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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
class Program{
	const int mod=1000000007;
	const long o=1;
	static void Main(){
		Sc sc=new Sc();
		int n=sc.I;
		Bit bit=new Bit(n*2);
		int[] b=new int[n+1],w=new int[n+1];
		string[] a=new string[n*2];
		int[] r=new int[n*2];
		for(int i = 0;i<n*2;i++) {
			a[i]=sc.S;
			r[i]=int.Parse((a[i].Split())[1]);
			if(a[i][0]=='B'){b[r[i]]=i;}
			else{w[r[i]]=i;}
		}
		long[,,] dp=new long[n+1,n+1,2];
		for(int i = 0;i<=n;i++) {
			bit=new Bit(n*2);
			if(i!=0){
				for(int j = 1;j<i;j++) {bit.Ud(b[j]+1,1);}
				dp[i,0,0]=dp[i-1,0,0]+b[i]-bit.Get(b[i]+1);
				bit.Ud(b[i]+1,1);
			}
			for(int j = 1;j<=n;j++) {
				dp[i,j,0]=dp[i,j-1,0]+w[j]-bit.Get(w[j]+1);
				if(i!=0){dp[i,j,0]=Math.Min(dp[i,j,0],dp[i-1,j,0]+b[i]-dp[i-1,j,1]);}
				if(j!=0){bit.Ud(w[j]+1,1);}
				if(i!=n){dp[i,j,1]=bit.Get(b[i+1]+1);}
			}
			bit.Clear();
		}
		Console.WriteLine("{0}",dp[n,n,0]);
	}
}
public class Bit{
	private int n;
	private long[] bit;
	public Bit(int n){
		this.n=n;
		bit=new long[n+1];
	}
	public void Ud(int a,long p){while(a<=n){bit[a]+=p;a+=a&-a;}}
	public long Get(int n){
		long a=0;
		while(n>0){a+=bit[n];n-=n&-n;}
		return a;
	}
	public long Get2(int n,int m){
		long a=0,b=0;
		while(n>m){a+=bit[n];n-=n&-n;}
		if(n==m){return a;}
		while(n!=m){b+=bit[m];m-=m&-m;}
		return a-b;
	}
	public void Clear(){bit=new long[n+1];}
}

class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
}