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) {
		Scanner s = new Scanner(System.in);
		solve(s);
		s.close();
	}

	public static void solve(Scanner sc) {
		int n = sc.nextInt();
		int[] p = new int[n];

		for (int i = 0; i < n; i++) {
			p[i] = sc.nextInt();
		}

		int[] a = new int[n];
		int[] b = new int[n];

		for (int i = 0; i < n; i++) {
			a[i] = i * n + 1;
			b[n - i - 1] = i * n + 1;
		}

		for (int i = 0; i < n; i++) {
			a[p[i] - 1] += i;
		}

		show(a);
		show(b);
	}

	private static void show(int[] a) {
		for (int i : a) {
			System.out.print(i + " ");
		}
		System.out.println();
	}
}