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;
typedef long long ll;

const int MAX_N = 20002;
int N;

int P[MAX_N];

ll A[MAX_N];
ll B[MAX_N];
ll C[MAX_N];

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    cin >> N;

    for (int i = 0; i < N; ++i) {
        cin >> P[i];
        P[i]--;

        C[P[i]] = i+1;
    }

    A[0] = C[0];
    B[0] = 0;

    for (int i = 1; i < N; ++i) {
        A[i] = A[i-1] + C[i];
        B[i] = -A[i-1]; 
    }

    for (int i = 0; i < N; ++i) {
        B[i] += (-B[N-1] + 1);
    }

    //for (int i = 0; i < N; ++i) {
    //    A[i] = 20000 * i + 1;
    //    B[i] = 20000 * (N - 1 - i) + 1;
    //}

    //for (int i = 0; i < N; ++i) {
    //    B[P[i]] += i;
    //}

    //for (int i = 0; i < N; ++i) {
    //    cout << B[i];
    //    if (i != N-1) {
    //        cout << " ";
    //    }
    //}
    //cout << endl;



    for (int i = 0; i < N; ++i) {
        cout << A[i];
        if (i != N-1) {
            cout << " ";
        }
    }
    cout << endl;

    for (int i = 0; i < N; ++i) {
        cout << B[i];
        if (i != N-1) {
            cout << " ";
        }
    }
    cout << endl;

    return 0;
}