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.Generic;
using System.Linq;
using static System.Console;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            label:
            var a = A();
            if (a == null)
            {
                WriteLine(-1);
            }
            else
            {
                foreach(var n in a)
                {
                    WriteLine(n);
                }
            }
        }

        static List<int> A()
        {
            var list = new List<int>();
            ReadLine();
            var li2 = ReadLine().Split(' ').Select(int.Parse).ToList();
            while (li2.Count > 0)
            {
                int i = li2.Count - 1;
                for (; 0 <=i; --i)
                {
                    if (li2[i] == i + 1)
                    {
                        list.Add(i + 1);
                        li2.RemoveAt(i);
                        break;
                    }
                }
                if (i < 0) return null;
            }
            list.Reverse();
            return list;
        }
    }
}