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
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

from collections import defaultdict

H,W = map(int,input().split())
grid = '*' * (W+2)
for _ in range(H):
    grid += '*' + input().rstrip() + '*'
grid += '*' * (W+2)

move = [1,-1,W+2,-(W+2)]

root = [None if x == '*' else -1 for x in grid]

answer = 0
for i in range((H+2)*(W+2)):
    if root[i] != -1:
        continue
    q = [i]
    root[i] = i
    counter = defaultdict(int)
    while q:
        x = q.pop()
        counter[grid[x]] += 1 
        for dx in move:
            y = x + dx
            if root[y] != -1:
                continue
            if grid[x] == grid[y]:
                continue
            root[y] = i
            q.append(y)
    answer += counter['.'] * counter['#']

print(answer)