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();
		int[] p = new int[n];
		int[] a = new int[n];
		int[] b = new int[n];



		for (int i = 0; i < n; i++) {

			p[i] = sc.nextInt();
			a[i] = i + 1;
			b[i] = n - i;

		}




		for (int i = 0; i < n; i++){
			for (int j = 0; j < n; j++){

				if (j > p[i] - 1) {
					a[j] = a[j]  + (n - i);


				}


				if (j < p[i] - 1) {

					b[j] = b[j] + (n - i);
				}



			}
		}

	for (int i = 0; i < n; i++) {
		if (i != 0) System.out.print(" ");
		System.out.print(a[i]);


	}

	System.out.println("");
	for (int i = 0; i < n; i++) {
		if (i != 0) System.out.print(" ");
		System.out.print(b[i]);

	}
	System.out.println("");

		sc.close();
	}


}