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 static java.lang.System.*;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(in);

        int n = sc.nextInt();
        ArrayList<Integer> b = new ArrayList<Integer>();
		for(int i=0; i<n; i++) b.add(sc.nextInt());
		
		ArrayList<Integer> ans = new ArrayList<Integer>();
		while(b.size() > 0) {
			for(int i=b.size()-1; i>=0; i--) {
				if(b.get(i) > i+1) {
					ans.clear();
					ans.add(-1);
					break;
				}
				else if(b.get(i) == i+1) {
					ans.add(b.get(i));
					b.remove(i);
					break;
				}
			}
			
			if(ans.get(0) < 0) break;
		}
		
		for(int i=ans.size()-1; i>=0; i--)
	        out.println(ans.get(i));
    }
}
