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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;


public class A
{
	public static void Main()
	{
		int N = Int32.Parse(Console.ReadLine());

		LinkedList<int> b = new LinkedList<int>();
		string[] args = Console.ReadLine().Split(' ');
		for(int i = 0; i < N; i++)
			b.AddLast(Int32.Parse(args[i]));
		
		bool isExist = true;
		int[] ans = new int[N];
		for(int i = 0; i < N; i++)
		{
			LinkedListNode<int> del = null;
			int pos = 1;
			for(LinkedListNode<int> node = b.First; node != null; node = node.Next)
			{				
				if(node.Value == pos)
					del = node;
				pos++;
			}

			if(del == null)
			{
				isExist = false;
				break;
			}
			else
			{				
				ans[i] = del.Value;
				b.Remove(del);
			}
		}

		if(isExist)
			for(int i = N - 1; i >= 0; i--)
				Console.WriteLine(ans[i]);
		else
			Console.WriteLine(-1);
	}
}