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;

namespace Key20D {
    class Program {
        static void Main(string[] args) {
            var n = int.Parse(Console.ReadLine());
            var aArray = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var bArray = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var cards = new List<Card>();
            var search = new List<List<Card>>();
            
            for (var i = 0; i < n; i++) {
                cards.Add(new Card(aArray[i], bArray[i]));
            }

            var i0Max = 0;
            var i0Fail = false;
            foreach (var t in cards) {
                if (i0Max <= t.a) i0Max = t.a;
                else {
                    i0Fail = true;
                    break;
                }
            }

            if (!i0Fail) {
                Console.WriteLine(0);
                return;
            }
            
            search.Add(cards);
            for (var i = 1; i < 9; i++) {
                var nextSearch = new List<List<Card>>();
                foreach (var s in search) {
                    for (var j = 0; j < s.Count - 1; j++) {
                        var list = new List<Card>(s);
                        var tmp = list[j];
                        list[j] = list[j + 1];
                        list[j + 1] = tmp;
                        list[j] = list[j].Flip();
                        list[j + 1] = list[j + 1].Flip();

                        var max = 0;
                        var fail = false;
                        foreach (var t in list) {
                            if (max <= t.a) max = t.a;
                            else {
                                fail = true;
                                break;
                            }
                        }

                        if (fail) {
                            nextSearch.Add(list);
                        } else {
                            Console.WriteLine(i);
                            return;
                        }
                    }
                }
                search.Clear();
                search.AddRange(nextSearch);
            }

            Console.WriteLine(-1);
        }

        struct Card {
            public int a;
            public int b;

            public Card(int a, int b) {
                this.a = a;
                this.b = b;
            }

            public Card Flip() {
               return new Card(b,a);
            }
        }
    }
}