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 (1.15.1) (judge verdict: Wrong Answer)

#![allow(unused)]

use std::cmp::{max, min};
use std::io::stdin;
use std::mem::swap;
use std::str::FromStr;

fn input<T: FromStr>() -> Result<T, T::Err> {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    buf.trim().parse()
}

fn input_vec<T: FromStr>() -> Result<Vec<T>, T::Err> {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    buf.trim().split_whitespace().map(|x| x.parse()).collect()
}

fn main() {
    let n: usize = input().unwrap();
    let mut a: Vec<usize> = input_vec().unwrap();

    let mut sorted = a.clone();
    sorted.sort();

    if sorted.iter().enumerate().all(|(i, e)| i + 1 >= *e) {
        let mut out = 0usize;
        while out < n {
            let mut seg: Vec<usize> = a
                .iter()
                .rev()
                .skip(out)
                .take_while(|x| **x != 1)
                .cloned()
                .collect();
            seg.push(1);
            seg.sort();
            out += seg.len();
            for i in seg {
                println!("{}", i);
            }
        }
    } else {
        println!("-1");
    }
}