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>
using namespace std;

int main() {
    int N;
    cin >> N;
    vector<int> p(N);
    for (auto& i : p) cin >> i;
    vector<int> idx(N+1);
    for (int i = 0; i < N; i++) {
        idx[p[i]] = i + 1;
    }


    vector<int> a(N+1), b(N+1);
    int r = p[0];
    for (int r = p[0]+1; r <= N; r++) {
        a[r] = max(a[r-1], -b[r-1]) + 1;
        b[r] = -max(a[r-1], -b[r-1])-1;

        a[r] += idx[r];
    }

    for (int l = p[0]-1; l > 0; l--) {
        a[l] = -max(a[l+1], -b[r+1])-1;
        b[l] = max(a[l+1], -b[r+1])+1;

        b[l] += idx[l];
    }

    int m = max(max(a[N], b[1]), abs(min(a[1], b[N])));

    for (int i = 1; i <= N; i++) {
        cout << a[i] + m + 1;
        if (i == N) cout << endl;
        else cout << " ";
    }
    for (int i = 1; i <= N; i++) {
        cout << b[i] + m + 1;
        if (i == N) cout << endl;
        else cout << " ";
    }

    return 0;
}