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)

fn main() {
    use std::io::Read;
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    
    let n: usize = iter.next().unwrap().parse::<usize>().unwrap();
    let mut b: Vec<usize> = (&mut iter).take(n).map(|x| x.parse::<usize>().unwrap() - 1).collect();
    
    let mut ret = vec![];
    let mut no_ans = false;
    while !b.is_empty() {
        let mut t = None;
        for i in 0..b.len() {
            let j = b.len()-1-i;
            if b[j] == j {
                t = Some(j);
                break;
            }
        }
        if let Some(v) = t {
            ret.push(v);
            b.remove(v);
        } else {
            no_ans = true;
            break;
        }
    }
    if no_ans {
        println!("-1");
    } else {
        ret = ret.iter().map(|x| *x + 1).collect();
        ret.reverse();
        for r in ret {
            println!("{}", r);
        }
    }
}