Problem: You are given a permutation p of the set {1, 2, ..., N}. Please construct two sequences of positive integers a_1, a_2, ..., a_N and b_1, b_2, ..., b_N satisfying the following conditions:

* 1 \leq a_i, b_i \leq 10^9 for all i
* a_1 < a_2 < ... < a_N
* b_1 > b_2 > ... > b_N
* a_{p_1}+b_{p_1} < a_{p_2}+b_{p_2} < ... < a_{p_N}+b_{p_N}

Constraints

* 2 \leq N \leq 20,000
* p is a permutation of the set {1, 2, ..., N}

Input

The input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

The output consists of two lines. The first line contains a_1, a_2, ..., a_N seperated by a space. The second line contains b_1, b_2, ..., b_N seperated by a space.

It can be shown that there always exists a solution for any input satisfying the constraints.

Examples

Input

2
1 2


Output

1 4
5 4


Input

3
3 2 1


Output

1 2 3
5 3 1


Input

3
2 3 1


Output

5 10 100
100 10 1

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;
import java.util.function.IntBinaryOperator;


public class Main {
    public static void main(String[] args) {
        FastScanner fsc = new FastScanner();
        int n = fsc.nextInt();
        int[] p = new int[n];
        int[] rv = new int[n];
        for (int i = 0; i < n; i++) {
            p[i] = fsc.nextInt() - 1;
            rv[p[i]] = i;
        }
        int d = 490000000 / (n - 1);
        int[] a = new int[n];
        int[] b = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = (n - 1 + i) * d + 1;
            b[i] = (n - 1 - i) * d + 1;
        }
        int min = Const.IINF;
        for (int i = 0; i < n; i++) {
            a[p[i]] += i;
        }
        StringBuilder asb = new StringBuilder();
        StringBuilder bsb = new StringBuilder();
        for (int i = 0; i < n; i++) {
            asb.append(a[i]).append(' ');
            bsb.append(b[i]).append(' ');
        }
        System.out.println(asb);
        System.out.println(bsb);
    }
}


class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    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 *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}


class IntUtil {
    public static int min(int... a) {
        int ret = Const.IINF;
        for (int c : a) ret = Math.min(ret, c);
        return ret;
    }

    public static int max(int... a) {
        int ret = -Const.IINF;
        for (int c : a) ret = Math.max(ret, c);
        return ret;
    }

    /**
     * Caluculate the ceil of a/b. Returns the smallest integer greater than or
     * equal to a/b while 'a/b' rounds fractional parts to ZERO.
     * 
     * @param a
     * @param b
     * @return the smallest integer greater than or equal to a/b
     */
    public static int cld(int a, int b) {
        if (a > 0 && b > 0) return (a + b - 1) / b;
        else if (a < 0 && b < 0) return (a + b + 1) / b;
        else return a / b;
    }

    /**
     * Caluculate the floor of a/b. Returns the largest integer less than or equal
     * to a/b while 'a/b' rounds fractional parts to ZERO.
     * 
     * @param a
     * @param b
     * @return the largest integer less than or equal to a/b
     */
    public static int fld(int a, int b) {
        if (a <= 0 && b > 0) return (a - b + 1) / b;
        else if (a > 0 && b <= 0) return (a - b - 1) / b;
        else return a / b;
    }

    public static int fold(IntBinaryOperator func, int a, int... b) {
        int ret = a;
        for (int c : b) ret = func.applyAsInt(ret, c);
        return ret;
    }
}

class Const {
    public static final long MOD7 = 1_000_000_007;
    public static final long MOD9 = 1_000_000_009;
    public static long MOD = MOD7;

    public static final long LINF = 1_000_000_000_000_000_000l;
    public static final int IINF = 1_000_000_000;

    public static void setMod(long mod) {
        MOD = mod;
    }
}