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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.lang.reflect.Field;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
import static java.lang.Math.max;
import static java.lang.Math.min;

public class Main {
    public static void main(String[] args) throws Exception {
        Field f = System.out.getClass().getDeclaredField("autoFlush");
        f.setAccessible(true);
        f.set(System.out, false);
        execute(System.in, System.out);
    }

    public static void execute(InputStream in, OutputStream out) {
        ExtendedScanner s = new ExtendedScanner(System.in);
        Out o = new Out(System.out);
        solve(s, o);
        o.flush();
        o.close();
    }

    public static void solve(ExtendedScanner sc, Out out) {
        int n = sc.nextInt();
        int[] a = sc.ints(n);
        int[] b = sc.ints(n);
        int[] x = new int[n];
        int inf = 1000000000;
        int min = inf;
        for (int i = 0; i < 1 << n; i++) {
            for (int j = 0; j < n; j++) {
                if ((i & (1 << j)) == 0) {
                    x[j] = a[j];
                } else {
                    x[j] = ~b[j];
                }
            }
            int c = 0;
            for (int p = 0; p < n - 1; p++) {
                for (int q = n - 1; q > p; q--) {
                    if (max(x[q - 1], ~x[q - 1]) > max(x[q], ~x[q])) {
                        swapAndFlip(x, q - 1, q);
                        c++;
                    }
                }
            }
            for (int j = 0; j < n - 1; j++) {
                if (x[j] < 0) {
                    if (x[j + 1] >= 0 && j + 2 < n) {
                        swapAndFlip(x, j + 1, j + 2);
                        c++;
                    }
                    swapAndFlip(x, j, j + 1);
                    c++;
                }
            }
            boolean ok = true;
            for (int j = 0; j < n; j++) {
                if (x[j] < 0) {
                    ok = false;
                }
            }
            for (int j = 0; j < n - 1; j++) {
                if (x[j] > x[j + 1]) {
                    ok = false;
                }
            }
            if (ok) {
                min = min(min, c);
            }
        }
        out.write(min == inf ? -1 : min).write('\n');
    }

    public static void swapAndFlip(int[] x, int i, int j) {
        int tmp = x[i]; x[i] = ~x[j]; x[j] = ~tmp;
    }
}


class BasicScanner {
    private final InputStream in;
    private final byte[] buf = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public BasicScanner(InputStream in) {this.in = in;}
    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try {buflen = in.read(buf);}
        catch (final IOException e) {e.printStackTrace();}
        return buflen > 0;
    }
    private int readByte() {return hasNextByte() ? buf[ptr++] : -1;}
    public boolean hasNext() {
        while (hasNextByte() && !(33 <= buf[ptr] && buf[ptr] <= 126)) ptr++;
        return hasNextByte();
    }
    private StringBuilder nextSequence() {
        if (!hasNext()) throw new NoSuchElementException();
        final StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (33 <= b && b <= 126) {sb.appendCodePoint(b); b = readByte();}
        return sb;
    }
    public char nextChar() {
        return (char) readByte();
    }
    public String next() {
        return nextSequence().toString();
    }
    public String next(int len) {
        return new String(nextChars(len));
    }
    public char[] nextChars() {
        final StringBuilder sb = nextSequence();
        int l = sb.length();
        char[] dst = new char[l];
        sb.getChars(0, l, dst, 0);
        return dst;
    }
    public char[] nextChars(int len) {
        if (!hasNext()) throw new NoSuchElementException();
        char[] s = new char[len];
        int i = 0;
        int b = readByte();
        while (33 <= b && b <= 126 && i < len) {s[i++] = (char) b; b = readByte();}
        if (i != len) throw new NoSuchElementException(String.format("length %d is longer than the sequence.", len));
        return s;
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {minus = true; b = readByte();}
        if (b < '0' || '9' < b) throw new NumberFormatException();
        while (true) {
            if ('0' <= b && b <= '9') n = n * 10 + b - '0';
            else if (b == -1 || !(33 <= b && b <= 126)) return minus ? -n : n;
            else throw new NumberFormatException();
            b = readByte();
        }
    }
    public int nextInt() {return Math.toIntExact(nextLong());}
    public double nextDouble() {return Double.parseDouble(next());}
}


class Out {
    private final OutputStream out;
    private byte[] buf = new byte[1024];
    private int ptr = 0;
    private static final int AUTO_FLUSH_THRETHOLD = 1 << 17;

    public Out(OutputStream out) {
        this.out = out;
    }

    public void flush() {
        try {
            out.write(buf, 0, ptr);
            out.flush();
            ptr = 0;
        } catch (IOException e) {e.printStackTrace();}
    }

    public void close() {
        try {out.close();} catch (IOException e) {e.printStackTrace();}
    }

    public Out write(Object o) {
        return write(o.toString());
    }

    public Out write(String s) {
        try {
            Field strValueField = s.getClass().getDeclaredField("value");
            strValueField.setAccessible(true);
            byte[] b = (byte[]) strValueField.get(s);
            int l = s.length();
            if (l > AUTO_FLUSH_THRETHOLD) {
                flush();
                int i = 0;
                while (i + AUTO_FLUSH_THRETHOLD < l) {
                    out.write(b, i, AUTO_FLUSH_THRETHOLD);
                    out.flush();
                    i += AUTO_FLUSH_THRETHOLD;
                }
                ensureCapacity(l - i);
                System.arraycopy(b, i, buf, 0, l - i);
                ptr = l - i;
            } else {
                ensureCapacity(ptr + l);
                System.arraycopy(b, 0, buf, ptr, l);
                ptr += l;
            }
        } catch (Exception e) {e.printStackTrace();}
        return this;
    }

