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: Wrong Answer)

fn main() {
    let mut buf = String::new();
    let handle = std::io::stdin();
    let info: Vec<usize> = {
        handle.read_line(&mut buf).unwrap();
        let tmp = buf
            .trim()
            .split_whitespace()
            .map(|a| a.parse().unwrap())
            .collect();
        buf.clear();
        tmp
    };
    let board: Vec<Vec<char>> = {
        let mut tmp = Vec::with_capacity(info[0]);
        for i in 0..info[0] {
            handle.read_line(&mut buf).unwrap();
            let t = buf.trim().chars().collect();
            buf.clear();
            tmp.push(t);
        }
        tmp
    };

    let mut memo: Vec<Vec<Option<usize>>> = vec![vec![None; info[1]]; info[0]];
    println!("{:?}", board);
    let mut count = 0;
    search(&info, &board, &mut memo, &mut count);
    println!("{}", count);
}
fn search(
    info: &Vec<usize>,
    board: &Vec<Vec<char>>,
    group_memo: &mut Vec<Vec<Option<usize>>>,
    count: &mut usize,
) {
    let mut group_num = 0;
    for i in 0..info[0] {
        for j in 0..info[1] {
            let mut b = 0;
            let mut w = 0;
            let (mut b, mut w) = dp(
                i, j, group_num, board, group_memo, info, &mut b, &mut w,
            );
            if b != 0 || w != 0 {
                if board[i][j] == '#' {
                    b += 1;
                } else {
                    w += 1;
                }
            }
            *count += b * w;
            group_num += 1;
        }
    }
}
fn dp(
    i: usize,
    j: usize,
    group_num: usize,
    board: &Vec<Vec<char>>,
    group_memo: &mut Vec<Vec<Option<usize>>>,
    info: &Vec<usize>,
    black: &mut usize,
    white:  &mut usize,
) -> (usize, usize) {
    if (i < info[0] - 1) && board[i + 1][j] != board[i][j] {
        match group_memo[i + 1][j] {
            Some(num) => {}
            None => {
                group_memo[i][j] = Some(group_num);
                group_memo[i + 1][j] = Some(group_num);
                dp(i + 1, j, group_num, board, group_memo, info, black, white);
                if board[i + 1][j] == '#' {
                    *black += 1;
                } else {
                    *white += 1;
                }
            }
        }
    }
    if (j < info[1] - 1) && board[i][j + 1] != board[i][j] {
        match group_memo[i][j + 1] {
            Some(num) => {}
            None => {
                group_memo[i][j] = Some(group_num);
                group_memo[i][j + 1] = Some(group_num);
                dp(i, j + 1, group_num, board, group_memo, info, black, white);
                if board[i][j + 1] == '#' {
                    *black += 1;
                } else {
                    *white += 1;
                }
            }
        }
    }
    if i > 0 && board[i - 1][j] != board[i][j] {
        match group_memo[i - 1][j] {
            Some(num) => {}
            None => {
                group_memo[i][j] = Some(group_num);
                group_memo[i - 1][j] = Some(group_num);
                dp(i - 1, j, group_num, board, group_memo, info, black, white);
                if board[i - 1][j] == '#' {
                    *black += 1;
                } else {
                    *white += 1;
                }
            }
        }
    }
    if j > 0 && board[i][j - 1] != board[i][j] {
        match group_memo[i][j - 1] {
            Some(num) => {}
            None => {
                group_memo[i][j] = Some(group_num);
                group_memo[i][j - 1] = Some(group_num);
                dp(i, j - 1, group_num, board, group_memo, info, black, white);
                if board[i][j - 1] == '#' {
                    *black += 1;
                } else {
                    *white += 1;
                }
            }
        }
    }
    return (*black, *white);
}