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.

Examples

Input

3
1 2 1


Output

1
1
2


Input

2
2 2


Output

-1


Input

9
1 1 1 2 2 1 2 3 2


Output

1
2
2
3
1
2
2
1
1
import java.io.*;
import java.math.*;
import java.util.*;
public class Main {
 
	public static void main(String[] args) {  
		Scanner input = new Scanner(System.in);
		ArrayList<Integer> arr = new ArrayList<Integer>();
		int N = input.nextInt();
		boolean bad=false;
		for (int i = 1; i <= N; i++) {
			int x = input.nextInt();
			arr.add(x);
			if (x>i) bad=true;
		}
		if (!bad) {
			int[] ans = new int[N];
			int cur = N-1;
			while (arr.size()>0) {
				int index = -1;
				for (int i = 0; i < arr.size(); i++) {
					if (arr.get(i)==i+1) index = i;
				}
				ans[cur] = arr.get(index);
				cur--;
				arr.remove(index);
			}
			for (int i = 0; i < N; i++) {
				System.out.println(ans[i]);
			}
			
		}else System.out.println(-1);
	}	
}