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;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		int[]A = new int[N];
		int[]B = new int[N];
		string[] str = Console.ReadLine().Split();
		string[] str2 = Console.ReadLine().Split();
		for(var i=0;i<N;i++){
			A[i] = int.Parse(str[i]);
			B[i] = int.Parse(str2[i]);
		}
		int NA = (int)Math.Pow(2,N);
		int[]P = new int[N];
		P[0] = 1;
		for(var i=1;i<N;i++){
			P[i] = P[i-1] * 2;
		}
		int ans = 99999;
		for(var i=0;i<NA;i++){
			int c1 = 0;
			int c2 = 0;
			int[]C = new int[N];
			int[]C2 = new int[N];
			int[]E = new int[N];
			for(var j=0;j<N;j++){
				int a1 = i/P[j]%2;
				if(a1==1){
					C[j] = B[j];
				} else {
					C[j] = A[j];
				}
				C2[j] = C[j];
				E[j] = a1;
				if(a1==1){
					if(j%2==0){
						c1++;
					} else {
						c2++;
					}
				}
			}
			if(c1!=c2){
				continue;
			}
			Array.Sort(C);
			int[]D = new int[N];
			int ad = 0;
			bool flag0 = true;
			for(var j=0;j<N;j++){
				bool flag = false;
				for(var k=0;k<N;k++){
					if(D[k]==0 && C[j] == C2[k]){
						if(Math.Abs(j-k)%2==E[k]){
							D[k]++;
							ad += Math.Abs(j-k);
							flag = true;
 							break;
						}
					}
				}
				if(!flag){
					flag0 = false;
					break;
				}
			}
			if(flag0){
				ans = Math.Min(ad,ans);
			}
		}
		if(ans==99999){
			Console.WriteLine("-1");
		} else {
			Console.WriteLine(ans/2);
		}
	}
}