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
from sys import stdin
sys.setrecursionlimit(10**7)
dx = (1, 0, -1, 0)
dy = (0, 1, 0, -1)
H, W = [int(_) for _ in stdin.readline().rstrip().split()]
field = [list(stdin.readline().rstrip()) for _ in range(H)]
seen = [[False for i in range(400)] for j in range(400)]
num_b, num_w = 0, 0
ans = 0

def dfs(h, w):
    seen[h][w] = True
    if field[h][w] == '#':
        global num_b
        num_b += 1
    else:
        global num_w
        num_w += 1

    for direction in range(4):
        nh = h + dx[direction]
        nw = w + dy[direction]

        if nh < 0 or nh >= H or nw < 0 or nw >= W:
            continue
        if field[nh][nw] == field[h][w]:
            continue
        if seen[nh][nw]:
            continue

        dfs(nh, nw)

for i in range(H):
    for j in range(W):
        if field[i][j] == '.':
            continue
        if seen[i][j]:
            continue
        num_b, num_w = 0, 0
        dfs(i, j)
        ans += num_b * num_w 

print(ans)