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: Accepted)

#include <bits/stdc++.h>

#define rep(i, a, b) for (int i = int(a); i < int(b); i++)
#define rrep(i, a, b) for (int i = int(a) - 1; i >= b; i--)
#define sz(x) (int)(x).size()

using namespace std;
using ll = long long;

const ll INF = 1e18;
const ll MOD = 1e9 + 7;

int main() {
  ll n;
  cin >> n;
  vector<ll> p(n);
  rep(i, 0, n) cin >> p[i];

  vector<ll> a(n, 0), b(n, 0);
  ll m = n + 10000;
  rep(i, 0, n) a[i] += (i * m);
  rep(i, 0, n) b[i] = a[n - i - 1] + 1;
  rep(i, 0, n) a[p[i] - 1] += i + 1;

  rep(i, 0, n) cout << a[i] << " ";
  cout << endl;
  rep(i, 0, n) cout << b[i] << " ";
  cout << endl;
}