Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3 3
.#.
..#
#..

Sample Output 1

10

Some of the pairs satisfying the condition are ((1, 2), (3, 3)) and ((3, 1), (3, 2)), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

Sample Input 2

2 4
....
....

Sample Output 2

0

Sample Input 3

4 3
###
###
...
###

Sample Output 3

6

Solution in Rust (1.42.0) (judge verdict: Time Limit Exceeded)

fn main() {
    proconio::input! {
        h: usize,
        w: usize,
        ss: [proconio::marker::Chars; h],
    }
    let mut group = vec![vec![None; w]; h];
    for i_origin in 0..h {
        for j_origin in 0..w {
            if ss[i_origin][j_origin] == '.' || group[i_origin][j_origin].is_some() {
                continue;
            }
            let mut deque = std::collections::VecDeque::new();
            deque.push_back((i_origin, j_origin));
            while let Some((i, j)) = deque.pop_front() {
                group[i][j] = Some((i_origin, j_origin));
                let nexts = [
                    (i.wrapping_sub(1), j),
                    (i, j.wrapping_sub(1)),
                    (i + 1, j),
                    (i, j + 1),
                ];
                for &(i_next, j_next) in &nexts {
                    if i_next < h
                        && j_next < w
                        && group[i_next][j_next].is_none()
                        && ss[i][j] != ss[i_next][j_next]
                    {
                        deque.push_back((i_next, j_next));
                    }
                }
            }
        }
    }
    let mut nums = std::collections::HashMap::new();
    for (i, group) in group.iter().enumerate() {
        for (j, group) in group.iter().enumerate() {
            if let Some(group) = group {
                let e = nums.entry(group).or_insert([0, 0]);
                let idx = if ss[i][j] == '#' { 0 } else { 1 };
                (*e)[idx] += 1;
            }
        }
    }
    let ans = nums.values().map(|x| x[0] * x[1]).sum::<usize>();
    println!("{}", ans);
}