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 ** 9)

H, W = map(int, input().split())
s_list = []
for i in range(H):
    s_list.append(input())
check = [[False for _ in range(W)] for _ in range(H)]
move_x = [1, 0, -1, 0]
move_y = [0, 1, 0, -1]


def dfs(i, j):
    check[i][j] = True

    if s_list[i][j] == "#":
        cnt[0] += 1
    else:
        cnt[1] += 1

    for m in range(4):
        next_i = i + move_y[m]
        next_j = j + move_x[m]
        if 0 <= next_i < H and 0 <= next_j < W and s_list[i][j] != s_list[next_i][next_j] \
                and not check[next_i][next_j]:
            dfs(next_i, next_j)


ans = 0
for i in range(H):
    for j in range(W):
        cnt = [0] * 2
        dfs(i, j)
        ans += cnt[0] * cnt[1]
print(ans)