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: Accepted)

use std::io::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n = read::<usize>();
    let mut seq = vec![0; n];
    for i in 0..n {
        seq[i] = read::<usize>();
    }
    let mut used = vec![false; n];
    let mut anss = vec![];
    let mut current = vec![];
    for i in 0..n {
        'j_loop: for j in (0..n).rev() {
            let v = seq[j];
            if used[j] || v > current.len() + 1 {
                continue;
            }
            let mut pos = v - 1;
            for k in (j + 1)..n {
                if seq[k] > v {
                    continue;
                }
                if pos >= current.len() || current[pos] != seq[k] {
                    continue 'j_loop;
                }
                pos += 1;
                while pos < current.len() && current[pos] > v {
                    pos += 1;
                }
            }
            if pos != current.len() {
                continue 'j_loop;
            }
            used[j] = true;
            anss.push(v);
            current.insert(v - 1, v);
            break;
        }
        if anss.len() != i + 1 {
            println!("-1");
            return;
        }
    }
    for &ans in anss.iter() {
        println!("{}", ans);
    }
}