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;
// use std::collections::HashMap;
// use std::collections::HashSet;


const INF: i64 = 1_000_000_000;


fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin);

    /*
    let mut xss = vec![vec![0; 3]; 4];
    println!("{:?}", xss);
    xss[1][2] = 3;
    println!("{:?}", xss);
    */

    let n = sc.read();
    let mut pos0 = vec![0; n];
    let mut pos1 = vec![0; n];
    for i in 0..2*n {
        let c = sc.read::<String>().chars().next().unwrap();
        let a = sc.read::<i64>() - 1;
        (*match c {
            'W' => &mut pos0,
            _   => &mut pos1,
        })[a as usize] = i;
    }
    // println!("{:?}", pos0);
    // println!("{:?}", pos1);

    let mut counts0 = Vec::new();
    let mut cnt = vec![0; 2*n];
    for &p in pos0.iter() {
        counts0.push(cnt.clone());
        for k in p..2*n {
            cnt[k] += 1;
        }
    }
    counts0.push(cnt);

    let mut counts1 = Vec::new();
    let mut cnt = vec![0; 2*n];
    for &p in pos1.iter() {
        counts1.push(cnt.clone());
        for k in p..2*n {
            cnt[k] += 1;
        }
    }
    counts1.push(cnt);

    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 {
            let now = dp[i][j];
            if i < n {
                let pos = pos0[i];
                let dst = &mut dp[i+1][j];
                *dst = cmp::min(*dst, now + pos as i64 - counts0[i][pos] - counts1[j][pos]);
            }
            if j < n {
                let pos = pos1[j];
                let dst = &mut dp[i][j+1];
                *dst = cmp::min(*dst, now + pos as i64 - counts0[i][pos] - counts1[j][pos]);
            }
        }
    }
    // println!("{:?}", counts0);
    // println!("{:?}", counts1);
    // println!("{:?}", dp);

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

// thanks, ir5
use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }
}