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 ** 9)

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

visited = [[False for _ in range(W)] for _ in range(H)]
vectors = [[0, -1], [-1, 0], [0, 1], [1, 0]]
ans = 0

def dfs(h, w):
    # 入力された値はindex out of rangeにならないvalidationが掛けられている
    if visited[h][w]:
        return (0, 0)
    
    visited[h][w] = True

    if inputs[h][w] == '#':
        black, white = 1, 0 
    else:
        black, white = 0, 1

    for vector in vectors:
        next_h = h + vector[0]
        next_w = w + vector[1]
        if not (0 <= next_h < H and 0 <= next_w < W):
            continue
        next_color = inputs[next_h][next_w]
        if inputs[h][w] != next_color:
            p_black, p_white = dfs(next_h, next_w)
            black += p_black
            white += p_white

    return (black, white)

for h in range(H):
    for w in range(W):
        black, white = dfs(h, w)
        ans += black * white  

print(ans)