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(200000)
input = sys.stdin.readline


H, W = [int(_) for _ in input().split()]
S = [input() for _ in range(H)]

move = ((1, 0), (-1, 0), (0, 1), (0, -1))
visited = [[False] * W for _ in range(H)]
b, w = 0, 0

def dfs(i, j):
    if visited[i][j]:
        return (0, 0)

    visited[i][j] = True

    if S[i][j] == '#':
        b, w = 1, 0
    else:
        b, w = 0, 1

    for di, dj in move:
        ni, nj = i + di, j + dj
        if not (0 <= ni < H and 0 <= nj < W):
            continue
        if S[i][j] != S[ni][nj]:
                db, dw = dfs(ni, nj)
                b, w = b + db, w + dw

    return (b, w)


result = 0
for i in range(H):
    for j in range(W):
        b, w = dfs(i, j)
        result += b * w
print(result)