Problem:
Score : 400 points

Problem Statement

Snuke has an empty sequence a.

He will perform N operations on this sequence.

In the i-th operation, he chooses an integer j satisfying 1 \leq j \leq i, and insert j at position j in a (the beginning is position 1).

You are given a sequence b of length N. Determine if it is possible that a is equal to b after N operations. If it is, show one possible sequence of operations that achieves it.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq b_i \leq N

Input

Input is given from Standard Input in the following format:

N
b_1 \dots b_N

Output

If there is no sequence of N operations after which a would be equal to b, print -1.
If there is, print N lines. In the i-th line, the integer chosen in the i-th operation should be printed. If there are multiple solutions, any of them is accepted.

Sample Input 1

3
1 2 1

Sample Output 1

1
1
2

In this sequence of operations, the sequence a changes as follows:

After the first operation: (1)

After the second operation: (1,1)

After the third operation: (1,2,1)

Sample Input 2

2
2 2

Sample Output 2

-1

2 cannot be inserted at the beginning of the sequence, so this is impossible.

Sample Input 3

9
1 1 1 2 2 1 2 3 2

Sample Output 3

1
2
2
3
1
2
2
1
1

Solution in Rust (1.42.0) (judge verdict: Accepted)

// -*- coding:utf-8-unix -*-

use std::cmp::*;
use std::collections::*;
use std::fs::File;
use std::io::prelude::*;
use std::io::*;
use std::vec;

const INF: i64 = 1223372036854775807;
const MEM_SIZE: usize = 202020;
const MOD: i64 = 1000000007;
use std::cmp::*;
use std::collections::*;
use std::io::stdin;
use std::io::stdout;
use std::io::Write;
#[allow(dead_code)]
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()
}
#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}
#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

#[allow(unused_macros)]
macro_rules! p {
    ([$($x:expr), *]) => {{
        let mut f = true;
        $(
            print!("{}{}", if f {""} else {" "}, $x);
            f = false;
        )*
78786    print!("\n");
    }};
    ($x:expr) => {{
        let mut f = true;
        for a in $x.iter() {
            print!("{}{}", if f {""} else {" "}, a);
            f = false;
        }
        print!("\n");
    }};
}
#[allow(dead_code)]
fn readii() -> (i64, i64) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<i64>().unwrap(),
        iter.next().unwrap().parse::<i64>().unwrap(),
    )
}
#[allow(dead_code)]
fn readuu() -> (usize, usize) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<usize>().unwrap(),
        iter.next().unwrap().parse::<usize>().unwrap(),
    )
}

#[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 solve() {
    let n: usize = read();
    let mut vec: Vec<i64> = read_vec();
    let mut res: Vec<i64> = vec![];

    for i in (0..n) {
        for j in (0..(n - i)).rev() {
            if j + 1 == vec[j] as usize {
                res.push((j + 1) as i64);
                vec.remove(j);
                // p!(vec);
                break;
            }
        }
    }
    res.reverse();
    if res.len() != n {
        println!("{:?}", -1);
    } else {
        for i in 0..n {
            println!("{}", res[i]);
        }
    }
    return;
}
fn main() {
    solve()
}