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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
int n,i,j,a[100005],tree[4005],f[2005][2005],w[100005],b[100005];
char c[100005];
int lowbit(int x)
{
	return -x&x;
}
void modify(int x)
{
	while(x<=n*2)
	{
		++tree[x];
		x+=lowbit(x);
	}
}
int Query(int x)
{
	int y=0;
	while(x)
	{
		y+=tree[x];
		x-=lowbit(x);
	}
	return y;
}
int main()
{
	scanf("%d\n",&n);
	for(i=1;i<=n*2;++i)
	{
		scanf("%c %d\n",&c[i],&a[i]);
		if(c[i]=='W')
			w[a[i]]=i;
		else
			b[a[i]]=i;
	}
	for(i=0;i<=n;++i)
	{
		memset(tree,0,sizeof(tree));
		for(j=1;j<i;++j)
			modify(w[j]);
		if(i!=0)
			f[i][0]=i-1-Query(w[i])+f[i-1][0];
		for(j=1;j<=n;++j)
		{
			int s=i+j-1-Query(b[j]);
			if(w[i]>b[j])
				--s;
			f[i][j]=f[i][j-1]+s;
			modify(b[j]);
			if(i!=0)
				f[i][j]=min(f[i][j],f[i-1][j]+i+j-1-Query(w[i]));
		}
	}
	cout<<f[n][n];
}