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.util.*;
import java.io.*;

public class Main {
	public static void main (String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		String[] line = br.readLine().split(" ", n);
		ArrayList<Integer> list = new ArrayList<>();
		for (int i = 0; i < n; i++) {
		    list.add(Integer.parseInt(line[i]));
		}
		ArrayList<Integer> ans = new ArrayList<>();
		while (list.size() > 0) {
		    for (int i = list.size() - 1; i >= 0; i--) {
		        if (list.get(i) > i + 1) {
		            System.out.println(-1);
		            return;
		        }
		        if (list.get(i) == i + 1) {
		            list.remove(i);
		            ans.add(i + 1);
		            break;
		        }
		    }
		}
		StringBuilder sb = new StringBuilder();
		for (int i = ans.size() - 1; i >= 0; i--) {
		    sb.append(ans.get(i)).append("\n");
		}
		System.out.print(sb);
    }
}

