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;

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.read();
    let mut pos_b = vec![0; n];
    let mut pos_w = vec![0; n];
    for i in 0..(2 * n) {
        let c = sc.read::<String>();
        let a = sc.read::<usize>() - 1;
        if c == "W" {
            pos_w[a] = i;
        } else {
            pos_b[a] = i;
        }
    }

    let calc_right = |pos: &Vec<usize>| {
        let mut right = vec![0; n];
        for i in 0..n {
            let mut sum = 0;
            for j in 0..i {
                if pos[i] < pos[j] {
                    sum += 1;
                }
            }
            right[i] = sum;
        }
        right
    };

    let right_b = calc_right(&pos_b);
    let right_w = calc_right(&pos_w);

    let calc_right_other = |pos: &Vec<usize>, other: &Vec<usize>| {
        let mut right = vec![vec![0; n + 1]; n];
        for i in 0..n {
            let mut sum = 0;
            for j in 0..n {
                if pos[i] < other[j] {
                    sum += 1;
                }
                right[i][j + 1] = sum;
            }
        }
        right
    };

    let other_b = calc_right_other(&pos_b, &pos_w);
    let other_w = calc_right_other(&pos_w, &pos_b);

    let inf = std::usize::MAX;
    let mut dp = vec![vec![inf; n + 1]; n + 1];
    dp[0][0] = 0;

    for i in 0..(n + 1) {
        for j in 0..(n + 1) {
            if dp[i][j] == inf {
                continue;
            }
            if i + 1 <= n {
                dp[i + 1][j] = cmp::min(
                    dp[i + 1][j],
                    dp[i][j] + pos_b[i] + right_b[i] + other_b[i][j] - (i + j),
                );
            }

            if j + 1 <= n {
                dp[i][j + 1] = cmp::min(
                    dp[i][j + 1],
                    dp[i][j] + pos_w[j] + right_w[j] + other_w[j][i] - (i + j),
                );
            }
        }
    }

    println!("{}", dp[n][n]);
}

struct Scanner {
    ptr: usize,
    length: usize,
    buf: Vec<u8>,
    small_cache: Vec<u8>,
}

impl Scanner {
    fn new() -> Scanner {
        Scanner {
            ptr: 0,
            length: 0,
            buf: vec![0; 1024],
            small_cache: vec![0; 1024],
        }
    }

    fn load(&mut self) {
        use std::io::Read;
        let mut s = std::io::stdin();
        self.length = s.read(&mut self.buf).unwrap();
    }

    fn byte(&mut self) -> u8 {
        if self.ptr >= self.length {
            self.ptr = 0;
            self.load();
            if self.length == 0 {
                self.buf[0] = b'\n';
                self.length = 1;
            }
        }

        self.ptr += 1;
        return self.buf[self.ptr - 1];
    }

    fn is_space(b: u8) -> bool {
        b == b'\n' || b == b'\r' || b == b'\t' || b == b' '
    }

    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        let mut b = self.byte();
        while Scanner::is_space(b) {
            b = self.byte();
        }

        for pos in 0..self.small_cache.len() {
            self.small_cache[pos] = b;
            b = self.byte();
            if Scanner::is_space(b) {
                return String::from_utf8_lossy(&self.small_cache[0..(pos + 1)])
                    .parse()
                    .unwrap();
            }
        }

        let mut v = self.small_cache.clone();
        while !Scanner::is_space(b) {
            v.push(b);
            b = self.byte();
        }
        return String::from_utf8_lossy(&v).parse().unwrap();
    }
}