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.IO;
using System.Threading;

using Pair = System.Collections.Generic.KeyValuePair<int, int>;

class Program
{
	public Program() { }

	static void Main(string[] args)
	{
		new Program().prog();
	}
	Scanner cin;
	const int MOD = 1000000007;
	const int INF = int.MaxValue - 10;
	const long INFL = long.MaxValue - 10;
	const double EPS = 1e-7;
	const double PI = 3.1415926536;

	int N;
	void prog()
	{
		cin = new Scanner();
		int[,] dir8 = new int[8, 2] { { -1, -1 }, { -1, 0 }, { -1, 1 }, { 0, -1 }, { 0, 1 }, { 1, -1 }, { 1, 0 }, { 1, 1 } };
		int[,] dir4 = new int[4, 2] { { -1, 0 }, { 0, -1 }, { 0, 1 }, { 1, 0 } };

		int N = cin.nextInt();
		int[] p = new int[N];
		long[] pa = new long[N];
		long[] pb = new long[N];
		long[] A = new long[N];
		long[] B = new long[N];
		long amin = INFL, bmin = INFL;
		for (int i = 0; i < N; i++)
		{
			p[i] = cin.nextInt() - 1;
			A[i] = i + 1;
			B[i] = N - i;
		}
		for (int i = 0; i < N; i++)
		{
			pa[p[i]] = pb[p[i]] = i;
		}
		for (int i = 1; i < N; i++)
		{
			pa[i] += pa[i - 1];
			pb[N - 1 - i] += pb[N - i];
		}
		for (int i = 0; i < N; i++)
		{
			A[i] += pa[i];
			B[i] += pb[i];
			amin = Math.Min(amin, A[i]);
			bmin = Math.Min(bmin, B[i]);
		}
		for (int i = 0; i < N; i++)
		{
			if (i < N - 1)
			{
				Console.Write("{0} ", A[i] - amin + 1);
			}
			else
			{
				Console.WriteLine(A[i] - amin + 1);
			}
		}
		for (int i = 0; i < N; i++)
		{
			if (i < N - 1)
			{
				Console.Write("{0} ", B[i] - bmin + 1);
			}
			else
			{
				Console.WriteLine(B[i] - bmin + 1);
			}
		}
	}
}

class Scanner
{
	string[] s;
	int i;

	char[] cs = new char[] { ' ' };

	public Scanner()
	{
		s = new string[0];
		i = 0;
	}

	public string next()
	{
		if (i < s.Length) return s[i++];
		string st = Console.ReadLine();
		while (st == "") st = Console.ReadLine();
		s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
		i = 0;
		return next();
	}

	public int nextInt()
	{
		return int.Parse(next());
	}

	public long nextLong()
	{
		return long.Parse(next());
	}

	public double nextDouble()
	{
		return double.Parse(next());
	}
}