Problem:
Score : 400 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

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.

Sample Input 1

2
1 2

Sample Output 1

1 4
5 4

a_1 + b_1 = 6 and a_2 + b_2 = 8. So this output satisfies all conditions.

Sample Input 2

3
3 2 1

Sample Output 2

1 2 3
5 3 1

Sample Input 3

3
2 3 1

Sample Output 3

5 10 100
100 10 1

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.math.*;

public class Main {
  private static final int BASE = 30000;
  private static final int MAX_N = 20000;

  public static void main(String[] args) {
    Scanner s = new Scanner(System.in);
    int n = s.nextInt();
    int[] p = new int[n];
    for (int i = 0; i < n; i++) {
      p[i] = s.nextInt();
    }
    int[] a = new int[n];
    int[] b = new int[n];
    for (int i = 0; i < n; i++) {
      a[i] = 1 + BASE * i;
      b[i] = BASE * (n - i);
    }
    for (int i = 0; i < n; i++) {
      a[p[i]-1] += i;
    }

    System.out.print(a[0]);
    for (int i = 1; i < n; i++) {
      System.out.print(" ");
      System.out.print(a[i]);
    }
    System.out.println();

    System.out.print(b[0]);
    for (int i = 1; i < n; i++) {
      System.out.print(" ");
      System.out.print(b[i]);
    }
    System.out.println();
  }
}