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)

fn main() {
    let n = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let mut iter = buf.trim_end().split_whitespace();
        let n: usize = iter.next().unwrap().parse().unwrap();
        n
    };

    let mut b: Vec<usize> = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let mut iter = buf.trim_end().split_whitespace();
        let b: Vec<usize> = (0..n)
            .map(|_| {
                let a: usize = iter.next().unwrap().parse().unwrap();
                a
            })
            .collect();
        b
    };
    
    let mut ans: Vec<usize> = Vec::new();
    while b.len() > 0 {
        let mut nB: Vec<usize> = Vec::new();
        let mut done: bool = false;
        for (i, val) in b.iter().rev().enumerate() {
            if b.len() - i == *val && !done {
                ans.push(*val);
                done = true;
            } else {
                nB.push(*val);
            }
        }
        if nB.len() == b.len() {
            println!("{}", -1);
            return;
        } else {
            nB.reverse();
            b = nB;
        }
    }
    ans.reverse();
    for v in ans {
        println!("{}", v);
    }
}