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: Wrong Answer)

using System;
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 p2 = Enumerable.Range(0, n + 1).Select(i => 1 << i).ToArray();
		var m = 1 << 30;

		for (int x = 0; x < p2[n]; x++)
		{
			var c = new (int i, int v, bool rev)[n];
			for (int i = 0; i < n; i++)
				c[i] = (x & p2[i]) == 0 ? (i, a[i], false) : (i, b[i], true);

			var t = 0;
			for (int i = 0; i < n; i++)
				for (int j = i + 1; j < n; j++)
				{
					if (c[j - 1].v <= c[j].v) continue;
					(c[j], c[j - 1]) = (c[j - 1], c[j]);
					t++;
				}

			var ok = true;
			for (int i = 0; i < n; i++)
			{
				if ((i - c[i].i) % 2 != 0 == c[i].rev) continue;
				if (i + 1 == n || c[i].v < c[i + 1].v) { ok = false; break; }

				// 同じ数が続く場合
				for (int j = i + 1; j < n; j++)
				{
					if (c[i].v < c[j].v) break;
					if ((i - c[j].i) % 2 != 0 != c[i].rev) continue;

					// c[j] を c[i] に移動
					for (int k = j; k > i; k--)
					{
						(c[k], c[k - 1]) = (c[k - 1], c[k]);
						t++;
					}
					break;
				}
				if ((i - c[i].i) % 2 != 0 != c[i].rev) { ok = false; break; }
			}
			if (ok) m = Math.Min(m, t);
		}
		Console.WriteLine(m == 1 << 30 ? -1 : m);
	}
}