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: Time Limit Exceeded)

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

namespace AGC007 {
    class Program {
        static void Main(string[] args) {
            int n = int.Parse(Console.ReadLine());
            int[] pn = scan;
            int[] an = new int[n];
            int[] bn = new int[n];
            int sum;//最大の組み合わせを1として求め、底上げ作戦。
            for(int i = 0; i < n; i++) {
                an[i] = i+1;
                bn[i] = 0;
            }
            sum = an[pn[0]-1] + bn[pn[0]-1];
            for (int i = 1; i < n; i++) {
                sum++;
                while ((an[pn[i]-1] + bn[pn[i]-1])!= sum) {
                    if((an[pn[i]-1] + bn[pn[i]-1]) > sum) {
                        bn[pn[i]-1]--;
                    }else if((an[pn[i]-1] + bn[pn[i]-1]) < sum) {
                        bn[pn[i]-1]++;
                    }
                }
            }
            //bnの処理
            for(int i = 1; i < n; i++) {
                while (bn[i] >= bn[i - 1]) {
                    an[i]++;
                    bn[i]--;
                }
                while (an[i] <= an[i - 1]) {
                    an[i]++;
                    bn[i]--;
                }
                while (bn[i] >= bn[i - 1]) {
                    an[i]++;
                    bn[i]--;
                }
            }
            var sokoage = Math.Abs(bn[n - 1]) + 1;
            for(int i = 0; i < n; i++) {
                an[i] += sokoage;
                bn[i] += sokoage;
            }
            for(int i = 0; i < n; i++) {
                Console.Write(an[i] + " ");
            }
            Console.WriteLine();
            for(int i = 0; i < n; i++) {
                Console.Write(bn[i] + " ");
            }
            Console.WriteLine();


        }
        static int[] scan {
            get {
                return Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            }
        }
    }
}