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;
use std::cmp;
use std::collections::BinaryHeap;
use std::collections::HashMap;
use std::collections::HashSet;
use std::f64::consts::PI;

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf
}

const C: [char; 2] = ['.', '#'];

fn dfs(x: usize, y: usize, s: &Vec<Vec<char>>, memo: &mut Vec<Vec<Option<bool>>>, c: usize) -> (u64,u64) {
    if memo[x][y].is_some() {
        return (0,0)
    }
    if s[x-1][y-1] == C[c] {
        let mut ans = [0, 0];
        ans[c] += 1;
        memo[x][y] = Some(true);
        let (w,b) = dfs(x-1, y, s, memo, (c+1)%2);
        ans[0] += w;
        ans[1] += b;
        let (w,b)= dfs(x+1, y, s, memo, (c+1)%2);
        ans[0] += w;
        ans[1] += b;
        let (w,b)= dfs(x, y-1, s, memo, (c+1)%2);
        ans[0] += w;
        ans[1] += b;
        let (w,b)= dfs(x, y+1, s, memo, (c+1)%2);
        ans[0] += w;
        ans[1] += b;
        (ans[0], ans[1])
    } else {
        memo[x][y] = Some(false);
        (0,0)
    }
}

fn main() {
    let line: Vec<usize> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
    let h = line[0];
    let w = line[1];
    let mut s = Vec::with_capacity(h);
    for _ in 0..h {
        let line: Vec<char> = read_line().trim().chars().collect();
        s.push(line);
    }
    let mut memo = vec![vec![None; w+2]; h+2];
    for i in 0..h+2 {
        memo[i][0] = Some(false);
        memo[i][w+1] = Some(false);
    }
    for i in 0..w+2 {
        memo[0][i] = Some(false);
        memo[h+1][i] = Some(false);
    }

    let mut ans = 0;
    for i in 0..h {
        for j in 0..w {
            let (tmp1, tmp2) = dfs(i+1, j+1, &s, &mut memo, (i+j)%2);       
            ans += tmp1 * tmp2;
        }
    }
    let mut memo = vec![vec![None; w+2]; h+2];
    for i in 0..h+2 {
        memo[i][0] = Some(false);
        memo[i][w+1] = Some(false);
    }
    for i in 0..w+2 {
        memo[0][i] = Some(false);
        memo[h+1][i] = Some(false);
    }
    for i in 0..h {
        for j in 0..w {
            let (tmp1, tmp2) = dfs(i+1, j+1, &s, &mut memo, (i+j+1)%2);       
            ans += tmp1 * tmp2;
        }
    }
    println!("{}", ans);
}