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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author AnandOza
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DSwapAndFlip solver = new DSwapAndFlip();
        solver.solve(1, in, out);
        out.close();
    }

    static class DSwapAndFlip {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = in.readIntArray(n);
            int[] b = in.readIntArray(n);

            int answer = Integer.MAX_VALUE;
            for (int flips = 0; flips < (1 << n); flips++) {
                int[] x = new int[n];
                int[] flip = new int[n];
                for (int i = 0; i < n; i++) {
                    flip[i] = ((flips >> i) & 1);
                    x[i] = flip[i] == 0 ? a[i] : b[i];
                }
                int f = f(x, flip);
                answer = Math.min(answer, f);
            }

            if (answer == Integer.MAX_VALUE)
                answer = -1;

            out.println(answer);
        }

        private static int f(int[] x, int[] flip) {
            final int n = x.length;
            int[] inv = new int[n];
            for (int i = 0; i < n; i++) {
                for (int j = i + 1; j < n; j++) {
                    if (x[i] > x[j]) {
                        inv[i]++;
                        inv[j]++;
                    }
                }
            }

            int answer = 0;

            for (int i = 0; i < n; i++) {
                answer += inv[i];

                if (inv[i] % 2 != flip[i]) {
                    inv[i] = 1;
                } else {
                    inv[i] = 0;
                }
            }

            int[] count = new int[51];
            for (int i = 0; i < n; i++) {
                count[x[i]] += inv[i];
            }
            for (int c : count) {
                if (c % 2 == 0)
                    answer += c;
                else
                    return Integer.MAX_VALUE;
            }

            answer /= 2;

            return answer;
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public int[] readIntArray(int n) {
            int[] x = new int[n];
            for (int i = 0; i < n; i++) {
                x[i] = nextInt();
            }
            return x;
        }

    }
}