Problem:
Score : 400 points

Problem Statement

#nck {
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}

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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>

using namespace std;

#define debug(x) cout << #x << "==" << x << endl;

const int inf = 100000000;

const int dif = 30000;

typedef long long ll;

int main() {
  ios::sync_with_stdio(false);

  int N;
  cin >> N;

  vector<int> p(N);
  for(int i = 0; i < N; i++) { cin >> p[i]; }

  vector<int> a(N);
  vector<int> b(N);
  for(int i = 0; i < N; i++) {
    a[i] = dif * i + 1;
    b[N-i-1] = dif * i + 1;
  }

  for(int i = 0; i < N; i++) {
    a[i] += p[i];
  }

  for(int i = 0; i < N; i++) {
    cout << a[i] << " ";
  }
  cout << "\n";
  for(int i = 0; i < N; i++) {
    cout << b[i] << " ";
  }
  cout << "\n";
  return 0;
}