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.io.PrintWriter;
import java.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);

		int N = sc.nextInt();
		int[] p = new int[N];
		for(int i=0; i<N; i++)
			p[i] = sc.nextInt()-1;
		
		int[] ad = new int[N];
		int[] bd = new int[N];
		
		for(int i=0; i<N; i++) {
			ad[p[i]] += i+1;
			if(p[i]<N-1)
				bd[p[i]+1] -= i+1;
		}
		int a=1;
		for(int i=0; i<N; i++) {
			a += ad[i];
			pw.print(a + (i<N-1 ? " " : "\n"));
		}
		int b=1000000000;
		for(int i=0; i<N; i++) {
			b += bd[i];
			pw.print(b + (i<N-1 ? " " : "\n"));
		}
		
		sc.close();
		pw.close();
	}
}