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;
const int N=4005;

int n,a[N],ans=INT_MAX,cur,BIT[N];
char c[N];

void update(int pos){
	for (int i=pos;i;i-=(i&-i)){
		BIT[i]++;
	}
}

int query(int pos){
	int ret=0;
	for (int i=pos;i<N;i+=(i&-i)){
		ret+=BIT[i];
	}
	return ret;
}

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n;
	for (int i=1;i<=n*2;i++){
		cin >> c[i] >> a[i];
	}
	for (int i=1;i<=n+1;i++){
		memset(BIT,0,sizeof(BIT));
		int now=0;
		for (int j=1;j<=n*2;j++){
			if (c[j]=='B'){
				cur=i+a[j]-1;
			}else{
				if (a[j]<i){
					cur=a[j];
				}else{
					cur=i+n-1+a[j]-(i-1);
				}
			}
			now+=query(cur+1);
			update(cur);
		}
		ans=min(ans,now);
		memset(BIT,0,sizeof(BIT));
		now=0;
		for (int j=1;j<=n*2;j++){
			if (c[j]=='W'){
				cur=i+a[j]-1;
			}else{
				if (a[j]<i){
					cur=a[j];
				}else{
					cur=i+n-1+a[j]-(i-1);
				}
			}
			now+=query(cur+1);
			update(cur);
		}
		ans=min(ans,now);
	}
	cout << ans << "\n";
}