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.HashMap;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] p = new int[n];
		HashMap<Integer, Integer> hm = new HashMap<Integer, Integer>();
		for(int i=0; i<n; i++){
			p[i] = sc.nextInt();
			hm.put(p[i], i);
		}
		sc.close();
		
		int[] a = new int[n];
		int[] b = new int[n];
		
		for(int i=0; i<n; i++){
			a[i] = 20000 * i + hm.get(i+1) + 1;
			b[i] = 20000 * (n-i) + 1;
		}
		
		StringBuilder sba = new StringBuilder();
		StringBuilder sbb = new StringBuilder();
		
		for(int i=0; i<n; i++){
			sba.append(a[i] + " ");
			sbb.append(b[i] + " ");
		}
		System.out.println(sba.toString());
		System.out.println(sbb.toString());

	}

}