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: Accepted)

using System;
using System.Linq;

static class D
{
    static void Main()
    {
        int n = Int32.Parse(Console.ReadLine());
        int[] a = Console.ReadLine().Split().Select(Int32.Parse).ToArray();
        int[] b = Console.ReadLine().Split().Select(Int32.Parse).ToArray();

        var x = new int[n];
        var y = new int[n];

        int ans = -1;

        for (int bits = 0; bits < (1 << n); bits++)
        {
            for (int i = 0; i < n; i++)
            {
                int bit = (bits >> i) & 1;
                int x_i = (bit == 0) ? a[i] : b[i];
                x[i] = x_i;
            }

            Array.Sort(x);

            for (int i = 0; i < n; i++)
            {
                int bit = (bits >> i) & 1;
                int x_i = (bit == 0) ? a[i] : b[i];

                y[i] = -1;

                for (int j = 0; j < n; j++)
                {
                    if (x[j] == x_i && Math.Abs(j - i) % 2 == bit)
                    {
                        x[j] = 0;
                        y[i] = j;
                        break;
                    }
                }
                if (y[i] == -1) goto fail;
            }

            int flips = 0;

            for (int i = 0; i < n; i++)
            for (int j = 0; j < i; j++)
            {
                if (y[j] > y[i]) ++flips;
            }

            if (ans == -1 || ans > flips)
                ans = flips;
        fail: ;
        }

        Console.WriteLine(ans);
    }
}