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) {
		new Main().solve();
	}
	void solve(){
		Scanner sc=new Scanner(System.in);
		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+1;
			b[i]=n-i;
		}
		for(int i=0;i<n;i++){
			for(int j=p[i];j<=n;j++){
				a[j-1]+=i;
			}
			for(int j=1;j<=p[i];j++){
				b[j-1]+=i;
			}
		}
		
		for(int i=0;i<n-1;i++){
			System.out.print(a[i]+" ");
		}
		System.out.println(a[n-1]);
		for(int i=0;i<n-1;i++){
			System.out.print(b[i]+" ");
		}
		System.out.println(b[n-1]);
	}
	
}