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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AGC007B {
    class Program {
        static void Main(string[] args) {
            int N = int.Parse(Console.ReadLine());
            int[] input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            int[] rank = new int[N];
            for (int i = 0; i < N; i++) {
                rank[input[i] - 1] = i;
            }
            int[] A = new int[N];
            int[] B = new int[N];
            A[0] = 1;
            B[0] = 1000000000;
            for (int i = 1; i < N; i++) {
                int pre = rank[i - 1];
                int nex = rank[i];
                if (pre < nex) {
                    A[i] = A[i - 1] + 1 + (nex - pre);
                    B[i] = B[i - 1] - 1;
                } else {
                    A[i] = A[i - 1] + 1;
                    B[i] = B[i - 1] - 1 - (pre - nex);
                }
            }
            Console.WriteLine(String.Join(" ", A));
            Console.WriteLine(String.Join(" ", B));
        }
    }
}