for w in range(W):
        if S[h][w] == '#':
            b_cnt, w_cnt = dfs(h, w, '.')
            ans += b_cnt * w_cnt

print(ans)