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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let n = read::<usize>();
    let p = read_vec::<usize>()
        .iter()
        .map(|&x| x - 1)
        .collect::<Vec<_>>();
    let mut a = (1i64..n as i64 + 1).collect::<Vec<_>>();
    let mut b = a.clone();
    b.reverse();

    let mut sum_along_a = vec![0; n];
    let mut sum_along_b = vec![0; n];

    for (i, pidx) in p.into_iter().enumerate() {
        let adding = (2 * (n - i)) as i64;
        if pidx == 0 {
            sum_along_a[pidx + 1] = adding;
        } else if pidx == n - 1 {
            sum_along_b[pidx - 1] = adding;
        } else {
            sum_along_a[pidx + 1] = adding;
            sum_along_b[pidx - 1] = adding;
        }
    }
    for i in 1..n {
        sum_along_a[i] += sum_along_a[i - 1];
    }
    for i in (0..n - 1).rev() {
        sum_along_b[i] += sum_along_b[i + 1];
    }
    for i in 0..n {
        a[i] += sum_along_a[i];
        b[i] += sum_along_b[i];
    }
    print_array(&a);
    print_array(&b);
    let c = a.iter()
        .zip(b.iter())
        .map(|(&x, &y)| x + y)
        .collect::<Vec<_>>();
    debug!(c);
}

fn print_array<T: std::string::ToString>(array: &Vec<T>) {
    println!(
        "{}",
        array
            .iter()
            .map(|ref x| x.to_string())
            .collect::<Vec<_>>()
            .join(" ")
    );
}

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

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}