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;
class Program{
	static void Main(){
		int n=int.Parse(Console.ReadLine());
		int[] p=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
		int[] a=new int[n],b=new int[n];
		for(int i=0;i<n;i++){b[p[i]-1]=(i+1)*1;}
		a[0]=1;
		b[0]--;
		int m=0;
		for(int i=1;i<n;i++){
			a[i]=a[i-1]+1;
			b[i]-=a[i-1]+1;
			if(b[i]>=b[i-1]){
				a[i]+=b[i]-b[i-1]+1;
				b[i]=b[i-1]-1;
			}
			m=Math.Min(m,b[i]);
		}
		for(int i=0;i<n;i++){b[i]-=m-1;}
		Console.WriteLine(String.Join(" ",a));
		Console.WriteLine(String.Join(" ",b));
	}
}