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.Linq;
using System.Text;
using System.Diagnostics;

namespace AtCoder
{
    class Program
    {
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static int Bubble(List<int> values)
        {
            int N = values.Count;
            int count = 0;
            for (int i = 0; i < N; ++i)
            {
                for (int j = N - 2; j >= 0; --j)
                {
                    if (values[j] > values[j + 1])
                    {
                        var tmp = values[j];
                        values[j] = values[j + 1];
                        values[j + 1] = tmp;
                        ++count;
                    }
                }
            }
            return count;
        }

        static int Search(List<Tuple<int, int, bool>> list, List<int> values, int max, int s, bool[] used)
        {
            int C = values.Count;
            if (C == list.Count / 2) { return Bubble(values); }
            int ans = int.MaxValue;
            for (int i = s; i < list.Count; ++i)
            {
                if (list[i].Item1 >= max && !used[list[i].Item2] && (values.Count % 2 != 0) == list[i].Item3)
                {
                    values.Add(list[i].Item2);
                    used[list[i].Item2] = true;
                    ans = Math.Min(Search(list, values, list[i].Item1, s + 1, used), ans);
                    used[list[i].Item2] = false;
                    values.RemoveAt(C);
                }
            }
            return ans;
        }

        static int Solve(int N, int[] A, int[] B)
        {
            var list = new List<Tuple<int, int, bool>>();
            for (int i = 0; i < N; ++i)
            {
                if (i % 2 == 0)
                {
                    list.Add(Tuple.Create(A[i], i, false));
                    list.Add(Tuple.Create(B[i], i, true));
                }
                else
                {
                    list.Add(Tuple.Create(B[i], i, false));
                    list.Add(Tuple.Create(A[i], i, true));
                }
            }
            list.Sort();
            var ans = Search(list, new List<int>(), 0, 0, new bool[N]);
            return (ans < int.MaxValue) ? ans : -1;
        }

        static void Main(string[] args)
        {
            int N = ReadInt();
            var A = ReadInts();
            var B = ReadInts();
            Console.WriteLine(Solve(N, A, B));
        }
    }
}