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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main {

    static Parser parser = new Parser();

    public static void main(String[] args) throws IOException {

        int N = parser.parseInt();

        int wIdx[] = new int[N + 1];
        int bIdx[] = new int[N + 1];

        for(int i = 0; i < 2 * N; i++){
            char ch = parser.parseString().charAt(0);
            int idx = parser.parseInt();

            if(ch == 'W'){
                wIdx[idx] = i;
            }else{
                bIdx[idx] = i;
            }
        }

        int wCost[][] = new int[N + 1][N + 1];
        int bCost[][] = new int[N + 1][N + 1];

        for(int i = 1; i <= N; i++){
            for(int j = i + 1; j <= N; j++){
                if(wIdx[i] > wIdx[j]){
                    wCost[i][N] += 1;
                }
                if(bIdx[i] > bIdx[j]){
                    bCost[N][i] += 1;
                }
            }
        }

        for(int i = 1; i <= N; i++){
            for(int j = N - 1; j >= 0; j--){
                wCost[i][j] = wCost[i][j + 1] + (wIdx[i] > bIdx[j + 1] ? 1 : 0);
            }
        }

        for(int i = 1; i <= N; i++){
            for(int j = N - 1; j >= 0; j--){
                bCost[j][i] = bCost[j + 1][i] + (bIdx[i] > wIdx[j + 1] ? 1 : 0);
            }
        }

        int dp[][] = new int[N + 1][N + 1];
        for(int i = 0; i <= N; i++){
            Arrays.fill(dp[i], (int)1e9);
        }

        dp[0][0] = 0;
        for(int i = 0; i <= N; i++){
            for(int j = 0; j <= N; j++){

                if(i > 0){
                    dp[i][j] = Math.min(dp[i][j], dp[i - 1][j] + wCost[i][j]);
                }

                if(j > 0){
                    dp[i][j] = Math.min(dp[i][j], dp[i][j - 1] + bCost[i][j]);
                }
            }
        }

        System.out.println(dp[N][N]);
    }
}

class Parser {
    private static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private static final Iterator<String> stringIterator = br.lines().iterator();
    private static final Deque<String> inputs = new ArrayDeque<>();

    void fill() throws IOException {
        if(inputs.isEmpty()){
            if(!stringIterator.hasNext()) throw new IOException();
            inputs.addAll(Arrays.asList(stringIterator.next().split(" ")));
        }
    }

    Integer parseInt() throws IOException {
        fill();
        if(!inputs.isEmpty()) {
            return Integer.parseInt(inputs.pollFirst());
        }
        throw new IOException();
    }

    Long parseLong() throws IOException {
        fill();
        if(!inputs.isEmpty()) {
            return Long.parseLong(inputs.pollFirst());
        }
        throw new IOException();
    }

    Double parseDouble() throws IOException {
        fill();
        if(!inputs.isEmpty()) {
            return Double.parseDouble(inputs.pollFirst());
        }
        throw new IOException();
    }

    String parseString() throws IOException {
        fill();
        return inputs.pollFirst();
    }

}