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 = new BinaryIndexedTree(N);
            var b = new BinaryIndexedTree(N);
            a.Add(1, 1);
            b.Add(1, 1000000000);
            for (int i = 2; i <= N; i++)
            {
                a.Add(i, 1);
                b.Add(i, -1);
            }
            for (int i = 1; i < P.Length; i++)
            {
                a.Add(P[i], 1);
            }
            Console.WriteLine(string.Join(" ", Enumerable.Range(0, N).Select(i => a.Sum(i + 1))));
            Console.WriteLine(string.Join(" ", Enumerable.Range(0, N).Select(i => b.Sum(i + 1))));
        }

        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);
            }
        }

        public class BinaryIndexedTree
        {
            private readonly int Max;
            private readonly int Mod;
            private readonly int[] a;

            public BinaryIndexedTree(int max, int mod = int.MaxValue)
            {
                Max = max;
                Mod = mod;
                a = new int[Max + 1];
            }
            public void Add(int i, int val)
            {
                if (i <= 0) { throw new ArgumentOutOfRangeException("i"); }
                while (i <= Max)
                {
                    a[i] = (a[i] + val) % Mod;
                    i += i & -i;
                }
            }
            public int Sum(int i)
            {
                int s = 0;
                while (i > 0)
                {
                    s = (s + a[i]) % Mod;
                    i -= i & -i;
                }
                return s;
            }
        }
    }
}