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


class Program
{
    static void Main(string[] args)
    {
        // 入力
        //var s = Console.ReadLine();
        int n = int.Parse(Console.ReadLine());
        var b = Console.ReadLine().Split().Select(int.Parse).ToList();

        var ans = new List<string>();
        //bool[] skip = new bool[n];
        for (int i = 0; i < n; i++)
        {
            var j = 1;
            for (int k = n - i - 1; k >= 0; k--)
            {

                if (b[k] == k + j)
                {
                    ans.Add(b[k].ToString());
                    b.RemoveAt(k);
                    break;
                }
            }
        }

        if (b.Count() > 0)
        {
            Console.WriteLine(-1);
        }
        else
        {
            ans.Reverse();
            foreach (var item in ans)
            {
                Console.WriteLine(item);
            }
        }
    }
}