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[] az = new int[n];
    int[] bz = new int[n];
    for(int i = 0; i < n; i++) {
      int p = sc.nextInt() - 1;
      az[p] += i;
      bz[0] += i;
      if(p < n - 1) bz[p + 1] -= i;
    }
    for(int i = 1; i < n; i++) {
      az[i] += az[i - 1];
      bz[i] += bz[i - 1]; 
    }
    for(int i = 0; i < n; i++) {
      System.out.print((i + 1) + az[i]);
      if(i < n - 1) System.out.print(" ");
    }
    System.out.println();
    for(int i = 0; i < n; i++) {
      System.out.print((n - i) + bz[i]);
      if(i < n - 1) System.out.print(" ");
    }
    System.out.println();
  }
}