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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num::clamp;
use proconio::{input, marker::*, fastout};
use superslice::*;

#[fastout()]
fn main() {
    input! {
        h: usize, w: usize,
        s: [Chars; h]
    }

    let mut visited = vec![vec![false; w]; h];
    let mut ans = 0usize;
    for y in 0..h {
        for x in 0..w {
            if visited[y][x] {
                continue;
            }
            let mut black = 0;
            let mut white = 0;
            let mut que = Vec::new();
            que.push((x, y));
            visited[y][x] = true;
            while let Some((x1, y1)) = que.pop() {
                if s[y1][x1] == '#' {
                    black += 1;
                } else {
                    white += 1;
                }
                let d = [(0, 1), (1, 0), (-1, 0), (0, -1)];
                for &(dx, dy) in &d {
                    let x2 = clamp(x1 as isize + dx, 0, w as isize - 1) as usize;
                    let y2 = clamp(y1 as isize + dy, 0, h as isize - 1) as usize;
                    if visited[y2][x2] || s[y1][x1] == s[y2][x2] {
                        continue;
                    }
                    visited[y2][x2] = true;
                    que.push((x2, y2));
                }
            }
            ans += black * white;
        }
    }
    println!("{}", ans);
}