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: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var cin = new Scanner2();
			int n = cin.Int();
			int[] a = cin.ArrayInt(n);
			int[] b = cin.ArrayInt(n);

			long ans = long.MaxValue;
			for (int k = 0; k < 1 << n; k++) {
				var qblue = new PriorityQueue<PriorityPair<int, int>>(true);
				var qred = new PriorityQueue<PriorityPair<int, int>>(true);
				for (int i = 0; i < n; i++) {
					if ((k & (1 << i)) != 0) {
						qblue.Enqueue(new PriorityPair<int, int>(b[i], i));
					} else {
						qred.Enqueue(new PriorityPair<int, int>(a[i], i));
					}
				}

				bool ok = true;
				var nums = new List<int>(n);
				while (qblue.Count > 0 || qred.Count > 0) {
					if (qblue.Count > 0 && qred.Count > 0 && qblue.Top.Priority == qred.Top.Priority) {
						int p = qred.Top.Priority;
						var first = new PriorityQueue<int>();
						var second = new PriorityQueue<int>();
						while (qred.Count > 0 && qred.Top.Priority == p) {
							var next = qred.Dequeue();
							if (Math.Abs(nums.Count - next.Item) % 2 == 0) {
								first.Enqueue(next.Item);
							} else {
								second.Enqueue(next.Item);
							}
						}

						while (qblue.Count > 0 && qblue.Top.Priority == p) {
							var next = qblue.Dequeue();
							if (Math.Abs(nums.Count - next.Item) % 2 == 0) {
								second.Enqueue(next.Item);
							} else {
								first.Enqueue(next.Item);
							}
						}

						bool ok2 = true;
						while (first.Count > 0 || second.Count > 0) {
							if (first.Count == 0) {
								ok2 = false;
								break;
							}

							nums.Add(first.Dequeue());

							if (second.Count == 0) {
								if (first.Count > 0) {
									ok2 = false;
									break;
								}
							}

							nums.Add(second.Dequeue());
						}

						if (ok2 == false) {
							ok = false;
							break;
						}
					} else if ((qblue.Count > 0 && qred.Count > 0 && qblue.Top.Priority < qred.Top.Priority)
						|| qred.Count == 0) {
						var next = qblue.Dequeue();
						if (Math.Abs(nums.Count - next.Item) % 2 == 0) {
							ok = false;
							break;
						}

						nums.Add(next.Item);
					} else if ((qblue.Count > 0 && qred.Count > 0 && qblue.Top.Priority > qred.Top.Priority)
						|| qblue.Count == 0) {
						var next = qred.Dequeue();
						if (Math.Abs(nums.Count - next.Item) % 2 != 0) {
							ok = false;
							break;
						}

						nums.Add(next.Item);
					}
				}

				if (ok == false) {
					continue;
				}

				int cnt = 0;
				for (int i = 0; i < n - 1; i++) {
					for (int j = i + 1; j < n; j++) {
						if (nums[j] < nums[i]) {
							++cnt;
						}
					}
				}

				ans = Math.Min(ans, cnt);
			}

			if (ans != long.MaxValue) {
				Console.WriteLine(ans);
			} else {
				Console.WriteLine(-1);
			}
		}
	}

	public class PriorityQueue<T>
	{
		private readonly List<T> heap_;
		private readonly Comparison<T> comparison_;
		private readonly bool reverses_;

		public T Top => heap_[0];
		public int Count => heap_.Count;

		public PriorityQueue(bool reverses = false)
			: this(Comparer<T>.Default, reverses) { }

		public PriorityQueue(int capacity, bool reverses = false)
			: this(capacity, Comparer<T>.Default.Compare, reverses) { }

		public PriorityQueue(IComparer<T> comparer, bool reverses = false)
			: this(16, comparer.Compare, reverses) { }

		public PriorityQueue(Comparison<T> comparison, bool reverses = false)
			: this(16, comparison, reverses) { }

		public PriorityQueue(
			int capacity,
			Comparison<T> comparison,
			bool reverses = false)
		{
			heap_ = new List<T>(capacity);
			comparison_ = comparison;
			reverses_ = reverses;
		}

		public void Enqueue(T item)
		{
			int c = heap_.Count;
			heap_.Add(item);
			while (c > 0) {
				int p = (c - 1) >> 1;
				if (Compare(p, c) < 0) {
					Swap(p, c);
				} else {
					break;
				}

				c = p;
			}
		}

		public T Dequeue()
		{
			T ret = heap_[0];
			int n = heap_.Count - 1;

			heap_[0] = heap_[n];
			heap_.RemoveAt(n);
			for (int p = 0, c; (c = (p << 1) + 1) < n; p = c) {
				if (c != n - 1 && Compare(c + 1, c) > 0) {
					++c;
				}

				if (Compare(p, c) < 0) {
					Swap(p, c);
				} else {
					break;
				}
			}

			return ret;
		}

		public void Clear() => heap_.Clear();

		private int Compare(int x, int y)
			=> comparison_(heap_[x], heap_[y]) * (reverses_ ? -1 : 1);

		private void Swap(int x, int y)
		{
			var t = heap_[x];
			heap_[x] = heap_[y];
			heap_[y] = t;
		}
	}

	public struct PriorityPair<T, U> : IComparable<PriorityPair<T, U>>
			where T : IComparable<T>
	{
		public T Priority { get; set; }
		public U Item { get; set; }

		public PriorityPair(T priority, U item)
		{
			Priority = priority;
			Item = item;
		}

		public int CompareTo(PriorityPair<T, U> target)
			=> Priority.CompareTo(target.Priority);

		public override string ToString()
			=> $"{Priority} {Item}";
	}

	public class Scanner2
	{
		private readonly char[] delimiter_ = new char[] { ' ' };
		private readonly string filePath_;
		private string[] buf_;
		private int index_;
		Func<string> reader_;

		public Scanner2(string file = "")
		{
			if (string.IsNullOrWhiteSpace(file)) {
				reader_ = Console.ReadLine;
			} else {
				filePath_ = file;
				var fs = new StreamReader(file);
				reader_ = fs.ReadLine;
			}
			buf_ = new string[0];
			index_ = 0;
		}

		public string Next()
		{
			if (index_ < buf_.Length) {
				return buf_[index_++];
			}

			string st = reader_();
			while (st == "") {
				st = reader_();
			}

			buf_ = st.Split(delimiter_, StringSplitOptions.RemoveEmptyEntries);
			if (buf_.Length == 0) {
				return Next();
			}

			index_ = 0;
			return buf_[index_++];
		}

		public int Int() => int.Parse(Next());
		public long Long() => long.Parse(Next());
		public double Double() => double.Parse(Next());

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Int() + add;
			}
			return Array;
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Long() + add;
			}
			return Array;
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++) {
				Array[i] = Double() + add;
			}
			return Array;
		}

		public void Save(string text)
		{
			if (string.IsNullOrWhiteSpace(filePath_)) {
				return;
			}

			File.WriteAllText(filePath_ + "_output.txt", text);
		}
	}
}