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 (1.15.1) (judge verdict: Accepted)

use std::cmp::*;
use std::io::*;

fn main() {
    let mut s: String = String::new();
    stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let h: usize = itr.next().unwrap().parse().unwrap();
    let w: usize = itr.next().unwrap().parse().unwrap();
    let g: Vec<Vec<char>> = (0..h)
        .map(|_| itr.next().unwrap().chars().collect())
        .collect();
    let dx: Vec<isize> = [0, -1, 0, 1].to_vec();
    let dy: Vec<isize> = [1, 0, -1, 0].to_vec();

    let mut used = vec![vec![false; w]; h];
    let mut ans = 0u64;
    for i in 0..h {
        for j in 0..w {
            if !used[i][j] {
                let mut q = std::collections::VecDeque::new();
                q.push_back((i, j));
                used[i][j] = true;

                let mut white = 0;
                let mut black = 0;
                while let Some((y, x)) = q.pop_front() {
                    if g[y][x] == '.' {
                        white += 1;
                    } else {
                        black += 1;
                    }
                    for k in 0..4 {
                        let nx = x as isize + dx[k];
                        let ny = y as isize + dy[k];
                        if 0 <= nx
                            && nx < w as isize
                            && 0 <= ny
                            && ny < h as isize
                            && g[y][x] != g[ny as usize][nx as usize]
                            && !used[ny as usize][nx as usize]
                        {
                            q.push_back((ny as usize, nx as usize));
                            used[ny as usize][nx as usize] = true;
                        }
                    }
                }
                ans += white * black;
            }
        }
    }
    println!("{}", ans);
}