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)

#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::prelude::BufRead;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufReader, BufWriter, Write};
#[allow(unused_imports)]
use std::mem::swap;
#[allow(unused_imports)]
use std::str::FromStr;

fn main() {
    let n = read::<usize>();
    let mut arr = read_vector::<usize>().into_iter().map(|x| x - 1).collect::<Vec<_>>();
    let mut diff = (0..n).map(|i| i - arr[i]).collect::<Vec<_>>();
    let mut operations = vec![];
    for _ in 0..n {
        let mut index = diff.len();
        for j in (0..diff.len()).rev() {
            if diff[j] == 0 {
                index = j;
                break;
            }
        }
        if index == diff.len() {
            println!("-1");
            return;
        }
        operations.push(index + 1);
        arr.remove(index);
        diff.remove(index);
        for i in index..arr.len() {
            diff[i] -= 1;
        }
    }

    for &num in operations.iter().rev() {
        println!("{}", num);
    }
}

#[allow(dead_code)]
fn read<T>() -> T
where
    T: std::str::FromStr,
    T::Err: std::fmt::Debug,
{
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    return buf.trim().parse().unwrap();
}

#[allow(dead_code)]
fn read_vector<T>() -> Vec<T>
where
    T: std::str::FromStr,
    T::Err: std::fmt::Debug,
{
    let mut buf = String::with_capacity(100);
    stdin().read_line(&mut buf).unwrap();
    return buf.split_whitespace().map(|s| s.parse().unwrap()).collect();
}

#[allow(dead_code)]
fn read_matrix<T>() -> Vec<Vec<T>>
where
    T: std::str::FromStr,
    T::Err: std::fmt::Debug,
{
    use std::io::prelude::*;
    let stdin = stdin();
    let mut reader = BufReader::with_capacity(100 * 1024, stdin);
    let mut line = String::with_capacity(100);
    let mut matrix: Vec<Vec<T>> = Vec::new();

    while reader.read_line(&mut line).unwrap() > 0 {
        matrix.push(
            line.trim()
                .split_whitespace()
                .map(|s| s.parse().unwrap())
                .collect(),
        );
        line.clear();
    }

    return matrix;
}

#[allow(dead_code)]
fn read_chars() -> Vec<char> {
    let stdin = stdin();
    let mut buf = String::new();
    let _bytes = stdin.read_line(&mut buf).unwrap();
    return buf.trim().chars().collect();
}