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 (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn main() {
    input!(n: usize, ca: [(char, proconio::marker::Usize1); 2 * n]);
    let mut b = vec![0; n];
    let mut w = vec![0; n];
    for (i, &(c, a)) in ca.iter().enumerate() {
        match c {
            'B' => {
                b[a] = i;
            }
            'W' => {
                w[a] = i;
            }
            _ => panic!(),
        }
    }

    let cal_cnt = |a: &Vec<usize>| {
        let mut ans = vec![vec![0; 2 * n + 1]; n + 1];
        for i in 0..n {
            ans[i + 1] = ans[i].clone();
            for j in 0..a[i] {
                ans[i + 1][j] += 1;
            }
        }
        ans
    };
    let cnt_b = cal_cnt(&b);
    let cnt_w = cal_cnt(&w);

    let mut dp = vec![vec![std::u32::MAX; n + 1]; n + 1];
    dp[0][0] = 0;
    for i in 0..=n {
        for j in 0..=n {
            if i < n {
                let x = dp[i][j] + cnt_b[i][b[i]] + cnt_w[j][b[i]];
                if x < dp[i + 1][j] {
                    dp[i + 1][j] = x;
                }
            }
            if j < n {
                let x = dp[i][j] + cnt_b[i][w[j]] + cnt_w[j][w[j]];
                if x < dp[i][j + 1] {
                    dp[i][j + 1] = x;
                }
            }
        }
    }
    println!("{}", dp[n][n]);
}