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

#include <bits/stdc++.h>
#define INF 100000000000
#define ll long long
#define pll pair<ll, ll>
using namespace std;

int main()
{
  ll N;
  cin >> N;
  vector<ll> p(N);
  for (ll i = 0; i < N; ++i) {
    cin >> p.at(i);
  }
  vector<ll> a(N);
  vector<ll> b(N);
  for (ll i = 0; i < N; ++i) {
    a.at(i) = i + 1;
  }
  ll temp = 1;
  for (ll i = N - 1; i >= 0; --i) {
    b.at(i) = temp;
    temp += 2;
  }
  vector<pll> ans(N);
  for (ll i = 0; i < N; ++i) {
    ans.at(p.at(i) - 1) = {a.at(N - i - 1), b.at(N - i - 1)};
  }
  for (ll i = 0; i < N; ++i) {
    cout << ans.at(i).first << ' ';
  }
  cout << endl;
  for (ll i = 0; i < N; ++i) {
    cout << ans.at(i).second << ' ';
  }
  cout << endl;
  // for (ll i = 0; i < N; ++i) {
  //   cout << a.at(i) << ' ';
  // }
  // cout << endl;
  // for (ll i = 0; i < N; ++i) {
  //   cout << b.at(i) << ' ';
  // }
}