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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Linq;

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

		var m = 1 << 30;
		for (int x = 0; x < (1 << n); x++)
		{
			var bx = new BitArray(new[] { x });
			var c = new (int, bool)[n];
			for (int i = 0; i < n; i++)
				c[i] = (bx[i] ? b[i] : a[i], bx[i]);
			m = Math.Min(m, Swap(c));
		}
		Console.WriteLine(m == 1 << 30 ? -1 : m);

		int Swap((int v, bool rev)[] c)
		{
			var g = Array.ConvertAll(c, _ => _.v);
			Array.Sort(g);
			var u = new bool[n];

			var map = new int[n];
			for (int i = 0; i < n; i++)
			{
				map[i] = -1;
				for (int j = 0; j < n; j++)
				{
					if (u[j] || g[i] != c[j].v || (i - j) % 2 != 0 != c[j].rev) continue;
					u[j] = true;
					map[i] = j;
					break;
				}
				if (map[i] == -1) return 1 << 30;
			}

			var t = 0;
			for (int i = 0; i < n; i++)
				for (int j = i + 1; j < n; j++)
					if (map[i] > map[j]) t++;
			return t;
		}
	}
}