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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.Keyence_2020
{
    class D
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            int[] arrayA = ReadInts();
            int[] arrayB = ReadInts();

            int all = 1 << n;
            int res = int.MaxValue;
            for(int i = 0; i < all; i++)
            {
                bool[] useBlue = new bool[n];
                int[][] vals = new int[n][];
                for (int j = 0; j < n; j++)
                {
                    if (((1 << j) & i) > 0)
                    {
                        useBlue[j] = true;
                    }
                    vals[j] = new int[2] { 0, j };
                    vals[j][0] = useBlue[j] ? arrayB[j] : arrayA[j];
                }
                vals = vals.OrderBy(a => a[0]).ToArray();
                Queue<int[]> que = new Queue<int[]>();
                for (int j = 0; j < n; j++) que.Enqueue(vals[j]);
                bool ok = true;
                int tmp = 0;
                int[][] inValues = new int[n][];
                for(int j = 0; j < n; j++)
                {
                    Queue<int[]> next = new Queue<int[]>();
                    while (que.Count > 0)
                    {
                        int[] val = que.Dequeue();
                        int index = val[1];
                        if (useBlue[index])
                        {
                            if (j % 2 == index % 2)
                            {
                                next.Enqueue(val);
                                continue;
                            }
                        }
                        else
                        {
                            if (j % 2 != index % 2)
                            {
                                next.Enqueue(val);
                                continue;
                            }
                        }
                        inValues[j] = val;
                        for (int k = 0; k < j; k++)
                        {
                            if (inValues[k][1] > index) tmp++;
                        }
                        break;
                    }
                    if (inValues[j] == null
                        || (next.Count > 0 && next.Peek()[0] < inValues[j][0]))
                    {
                        ok = false;
                        break;
                    }
                    while (que.Count > 0)
                    {
                        next.Enqueue(que.Dequeue());
                    }
                    que = next;
                }
                if (ok)
                {
                    res = Min(res, tmp);
                }
            }
            if (res == int.MaxValue) WriteLine(-1);
            else WriteLine(res);
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        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); }
    }
}