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(1000*1000)

H, W = map(int, input().split(" "))
map_info = [input() for i in range(H)]

visit = [[False for j in range(W)] for i in range(H)]
ans = 0


def search(i, j, want_color):
    if i < 0 or i >= H:
        return
    if j < 0 or j >= W:
        return
    if visit[i][j]:
        return
    this_color = map_info[i][j]
    if want_color != this_color:
        return

    global white
    global black

    visit[i][j] = True
    if this_color == '.':
        white += 1
        next_color = '#'
    else:
        black += 1
        next_color = '.'
    search(i, j+1, next_color)
    search(i, j-1, next_color)
    search(i+1, j, next_color)
    search(i-1, j, next_color)


for i in range(H):
    for j in range(W):
        white = 0
        black = 0
        search(i, j, map_info[i][j])
        ans += black * white
print(ans)