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>
using namespace std;

int main()
{
    int N;
    cin >> N;
    vector<int> p(N);
    for (int i = 0; i < N; i++)
    {
        cin >> p.at(i);
    }

    vector<int> q(N);
    for (int i = 0; i < N; i++)
    {
        q.at(p.at(i) - 1) = i + 1;
    }

    vector<int> a(N), b(N);
    a.at(0) = 1;
    b.at(0) = q.at(0) - 1;
    for (int i = 1; i < N; i++)
    {
        a.at(i) = max(a.at(i - 1) + 1, q.at(i) - (b.at(i - 1) - 1));
        b.at(i) = q.at(i) - a.at(i);
    }
    int b_mn = b.at(N - 1);
    for (int i = 0; i < N; i++)
    {
        cout << a.at(i) << " ";
    }
    cout << endl;
    for (int i = 0; i < N; i++)
    {
        cout << b.at(i) - b_mn + 1 << " ";
    }
    cout << endl;
    return 0;
}