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;
using System.Linq;
using System.Text;

namespace AGC007
{
    public class B
    {
        private void Run()
        {
            var N = int.Parse(Console.ReadLine().Trim());
            var P = Console.ReadLine().Trim().Split().Select(int.Parse).ToArray();

            var A = Enumerable.Repeat(1, N).ToArray();
            var B = Enumerable.Repeat(1000000000, N).ToArray();

            var dict = P.Select((v, i) => new { v, i }).ToDictionary(x => x.v, x => x.i);
            int sum = 0;
            for (int i = 0; i < P.Length; i++)
            {
                sum += dict[P[i]];
                A[P[i] - 1] += i + sum;
                B[P[i] - 1] -= i;
            }
            Console.WriteLine(string.Join(" ", A));
            Console.WriteLine(string.Join(" ", B));
        }

        public static void Main()
        {
            var old = Console.Out;
            using (var writer = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false })
            {
                Console.SetOut(writer);
                new B().Run();
                Console.Out.Flush();
                Console.SetOut(old);
            }
        }
    }
}