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;

public class CSharp
{
    public static void Main()
    {
        Kyopuro chokudai = new Kyopuro();
        chokudai.AtCoder();
    }
}

public class Kyopuro
{

    int n;
    int[] x, y;

    public void AtCoder()
    {
        string[] input;
        input = Console.ReadLine().Split(' ');
        n = int.Parse(input[0]);
        x = new int[n];
        y = new int[n];
        input = Console.ReadLine().Split(' ');
        for(int i=0; i<n; i++) x[i] = int.Parse(input[i]);
        input = Console.ReadLine().Split(' ');
        for (int i = 0; i < n; i++) y[i] = int.Parse(input[i]);

        int z = (int)Math.Pow(2, n);

        int[] w1 = new int[n];
        int[] w2 = new int[n];
        int[] w3 = new int[n];
        int[] w4 = new int[n];

        int kotae = 99999999;
        int tento;

        for (int i=0; i<z; i++)
        {
            
            int zz = i;
            for(int j=0; j<n; j++)
            {
                if (zz % 2 == 0)
                {
                    w1[j] = x[j];
                    w3[j] = 0;
                    w4[j] = w1[j];
                }
                else
                {
                    w1[j] = y[j];
                    w3[j] = 1;
                    w4[j] = w1[j];
                }
                w2[j] = j + 1;
                zz = zz / 2;
            }
            Array.Sort(w1, w2);
            Array.Sort(w4, w3);
            bool f = true;
            for (int j = 0; j < n; j++)
            {
                if (j%2 == 0)
                {
                    if (w2[j] % 2 == w3[j]) f = false;
                } else
                {
                    if (w2[j] % 2 != w3[j]) f = false;
                }
            }
            if (!f) continue;
            
            tento = Tento(n, w2);
            DebugWL(tento);
            if (tento < kotae) kotae = tento;
            
        }
        if (kotae == 99999999) kotae = -1;
        Console.WriteLine(kotae);
    }
    

    int[] bit;

    int Tento(int n, int[] s)
    {
        bit = new int[n + 1];
        long ans = 0;
        for (int i = 0; i < n; i++)
        {
            ans += i - bitr(s[i]);
            bitp(s[i], 1);
        }
        
        return (int) ans;
    }

    void bitp(int a, int p)
    {
        
        while (a <= n)
        {
            bit[a] += p;
            a += a & -a;
        }
    }

    int bitr(int n)
    {
        
        int a = 0;
        while (n > 0)
        {
            a += bit[n];
            n -= n & -n;
        }
        return a;
    }

    public static void DebugWL(object x) { System.Diagnostics.Debug.WriteLine(x); }

}