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 Rust (1.15.1) (judge verdict: Accepted)

fn main() {
  let n: usize = read();
  let ps: Vec<usize> = read_vec();
  
  let mut seqa: Vec<usize> = vec![];
  let mut seqb: Vec<usize> = vec![];
  let step = 20001;
  
  for d in 0 .. n {
    seqa.push(step * d + ps.iter().position(|&p|p==d+1).unwrap() + 1);
    seqb.push(step * (n - d));
  }
  
  print_vec(&seqa, " ");
  print_vec(&seqb, " ");
}

fn print_vec<T: std::string::ToString>(vec: &Vec<T>, sep: &str) {
  let out = vec.iter().map(|e| e.to_string()).collect::<Vec<_>>().as_slice().join(sep);
  println!("{}", out);
}

fn read<T: std::str::FromStr>() -> T {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  buf.trim().parse::<T>().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  buf.trim().split_whitespace().map(|t| t.parse::<T>().ok().unwrap()).collect()
}