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: Time Limit Exceeded)

use std::io::*;
use std::str::FromStr;
use std::collections::VecDeque;

fn main() {
    let h: usize = read();
    let w: usize = read();
    let s: Vec<Vec<char>> = (0..h).map(|_| read::<String>().chars().collect()).collect();

    let mut a: Vec<Vec<i64>> = vec![vec![-1; w]; h];
    let mut ans = 0;
    for i in 0..h {
        for j in 0..w {
            if s[i][j] == '.' {
                continue;
            }
            if a[i][j] >= 0 {
                ans += a[i][j];
                continue;
            }
            let mut check: Vec<Vec<bool>> = vec![vec![false; w]; h];
            let mut que: VecDeque<(usize, usize)> = VecDeque::new();
            let mut same: Vec<(usize, usize)> = Vec::new();
            let mut cnt: i64 = 0;
            que.push_back((i, j));
            while let Some((y, x)) = que.pop_front() {
                if check[y][x] {
                    continue;
                }
                check[y][x] = true;
                let c = s[y][x];
                if c == '.' {
                    cnt += 1;
                } else {
                    same.push((y, x));
                }
                if x > 0 && c != s[y][x-1] {
                    que.push_back((y, x-1));
                }
                if x < w-1 && c != s[y][x+1] {
                    que.push_back((y, x+1));
                }
                if y > 0 && c != s[y-1][x] {
                    que.push_back((y-1, x));
                }
                if y < h-1 && c != s[y+1][x] {
                    que.push_back((y+1, x));
                }
            }
            a[i][j] = cnt;
            for i in &same {
                let (y, x) = *i;
                a[y][x] = cnt;
            }
            ans += cnt;
        }
    }
    println!("{}", ans);
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}