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;
#ifndef ONLINE_JUDGE
#define dbg(x...) do { cout << "\033[32;1m " << #x << " -> "; err(x); } while (0)
void err() { cout << "\033[39;0m" << endl; }
template<template<typename...> class T, typename t, typename... A>
void err(T<t> a, A... x) { for (auto v: a) cout << v << ' '; err(x...); }
template<typename T, typename... A>
void err(T a, A... x) { cout << a << ' '; err(x...); }
#else
#define dbg(...)
#endif
typedef long long ll;
typedef pair<int,int> pi;
typedef vector<int> vi;
template<class T> using vc=vector<T>;
template<class T> using vvc=vc<vc<T>>;
template<class T> void mkuni(vector<T>&v)
{
    sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}
ll rand_int(ll l, ll r) //[l, r]
{
    static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
    return uniform_int_distribution<ll>(l, r)(gen);
}
template<class T>
void print(T x,int suc=1)
{
    cout<<x;
    if(suc==1) cout<<'\n';
    else cout<<' ';
}
template<class T>
void print(const vector<T>&v,int suc=1)
{
    for(int i=0;i<v.size();i++)
    print(v[i],i==(int)(v.size())-1?suc:2);
}
const int maxn=2005;
int dp[maxn][maxn];
int tree[2*maxn];
void add(int x,int val)
{
    while(x<maxn)
    {
        tree[x]+=val;
        x+=x&-x;
    }
}
int query(int x)
{
    int ret=0;
    while(x)
    {
        ret+=tree[x];
        x-=x&-x;
    }
    return ret;
}
int main()
{
    int n;
    cin>>n;
    vi posa(n+1,-1),posb(n+1,-1);
    vi a(2*n),c(2*n);
    for(int i=0;i<2*n;i++)
    {
        string col;
        cin>>col;
        cin>>a[i];
        if(col=="B")
        {
            c[i]=1;
            posa[a[i]]=i+1;
            add(i+1,1);
        }
        else {
            c[i]=0;
            posb[a[i]]=i+1;
        }
    }
    memset(dp,0x3f,sizeof(dp));
    dp[0][0]=0;
    for(int i=0;i<=n;i++)
    {
        for(int j=1;j<=n;j++)
            add(posb[j],1);
        for(int j=0;j<=n;j++)
        {
            if(!i&&!j) continue;
            if(i)
            {
                if(j) add(posb[j],-1);
                dp[i][j]=min(dp[i][j],dp[i-1][j]+query(posa[i]-1));
                if(j) add(posb[j],1);
            }
            if(j)
            {
                if(i) add(posa[i],-1);
                dp[i][j]=min(dp[i][j],dp[i][j-1]+query(posb[j]-1));
                if(i) add(posa[i],1);
            }
            if(j) add(posb[j],-1);
        }
        if(i)
            add(posa[i],-1);
    }
    print(dp[n][n]);
    
    
}