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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.LinkedList;
public class Main {
	public static void main(String[] args)  throws Exception{

		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		String line = reader.readLine();
		int N = Integer.parseInt(line);
		String[] b_str =reader.readLine().split(" ");

		LinkedList<Integer> b = new LinkedList<>();
		int num = 1;
		for (int i = 0; i < b_str.length; i++) {
			b.add(Integer.parseInt(b_str[i]));
			num *= (i+1);
		}
		LinkedList<Integer> a = new LinkedList<>();
		int[] ans = new int[b_str.length];
		boolean flag = false;

		for (int k = 0; k < num*num; k++) {    //num
			for (int i = 1; i <= b.size(); i++) {
				int j= (int)Math.round(Math.random()*(i-1) + 1);
				if (j > a.size()) {
					a.add(j);
				}
				else {
					a.add(j, j);
				}
				ans[i-1] = j;
			}
			
			
			if (b.equals(a)) {
				flag = true;
				break;
			}
			else {
				a = new LinkedList<>();
				ans = new int[b_str.length];
			}
		}

		if (flag) {
			for (int i = 0; i < b_str.length; i++) {
				System.out.println(ans[i]);
			}
		}
		else {
			System.out.println("-1");
		}
	}
}