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.*;
import java.util.stream.*;

class Main{
	public static void main(String[] $){
		Scanner s=new Scanner(System.in);
		
		int n=s.nextInt();
		int[]v=new int[n];
		int[]a=new int[n];
		int[]b=new int[n];
		Arrays.setAll(v,i->s.nextInt()-1);
		Arrays.setAll(a,i->i+1);
		Arrays.setAll(b,i->n-i);
		
		for(int i=1;i<n;++i) {
			for(int j=v[i];j<n;++j)
				a[j]+=i;
			for(int j=v[i];j>=0;--j)
				b[j]+=i;
		}
		
		System.out.println(Arrays.stream(a).mapToObj(String::valueOf).collect(Collectors.joining(" ")));
		System.out.println(Arrays.stream(b).mapToObj(String::valueOf).collect(Collectors.joining(" ")));
	}
}