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)

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

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

    let n = h * w;
    let mut uf = UnionFind::new(n);
    for i in 0..h {
        for j in 0..w {
            if i < h-1 && s[i][j] != s[i+1][j] {
                uf.unite(i*w + j, (i+1)*w + j);
            }
            if j < w-1 && s[i][j] != s[i][j+1] {
                uf.unite(i*w + j, i*w + j+1);
            }
        }
    }

    let mut black = vec![0; n];
    let mut white = vec![0; n];
    for i in 0..h {
        for j in 0..w {
            let root = uf.find(i*w + j);
            if s[i][j] == '#' {
                black[root] += 1;
            } else {
                white[root] += 1;
            }
        }
    }

    let mut used = vec![false; n];
    let mut ans = 0;
    for i in 0..h {
        for j in 0..w {
            let root = uf.find(i*w + j);
            if used[root] {
                continue;
            }
            ans += black[root] * white[root];
            used[root] = true;
        }
    }

    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()
}

#[derive(Debug)]
struct UnionFind {
    par: Vec<usize>,
    rank: Vec<usize>,
}

impl UnionFind {
    fn new(n: usize) -> UnionFind {
        UnionFind {
            par: (0..n).collect(),
            rank: vec![0; n],
        }
    }

    fn find(&mut self, x: usize) -> usize {
        let par = self.par[x];
        if par != x {
            self.par[x] = self.find(par);
        }
        self.par[x]
    }

    fn unite(&mut self, x: usize, y: usize) {
        let x = self.find(x);
        let y = self.find(y);
        if x == y {
            return;
        }

        let rx = self.rank[x];
        let ry = self.rank[y];
        if rx < ry {
            self.par[x] = y;
        } else {
            self.par[y] = x;
            if rx == ry {
                self.rank[x] += 1;
            }
        }
    }

    fn same(&mut self, x: usize, y: usize) -> bool {
        self.find(x) == self.find(y)
    }
}