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::io::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let h: usize = iterator.next().unwrap().parse().unwrap();
    let w: usize = iterator.next().unwrap().parse().unwrap();
    let mut map: Vec<Vec<char>> = Vec::new();
    for _ in 0..h {
        map.push(iterator.next().unwrap().chars().collect());
    }

    let mut count: usize = 0;
    let mut visited = vec![vec![false; w]; h];
    for y in 0..h {
        for x in 0..w {
            if visited[y][x] {
                continue;
            }

            let mut black: usize = 0;
            let mut white: usize = 0;

            let mut stack: Vec<(usize, usize)> = Vec::new();
            stack.push((y, x));
            visited[y][x] = true;
            if map[y][x] == '.' {
                white += 1;
            } else {
                black += 1;
            }
            while !stack.is_empty() {
                let top = *stack.last().unwrap();
                if top.1 > 0 && !visited[top.0][top.1 - 1] && map[top.0][top.1 - 1] != map[top.0][top.1] {
                    stack.push((top.0, top.1 - 1));
                    visited[top.0][top.1 - 1] = true;
                    if map[top.0][top.1 - 1] == '.' {
                        white += 1;
                    } else {
                        black += 1;
                    }
                } else if top.0 > 0 && !visited[top.0 - 1][top.1] && map[top.0 - 1][top.1] != map[top.0][top.1] {
                    stack.push((top.0 - 1, top.1));
                    visited[top.0 - 1][top.1] = true;
                    if map[top.0 - 1][top.1] == '.' {
                        white += 1;
                    } else {
                        black += 1;
                    }
                } else if top.1 + 1 < w && !visited[top.0][top.1 + 1] && map[top.0][top.1 + 1] != map[top.0][top.1] {
                    stack.push((top.0, top.1 + 1));
                    visited[top.0][top.1 + 1] = true;
                    if map[top.0][top.1 + 1] == '.' {
                        white += 1;
                    } else {
                        black += 1;
                    }
                } else if top.0 + 1 < h && !visited[top.0 + 1][top.1] && map[top.0 + 1][top.1] != map[top.0][top.1] {
                    stack.push((top.0 + 1, top.1));
                    visited[top.0 + 1][top.1] = true;
                    if map[top.0 + 1][top.1] == '.' {
                        white += 1;
                    } else {
                        black += 1;
                    }
                } else {
                    stack.pop();
                }
            }
            count += white * black;
        }
    }

    return count.to_string();
}