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.*;
public class Main {
	public static void main(String[] args) {
		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() - 1;
		}
		
		int r[] = new int[N];
		for (int i = 0; i < N; i++) {
			r[p[i]] = i + 1;
		}
		
		long a[] = new long[N];
		long b[] = new long[N];
		// 初期値の設定
		for (int i = 0; i < N; i++) {
			a[i] = (N + 1) * (i + 1);
			b[i] = (N + 1) * (N - i - 1) + r[i]; 
		}
		
		// 出力
		for (long n : a) {
			System.out.print(n + " ");
		}
		System.out.println("");
		for (long n : b) {
			System.out.print(n + " ");
		}
		
		sc.close();
	}
}