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.*;

public class Main {
    public void main(Scanner sc) {
        int n = sc.nextInt();
        int a[] = new int[n];
        int b[] = new int[n];

        int p[] = new int[n];
        for (int i = 0; i < n; i++) {
            p[sc.nextInt() - 1] = i + 1;
            a[i] = i * n + 1;
        }

        b[n - 1] = 1;
        for (int i = n - 2; i >= 0; i--) {
            b[i] = b[i + 1] + n + p[i] - p[i + 1];
        }

        System.out.println(Arrays.toString(a).replaceAll("[^0-9 ]", ""));
        System.out.println(Arrays.toString(b).replaceAll("[^0-9 ]", ""));
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        new Main().main(sc);
        sc.close();
    }
}