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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
const int N=2e4+5;

int n,a[N],b[N],p;

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n;
	for (int i=1;i<=n;i++){
		a[i]=i;
		b[i]=-i;
	}
	for (int i=1;i<=n;i++){
		cin >> p;
		a[p]+=i;
		b[p]=i-a[p];
		for (int j=p+1;j<=n;j++){
			int now=max(a[j-1]+1-a[j],
			b[j]-(b[j-1]-1));
			a[j]+=now;
			b[j]-=now;
		}
	}
	int mn=INT_MAX;
	for (int i=1;i<=n;i++){
		mn=min(mn,a[i]);
	}
	for (int i=1;i<=n;i++){
		cout << a[i]+1-mn << (i==n?"\n":" ");
	}
	mn=INT_MAX;
	for (int i=1;i<=n;i++){
		mn=min(mn,b[i]);
	}
	for (int i=1;i<=n;i++){
		cout << b[i]+1-mn << (i==n?"\n":" ");
	}
}