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[] arrA = new int[n + 1];
		int[] arrB = new int[n + 1];
		for (int i = 1; i <= n; i++) {
		    int x = sc.nextInt();
		    arrA[x] = i;
		    arrB[x] = i;
		}
		for (int i = 1; i < n; i++) {
		    arrA[i + 1] += arrA[i];
		    arrB[n - i] += arrB[n - i + 1];
		}
		StringBuilder sbA = new StringBuilder();
		StringBuilder sbB = new StringBuilder();
		for (int i = 1; i <= n; i++) {
		    if (i != 1) {
		        sbA.append(" ");
		        sbB.append(" ");
		    }
		    sbA.append(arrA[i]);
		    sbB.append(arrB[i]);
		}
		System.out.println(sbA);
		System.out.println(sbB);
   }
}