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: Wrong Answer)

use std::io;
use std::collections::VecDeque;

fn main() {
    let mut input = Input::new();
    let n: usize = input.next();
    let mut p: Vec<usize> = vec![0;n];
    let mut a: Vec<i64> = vec![0;n];
    let mut b: Vec<i64> = vec![0;n];
    for i in 0..n {
        p[i] = input.next::<usize>() - 1;
        a[i] = 100000 * (i + 1) as i64;
        b[i] = 100000 * (n - i) as i64;
    }
    for i in 0..n {
        a[p[i]] += i as i64;
        b[p[i]] += i as i64;
    }
    for i in 0..n {
        print!("{} ", a[i]);
    }
    println!("");
    for i in 0..n {
        print!("{} ", b[i]);
    }
    println!("");
}

struct Input {
    queue: VecDeque<String>,
}

impl Input {
    fn new() -> Input {
        Input { queue: VecDeque::new() }
    }

    fn next<T>(&mut self) -> T
        where T: std::str::FromStr,
              T::Err: std::fmt::Debug
    {
        if self.queue.is_empty() {
            let mut line = String::new();
            let _ = io::stdin().read_line(&mut line);
            for x in line.split_whitespace() {
                self.queue.push_back(String::from(x));
            }
        }
        return self.queue.pop_front().unwrap().parse::<T>().unwrap();
    }
}