    public Out write(char[] c) {
        int l = c.length;
        if (l > AUTO_FLUSH_THRETHOLD) {
            flush();
            ensureCapacity(AUTO_FLUSH_THRETHOLD);
            int i = 0;
            while (i + AUTO_FLUSH_THRETHOLD < l) {
                for (int j = 0; j < AUTO_FLUSH_THRETHOLD; j++) {
                    buf[ptr++] = (byte) c[i + j];
                }
                flush();
                i += AUTO_FLUSH_THRETHOLD;
            }
            for (; i < l; i++) {
                buf[ptr++] = (byte) c[i];
            }
        } else {
            ensureCapacity(ptr + l);
            for (char ch : c) buf[ptr++] = (byte) ch;
        }
        return this;
    }

    public Out write(char c) {
        ensureCapacity(ptr + 1);
        buf[ptr++] = (byte) c;
        return this;
    }

    public Out write(byte b) {
        ensureCapacity(ptr + 1);
        buf[ptr++] = b;
        return this;
    }

    public Out write(int x) {
        if (x == 0) {
            ensureCapacity(ptr + 1);
            buf[ptr++] = '0';
            return this;
        }
        int d = stringSize(x);
        ensureCapacity(ptr + d);
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr + d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        ptr += d;
        return this;
    }

    public Out write(long x) {
        if (x == 0) {
            ensureCapacity(ptr + 1);
            buf[ptr++] = '0';
            return this;
        }
        int d = stringSize(x);
        ensureCapacity(ptr + d);
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr + d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        ptr += d;
        return this;
    }

    public Out write(double d) {
        return write(Double.toString(d));
    }

    private void ensureCapacity(int cap) {
        if (cap > AUTO_FLUSH_THRETHOLD) {
            flush();
        }
        if (cap >= buf.length) {
            int newLength = buf.length;
            while (newLength < cap) newLength <<= 1;
            byte[] newBuf = new byte[newLength];
            System.arraycopy(buf, 0, newBuf, 0, buf.length);
            buf = newBuf;
        }
    }
    private static int stringSize(long x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        long p = -10;
        for (int i = 1; i < 19; i++, p *= 10) if (x > p) return i + d;
        return 19 + d;
    }
    private static int stringSize(int x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        int p = -10;
        for (int i = 1; i < 10; i++, p *= 10) if (x > p) return i + d;
        return 10 + d;
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 */
final class ExtendedScanner extends BasicScanner {
    public ExtendedScanner(InputStream in) {super(in);}
    public int[] ints(final int n) {
        final int[] a = new int[n];
        Arrays.setAll(a, $ -> nextInt());
        return a;
    }
    public int[] ints(final int n, final IntUnaryOperator f) {
        final int[] a = new int[n];
        Arrays.setAll(a, $ -> f.applyAsInt(nextInt()));
        return a;
    }
    public int[][] ints(final int n, final int m) {
        final int[][] a = new int[n][];
        Arrays.setAll(a, $ -> ints(m));
        return a;
    }
    public int[][] ints(final int n, final int m, final IntUnaryOperator f) {
        final int[][] a = new int[n][];
        Arrays.setAll(a, $ -> ints(m, f));
        return a;
    }
    public long[] longs(final int n) {
        final long[] a = new long[n];
        Arrays.setAll(a, $ -> nextLong());
        return a;
    }
    public long[] longs(final int n, final LongUnaryOperator f) {
        final long[] a = new long[n];
        Arrays.setAll(a, $ -> f.applyAsLong(nextLong()));
        return a;
    }
    public long[][] longs(final int n, final int m) {
        final long[][] a = new long[n][];
        Arrays.setAll(a, $ -> longs(m));
        return a;
    }
    public long[][] longs(final int n, final int m, final LongUnaryOperator f) {
        final long[][] a = new long[n][];
        Arrays.setAll(a, $ -> longs(m, f));
        return a;
    }
    public char[][] charArrays(final int n) {
        final char[][] c = new char[n][];
        Arrays.setAll(c, $ -> nextChars());
        return c;
    }
    public char[][] charArrays(final int n, final int m) {
        final char[][] c = new char[n][];
        Arrays.setAll(c, $ -> nextChars(m));
        return c;
    }
    public double[] doubles(final int n) {
        final double[] a = new double[n];
        Arrays.setAll(a, $ -> nextDouble());
        return a;
    }
    public double[][] doubles(final int n, final int m) {
        final double[][] a = new double[n][];
        Arrays.setAll(a, $ -> doubles(m));
        return a;
    }
    public String[] strings(final int n) {
        final String[] s = new String[n];
        Arrays.setAll(s, $ -> next());
        return s;
    }
    public String[] strings(final int n, final int m) {
        final String[] s = new String[n];
        Arrays.setAll(s, $ -> next(m));
        return s;
    }
    public boolean[][] grid(final int h, final int w, final char trueCharacter) {
        final boolean[][] grid = new boolean[h][w];
        for (int i = 0; i < h; i++) {
            final char[] s = nextChars(w);
            for (int j = 0; j < w; j++) grid[i][j] = s[j] == trueCharacter;
        }
        return grid;
    }
}