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 {
  static Scanner sc = new Scanner(System.in);

  public static void main(String[] args) {
    int N = sc.nextInt();
    int[] P = new int[N];
    for (int i = 0; i < N; i++) {
      P[i] = sc.nextInt() - 1;
    }
    int[] A = new int[N];
    int[] B = new int[N];
    for (int i = 0; i < N; i++) {
      A[i] = 30000 * (i + 1);
      B[i] = 30000 * (N - i);
    }
    for (int i = 0; i < N; i++) {
      B[P[i]] -= (N - i);
    }
    StringBuilder sb = new StringBuilder();
    for (int i = 0; i < N; i++) {
      if (i != 0) sb.append(" ");
      sb.append(A[i]);
    }
    sb.append("\n");
    for (int i = 0; i < N; i++) {
      if (i != 0) sb.append(" ");
      sb.append(B[i]);
    }
    System.out.println(sb);
  }
}