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 <iostream>
#include <vector>

using namespace std;

static const int32_t limit{ 20000 };
int main()
{
	int32_t n;
	cin >> n;

	int32_t p_i;
	vector<int32_t> a(n, 0), b(n, 0);
	for (auto i = 1; i <= n; ++i) {
		cin >> p_i;
		a[i - 1] += limit * i;
		b[i - 1] += limit * (n - i) ;
		b[p_i - 1] += p_i;
	}

	for (auto itr = a.cbegin(); itr != a.cend(); ++itr) cout << *itr << ' ';
	cout << '\n';
	for (auto itr = b.cbegin(); itr != b.cend(); ++itr) cout << *itr << ' ';
	cout << '\n';
}