Problem:
Score : 700 points

Problem Statement

We have N cards numbered 1, 2, ..., N.
Card i (1 \leq i \leq N) has an integer A_i written in red ink on one side and an integer B_i written in blue ink on the other side.
Initially, these cards are arranged from left to right in the order from Card 1 to Card N, with the red numbers facing up.

Determine whether it is possible to have a non-decreasing sequence facing up from left to right (that is, for each i (1 \leq i \leq N - 1), the integer facing up on the (i+1)-th card from the left is not less than the integer facing up on the i-th card from the left) by repeating the operation below. If the answer is yes, find the minimum number of operations required to achieve it.

Choose an integer i (1 \leq i \leq N - 1).
Swap the i-th and (i+1)-th cards from the left, then flip these two cards.

Constraints

1 \leq N \leq 18

1 \leq A_i, B_i \leq 50 (1 \leq i \leq N)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N
B_1 B_2 ... B_N

Output

If it is impossible to have a non-decreasing sequence, print -1.
If it is possible, print the minimum number of operations required to achieve it.

Sample Input 1

3
3 4 3
3 2 3

Sample Output 1

1

By doing the operation once with i = 1, we have a sequence [2, 3, 3] facing up, which is non-decreasing.

Sample Input 2

2
2 1
1 2

Sample Output 2

-1

After any number of operations, we have the sequence [2, 1] facing up, which is not non-decreasing.

Sample Input 3

4
1 2 3 4
5 6 7 8

Sample Output 3

0

No operation may be required.

Sample Input 4

5
28 15 22 43 31
20 22 43 33 32

Sample Output 4

-1

Sample Input 5

5
4 46 6 38 43
33 15 18 27 37

Sample Output 5

3

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static void Main(){
		Sc sc=new Sc();
		var n=sc.I;
		var z=sc.Ia;
		var a=new int[n][];
		var b=new int[n][];
		for(int i = 0;i<n;i++) {a[i]=new int[]{i,z[i]};}
		z=sc.Ia;
		for(int i = 0;i<n;i++) {b[i]=new int[]{i,z[i]};}
		a=a.OrderBy(x=>x[1]).ThenBy(x=>x[0]).ToArray();
		b=b.OrderBy(x=>x[1]).ThenBy(x=>x[0]).ToArray();
		int m=1<<n,ans=int.MaxValue;
		for(int i = 0;i<m;i++) {
			var ba=new bool[n];
			var bo=true;
			var g=new int[n];
			int p=0;
			for(int j = 0,k=0,l=0;j<n;j++) {
				if((i&(1<<j))==0){
					while(k<n&&(ba[a[k][0]]||p>a[k][1]||(a[k][0]&1)!=(j&1))){k++;}
					if(k==n){bo=false;break;}
					g[j]=a[k][0];
					ba[a[k][0]]=true;
					p=a[k][1];
					k++;
				}
				else{
					while(l<n&&(ba[b[l][0]]||p>b[l][1]||(b[l][0]&1)==(j&1))){l++;}
					if(l==n){bo=false;break;}
					g[j]=b[l][0];
					ba[b[l][0]]=true;
					p=b[l][1];
					l++;
				}
			}
			if(bo){
				p=0;
				Bit bit=new Bit(n+1);
				for(int k = n-1;k>=0;k--) {
					p+=(int)bit.Get(g[k]);
					bit.Ud(g[k]+1,1);
				}
				ans=Min(ans,p);
			}
		}
		Console.WriteLine("{0}",ans==int.MaxValue?-1:ans);
	}
}
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 m,int n){
		long a=0,b=0;
		m--;
		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];}
}
public 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();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}