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 (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());

    // a0 < a1
    // b0 > b1
    // a0+b0 > a1+b1
    //b0-b1 > a1-a0
    let n: usize = sc.read();
    let mut p = vec![];
    for _ in 0..n {
        p.push(sc.read::<usize>() - 1);
    }

    let cc = 30000;
    let mut a = vec![0; n];
    for i in 0..n {
        a[i] = (1 + cc * i) as i64;
    }
    let mut b = vec![0i64; n];
    for i in 1..n {
        let (p, q) = (p[i - 1], p[i]);
        if p < q {
            // ap < aq
            // bp > bq
            // ap+bp < aq+bq
            // bp-bq < aq-ap
            //            eprintln!("b[{p}]-b[{q}] < a[{q}]-a[{p}]", p = p, q = q);
            b[q] = b[p] - (a[q] - a[p] - 1);
        } else {
            let (p, q) = (q, p);
            // ap < aq
            // bp > bq
            // ap+bp > aq+bq
            // bp-bq > aq-ap
            //            eprintln!("b[{p}]-b[{q}] > a[{q}]-a[{p}]", p = p, q = q);
            b[p] = b[q] + a[q] - a[p] + 1;
        }
    }

    let min_b = *b.iter().min().unwrap();
    for i in 0..n {
        b[i] += 1 - min_b;
    }

    for i in 0..n {
        if i > 0 {
            sc.write(" ");
        }
        sc.write(format!("{}", a[i]));
    }
    sc.write("\n");
    for i in 0..n {
        if i > 0 {
            sc.write(" ");
        }
        sc.write(format!("{}", b[i]));
    }
    sc.write("\n");
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> IO<R, W> {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: std::ops::Deref<Target = str>>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}