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.*;

public class Main {

    static final int MOD=1000000007;

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int n =sc.nextInt();
        int b[] = new int[n];
        int ans[] = new int[n];
        for(int i=0;i<n;i++)b[i]=sc.nextInt();

        for(int j=n;j>0;j--) {

            int remove = -1;
            int index=-1;
            for (int i = 0; i < j; i++) {
                if (b[i] == i + 1) {
                    remove = Math.max(remove, b[i]);
                    index = i;
                }
            }

            if (remove == -1) {
                System.out.println(-1);
                return;
            }
            b[index]=-1;
            ans[j-1]=remove;
            boolean flag=false;
            for(int i=0;i<j-1;i++){
                if(flag){
                    b[i]=b[i+1];
                }else{
                    if(b[i]==-1){
                        flag=true;
                        b[i]=b[i+1];
                    }
                }

            }

        }
        for(Integer a:ans) System.out.println(a);
    }
}
