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: Wrong Answer)

using System;
using System.Collections.Generic;

namespace test
{
	class MainClass
	{
		static int max = 10000000;

		public static void Main(string[] args)
		{
			int N = int.Parse(Console.ReadLine());
			string[] sar = Console.ReadLine().Split(' ');
			int[] p = new int[sar.Length + 2];
			p[0] = 0;
			p[N + 1] = N + 1;
			for (int i = 1; i < sar.Length + 1; i++)
			{
				p[i] = int.Parse(sar[i - 1]);
			}
			int[] a = new int[N + 2];
			a[0] = 0;
			a[N + 1] = max;
			int[] b = new int[N + 2];
			b[0] = max;
			b[N + 1] = 0;
			List<int> list = new List<int>();
			list.Add(p[0]);
			list.Add(p[N + 1]);
			for (int i = 1; i < N + 1; i++)
			{
				list.Sort();
				for (int j = 0; j < list.Count; j++)
				{
					if (list[j] < p[i] && p[i] < list[j + 1])
					{
						a[p[i]] = (a[list[j]] + a[list[j + 1]]) / 2 + i;
						b[p[i]] = (b[list[j]] + b[list[j + 1]]) / 2 - i;
						list.Add(p[i]);
						break;
					}
					Console.WriteLine(list.Count);
						
				}
			}
			for (int i = 0; i < N; i++)
			{
				Console.Write(a[i + 1]);
				Console.Write(i == N - 1 ? "\n" : " ");
			}
			for (int i = 0; i < N; i++)
			{
				Console.Write(b[i + 1]);
				Console.Write(i == N - 1 ? "\n" : " ");
			}
		}
	}
}