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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using static System.Console;
using System.Linq;
using System.Collections.Generic;
class Program
{
    static void Main(string[] args)
    {
      int n = int.Parse(ReadLine());
      List<int> b = ReadLine().Split().ToList().ConvertAll(x=>int.Parse(x));
      List<int> ans = new List<int>();
     
      for (int i=0;i<n;i++)
      {
        for (int j=b.Count-1;j>=0;j--)
        {
          if ((j+1)==b[j])
          {
            ans.Add(j+1);
            b.RemoveAt(j);
            break;
          }
        }
      }
      ans.Reverse();
      if (ans.Count==n)
      {
        foreach (var i in ans)
        {
          WriteLine(i);
        }
      }
      else
      {
        WriteLine(-1);
      }
      
    }
}