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**7)
h, w = [int(item) for item in input().split()]
field = []
for i in range(h):
    field.append(input().rstrip())

black = 0; white = 0
visited = [[0] * w for _ in range(h)]

def dfs(is_black, i, j):
    global black
    global white
    visited[i][j] = 1
    for x, y in [[1,0], [0,1], [0,-1], [-1,0]]:
        if i+x < 0 or i+x >= h or j+y < 0 or j+y >= w:
            continue
        if visited[i + x][j + y] != 0:
            continue
        if is_black:
            if field[i+x][j+y] == ".":
                white += 1
                dfs(False, i+x, j+y)
        if not is_black:
            if field[i+x][j+y] == "#":
                black += 1
                dfs(True, i+x, j+y)

ans = 0
for i in range(h):
    for j in range(w):
        if visited[i][j] != 0:
            continue
        if field[i][j] == "#":
            white = 0; black = 1
            dfs(True, i, j)
        else:
            white = 1; black = 0
            dfs(False, i, j)
        ans += white * black

print(ans)