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 <bits/stdc++.h>
using namespace std;
const int N=20003;

  int n;
  int a[N],b[N];
int main()
{
  cin>>n;
  for (int i=0;++i<=n;)
    a[i]=a[i-1]+N,
		b[i]=N*N;
  for (int i=0;++i<=n;)
    {
      int x;
      cin>>x;
      b[x]-=n-i+1+a[x];
    }
  for (int i=0;++i<=n;)
    printf("%d ",a[i]);
  puts("");
  for (int i=0;++i<=n;)
    printf("%d ",b[i]);
  exit(0);
}