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.util.Scanner;

public class Main {

    public static void main(String[] args) {
        try (Scanner in = new Scanner(System.in)) {
            solve(in);
        }
    }

    private static void solve(Scanner in) {
        int N = in.nextInt();
        int[] P = new int[N];
        int[] R = new int[N];
        for (int i = 0; i < N; i++) {
            int nextInt = in.nextInt();
            P[i] = nextInt;
            R[nextInt - 1] = i;
        }

        // R < N <= 20,000
        int X = 30000;

        int a[] = new int[N];
        int b[] = new int[N];
        for (int i = 0; i < N; i++) {
            a[i] = (i + 1) * X;
            b[i] = (N - i) * X + R[i];
        }
        for (int ai : a) {
            System.out.print(ai + " ");
        }
        System.out.println();
        for (int bi : b) {
            System.out.print(bi + " ");
        }
        System.out.println();
    }
}