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 sc=new Scanner(System.in);
		int n = sc.nextInt();
		long[] a=new long[n];
		long[] b = new long[n];
		int[] p=new int[n];
		a[0]=1;
		b[n-1]=1;
		for(int i =0; i<n; i++){
			int p1 = sc.nextInt()-1;
			p[i]=p1;
			if(i>0){
				a[i]=a[i-1]+20000;
				b[n-1-i]=b[n-i]+20000;
			}
		}
		for(int i=0; i<n; i++){
			a[p[i]]+=i;
		}
		for(int i =0; i<n; i++){
			System.out.print(a[i]+" ");
		}
		System.out.println();
		for(int i =0; i<n; i++){
			System.out.print(b[i]+" ");
		}
	}
}