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)

use proconio::input;

fn main() {
    input! {
        n: usize,
        b: [usize; n],
    };
    let mut ans = std::collections::VecDeque::new();
    let mut bd = b.into_iter().collect::<std::collections::VecDeque<_>>();
    for _ in 0..n {
        let mut found = None;
        for (j, &b_i) in bd.iter().enumerate().rev() {
            if j + 1 == b_i {
                found = Some(j);
                ans.push_front(b_i);
                break;
            }
        }
        match found {
            Some(j) => {
                bd.remove(j);
            }
            None => {
                println!("-1");
                return;
            }
        }
    }
    for &a_i in ans.iter() {
        println!("{}", a_i);
    }
}