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::stdin;

fn main() {
    let mut st = String::new();
    stdin().read_line(&mut st).unwrap();
    let n:usize = st.trim().parse().unwrap();
    let mut st = String::new();
    stdin().read_line(&mut st).unwrap();
    let mut v:Vec<i32> = st.trim().split(" ").map(|x| x.parse().unwrap()).collect();
    let mut result:Vec<i32> = Vec::new();

    while result.len() < n {
        let mut c:usize = 0;
        let mut r:i32 = -1;
        for i in 0..n {
            if v[i] < 0 {
                c += 1;
            } else {
            	let num = (i+1-c) as i32;
                if v[i] == num {
                    r = i as i32;
                };
            };
        };
        if r >= 0 {
        	let num = r as usize;
            result.insert(0, v[num]);
            v[num] = -1;
        } else {
            result = [-1].to_vec();
            break;
        };
    };
    for i in result {
        println!("{}", i);
    };
}