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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
const int N=2e3+5;
int n,w[N],b[N],x;
int dp[N][N],cw[N][N],cb[N][N];
int main()
{
    ios::sync_with_stdio(0);
	memset(cw,0,sizeof(cw));
	memset(cb,0,sizeof(cb));
	cin>>n;
	for(int i=1;i<=2*n;i++)
	{
		char op[2];
		cin>>op>>x;
		if(op[0]=='W')
			w[x]=i;
		else
			b[x]=i;
	}
	for(int i=1;i<=n;i++)
	{
		for(int j=1;j<i;j++)
			if(w[i]<w[j])
				cw[i][0]++;
		for(int j=1;j<=n;j++)
		{
			cw[i][j]=cw[i][j-1];
			if(w[i]<b[j])
				cw[i][j]++;	
		}
	}	
	for(int i=1;i<=n;i++)
	{
		for(int j=1;j<i;j++)	
			if(b[i]<b[j])
				cb[0][i]++;
		for(int j=1;j<=n;j++)
		{
			cb[j][i]=cb[j-1][i];
			if(b[i]<w[j])
				cb[j][i]++;
		}
	}
	int c1=0,c2=0;
	for(int i=1;i<=n;i++)
	{
		c1+=cw[i][0],c2+=cb[0][i];
		dp[i][0]=c1,dp[0][i]=c2;
	}
	for(int i=1;i<=n;i++)
		for(int j=1;j<=n;j++)
			dp[i][j]=min(dp[i-1][j]+cw[i][j],dp[i][j-1]+cb[i][j]);	
	cout<<dp[n][n];
	return 0;
}