Problem:
Score : 600 points

Problem Statement

There are 2N balls, N white and N black, arranged in a row. The integers from 1 through N are written on the white balls, one on each ball, and they are also written on the black balls, one on each ball.
The integer written on the i-th ball from the left (1 ≤ i ≤ 2N) is a_i, and the color of this ball is represented by a letter c_i.
c_i = W represents the ball is white; c_i = B represents the ball is black.

Takahashi the human wants to achieve the following objective:

For every pair of integers (i,j) such that 1 ≤ i < j ≤ N, the white ball with i written on it is to the left of the white ball with j written on it.

For every pair of integers (i,j) such that 1 ≤ i < j ≤ N, the black ball with i written on it is to the left of the black ball with j written on it.

In order to achieve this, he can perform the following operation:

Swap two adjacent balls.

Find the minimum number of operations required to achieve the objective.

Constraints

1 ≤ N ≤ 2000

1 ≤ a_i ≤ N

c_i = W or c_i = B.

If i ≠ j, (a_i,c_i) ≠ (a_j,c_j).

Input

Input is given from Standard Input in the following format:

N
c_1 a_1
c_2 a_2
:
c_{2N} a_{2N}

Output

Print the minimum number of operations required to achieve the objective.

Sample Input 1

3
B 1
W 2
B 3
W 1
W 3
B 2

Sample Output 1

4

The objective can be achieved in four operations, for example, as follows:

Swap the black 3 and white 1.

Swap the white 1 and white 2.

Swap the black 3 and white 3.

Swap the black 3 and black 2.

Sample Input 2

4
B 4
W 4
B 3
W 3
B 2
W 2
B 1
W 1

Sample Output 2

18

Sample Input 3

9
W 3
B 1
B 4
W 1
B 5
W 9
W 2
B 6
W 5
B 3
W 8
B 9
W 7
B 2
B 8
W 4
W 6
B 7

Sample Output 3

41

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::cmp;

const INF: usize = 1 << 50;
fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());
    let n: usize = sc.read();
    let mut balls = vec![];
    for _ in 0..(2 * n) {
        let is_black = sc.chars()[0] == 'B';
        let a = sc.read::<usize>() - 1;
        balls.push((a, is_black));
    }

    let mut black_front = vec![0; n];
    let mut white_front = vec![0; n];
    for i in 0..(2 * n) {
        let (a, is_black) = balls[i];
        for i in 0..i {
            if is_black == balls[i].1 && balls[i].0 < a {
                if is_black {
                    black_front[a] += 1;
                } else {
                    white_front[a] += 1;
                }
            }
        }
    }

    let mut black_pos = vec![0; n];
    let mut white_pos = vec![0; n];
    for i in 0..(2 * n) {
        let (a, is_black) = balls[i];
        if is_black {
            black_pos[a] = i;
        } else {
            white_pos[a] = i;
        }
    }

    let mut white_black = vec![vec![0; n + 1]; n];
    for white in 0..n {
        for black in 0..n {
            white_black[white][black + 1] = white_black[white][black];
            if black_pos[black] < white_pos[white] {
                white_black[white][black + 1] += 1;
            }
        }
    }
    let mut black_white = vec![vec![0; n + 1]; n];
    for black in 0..n {
        for white in 0..n {
            black_white[black][white + 1] = black_white[black][white];
            if white_pos[white] < black_pos[black] {
                black_white[black][white + 1] += 1;
            }
        }
    }

    let mut dp = vec![INF; n + 1];
    dp[0] = 0;
    for cur_ball in 0..(2 * n) {
        let mut next = vec![INF; n + 1];
        for cur_black in 0..(n + 1) {
            if cur_ball < cur_black {
                break;
            }
            let cur_white = cur_ball - cur_black;
            if cur_white > n {
                continue;
            }
            if cur_black < n {
                let next_black = cur_black;
                let pos = black_pos[next_black];
                let smaller_blacks = black_front[next_black];
                let ignore_whites = black_white[next_black][cur_white];
                //                eprintln!(
                //                    "next_black={} pos={} smaller={} cur_white={} ignore={}",
                //                    next_black, pos, smaller_blacks, cur_white, ignore_whites
                //                );
                let cost = pos - (smaller_blacks + ignore_whites);
                next[cur_black + 1] = cmp::min(next[cur_black + 1], dp[cur_black] + cost);
            }
            if cur_white < n {
                let next_white = cur_white;
                let pos = white_pos[next_white];
                let smaller_whites = white_front[next_white];
                let ignore_blacks = white_black[next_white][cur_black];
                let cost = pos - smaller_whites - ignore_blacks;
                next[cur_black] = cmp::min(next[cur_black], dp[cur_black] + cost);
            }
        }
        dp = next;
    }
    println!("{}", dp[n]);
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> IO<R, W> {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: std::ops::Deref<Target = str>>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}