Problem: 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.

Examples

Input

3
3 4 3
3 2 3


Output

1


Input

2
2 1
1 2


Output

-1


Input

4
1 2 3 4
5 6 7 8


Output

0


Input

5
28 15 22 43 31
20 22 43 33 32


Output

-1


Input

5
4 46 6 38 43
33 15 18 27 37


Output

3

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.Reader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInput in = new MyInput(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, MyInput in, PrintWriter out) {
            int n = in.nextInt();
            int[][] ab = new int[n][2];
            for (int i = 0; i < n; i++) {
                ab[i][0] = in.nextInt();
            }
            for (int i = 0; i < n; i++) {
                ab[i][1] = in.nextInt();
            }

            int ans = Integer.MAX_VALUE;
            int[] val = new int[n];
            for (int i = 0; i < 1 << n; i++) {
                if (Integer.bitCount(i) % 2 == 1) continue;
                for (int j = 0; j < n; j++) {
                    val[j] = ab[j][i >>> j & 1];
                }
                int[] tmp = val.clone();
                Arrays.sort(val);

                int cnt = 0;
                int[] cur = new int[n];
                for (int j = 0; j < n; j++) cur[j] = j;
                for (int j = 0; j < n; j++) {
                    int idx = -1;
                    for (int k = j; k < n; k++) {
                        if (tmp[cur[k]] == val[j]) {
                            if (((i >>> cur[k] & 1) == 0) == (cur[k] % 2 == j % 2)) {
                                idx = k;
                                break;
                            }
                        }
                    }
                    if (idx >= 0) {
                        cnt += move(cur, idx, j);
                    } else {
                        cnt = Integer.MAX_VALUE;
                        break;
                    }
                }
//            if (cnt != Integer.MAX_VALUE) {
//                dump(i, Arrays.copyOf(val[0], len[0]), Arrays.copyOf(val[1], len[1]), cur);
//            }
                ans = Math.min(ans, cnt);
            }
            if (ans == Integer.MAX_VALUE) ans = -1;
            out.println(ans);
        }

        int move(int[] cur, int p, int i) {
            int res = 0;
            while (p > i) {
                res++;
                swap(cur, p, p - 1);
                p--;
            }
            return res;
        }

        static void swap(int[] xs, int i, int j) {
            int t = xs[i];
            xs[i] = xs[j];
            xs[j] = t;
        }

    }

    static class MyInput {
        private final BufferedReader in;
        private static int pos;
        private static int readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500 * 8 * 2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];

        static {
            for (int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
            isLineSep['\r'] = isLineSep['\n'] = true;
        }

        public MyInput(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
        }

        public int read() {
            if (pos >= readLen) {
                pos = 0;
                try {
                    readLen = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (readLen <= 0) {
                    throw new MyInput.EndOfFileRuntimeException();
                }
            }
            return buffer[pos++];
        }

        public int nextInt() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            int ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++) ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public char nextChar() {
            while (true) {
                final int c = read();
                if (!isSpace[c]) {
                    return (char) c;
                }
            }
        }

        int reads(int len, boolean[] accept) {
            try {
                while (true) {
                    final int c = read();
                    if (accept[c]) {
                        break;
                    }
                    if (str.length == len) {
                        char[] rep = new char[str.length * 3 / 2];
                        System.arraycopy(str, 0, rep, 0, str.length);
                        str = rep;
                    }
                    str[len++] = (char) c;
                }
            } catch (MyInput.EndOfFileRuntimeException e) {
            }
            return len;
        }

        static class EndOfFileRuntimeException extends RuntimeException {
        }

    }
}