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.util.*;

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

		int n=sc.nextInt();

		int b[]=new int[n];
		boolean bnum[]= new boolean [n];
		Arrays.fill(bnum, false);
		int b0[]=new int[n];
		
		for(int i=0;i<n;++i) {
			b[i]=sc.nextInt();
			b0[i]=b[i];
		}
		Arrays.sort(b);
		
		boolean boo=true;
		for(int i=0;i<n;++i) {
			if (b[i]>i+1) {
				boo=false;
				break;
			}
		}
		if (boo==false)System.out.println(-1);
		else {
			
			for( int i=0;i<n;++i) {
				System.out.println(b[i]);
			}
			
		}
	}
	
}