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**9)

from collections import deque

h, w = map(int, input().split())
s = [input() for _ in range(h)]

memo = [[0] * w for _ in range(h)]

dir = [(0, 1), (0, -1), (1, 0), (-1, 0)]

def dfs(i, j, color):
    if not (0 <= i <= h-1 and 0 <= j <= w-1):
        return 0, 0
    if memo[i][j] == 1:
        return 0, 0
    if s[i][j] == color:
        return 0, 0
    memo[i][j] = 1
    white, black = 0, 0
    if s[i][j] == ".":
        white += 1
    else:
        black += 1
    for dx, dy in dir:
        cur_w, cur_b = dfs(i + dx, j + dy, s[i][j])
        white += cur_w
        black += cur_b
    return white, black

ans = 0
for i in range(h):
    for j in range(w):
        if s[i][j] == ".":
            white, black = dfs(i, j, "#")
        else:
            white, black = dfs(i, j, ".")

        ans += white * black

print(ans)