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: Wrong Answer)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] black = new int[n];
		int[] white = new int[n];

		for (int i=0;i<2*n;i++) {
			char c = sc.next().charAt(0);
			int a = sc.nextInt()-1;
			if (c == 'B') {
				black[a] = i;
			} else {
				white[a] = i;
			}
		}

		int blackCount = 0;
		int whiteCount = 0;

		int[] black2 = new int[n];
		int[] white2 = new int[n];

		while(blackCount < n || whiteCount < n) {
			if (whiteCount == n || (blackCount < n && black[blackCount] < white[whiteCount])) {
				black2[blackCount] = blackCount + whiteCount;
				blackCount++;
			} else {
				white2[whiteCount] = blackCount + whiteCount;
				whiteCount++;
			}
		}
		int change = 0;
		for (int i=0;i<n;i++) {
			for (int j=i+1;j<n;j++) {
				if ((black[i]-black[j])*(black2[i]-black2[j]) < 0) {
					change++;
				}
				if ((white[i]-white[j])*(white2[i]-white2[j]) < 0) {
					change++;
				}
			}
		}

		for (int i=0;i<n;i++) {
			for (int j=0;j<n;j++) {

				if ((black[i]-white[j])*(black2[i]-white2[j]) < 0) {
					change++;
				}

			}
		}

		System.out.println(change);
	}

}