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 System.Text;
using System.Threading.Tasks;

namespace AGC032_A
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            string[] strs = Console.ReadLine().Split(' ');
            int[] b = new int[n];
            List<int> bList = new List<int>(n);
            Stack<int> ans = new Stack<int>(n);

            for (int i = 0; i < n; ++i)
            {
                b[i] = int.Parse(strs[i]);
                bList.Add(b[i]);
            }

            int count = n;

            for (int i = n; i >= 1; --i)
            {
                if (bList[i-1] == i)
                {
                    ans.Push(i);
                    bList.RemoveAt(i-1);

                    i = count;
                    --count;
                }
            }

            if (bList.Count != 0)
            {
                Console.WriteLine("-1");
            }
            else
            {
                int ansCount = ans.Count;
                for (int i = 0; i < ansCount; ++i)
                {
                    Console.WriteLine("{0}", ans.Pop());
                }
            }
        }
    }
}