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 CPP):

Solution:
#include <iostream>
#include <algorithm>
using namespace std;

int main(){
  int n; cin >> n;
  int p[n+1], a[n+1], b[n+1];
  for(int i=1; i<=n; i++){
    cin >> p[i];
    a[i] = i*n;
    b[i] = n*(n-i+1);
  }
  
  for(int i=1; i<=n; i++){
    b[p[i]] += i-1;
  }

  for(int i=1; i<=n; i++) 
    cout << a[i] << " ";
  cout << endl;

  for(int i=1; i<=n; i++)
    cout << b[i] << " ";
  cout << endl;

  return 0;
}