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: Time Limit Exceeded)

using System;
using System.Text;
using System.Collections.Generic;
using System.Collections;
using static System.Math;
using System.Linq;
using static System.Array;

namespace ConsoleApp2
{
    class Program
    {
        static long N;
        static int[] B;
        static List<int> ans;
        static bool possible = false;
        static void Main(string[] args)
        {
            N = long.Parse(Console.ReadLine());
            B = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            Solve(1, new List<int>(), new List<int>());
            if (possible)
            {
                for (int i = 0; i < N; i++)
                {
                    Console.WriteLine(ans[i]);
                }
                
            }
            else
            {
                Console.WriteLine(-1);
            }
            

        }

        static void Solve(int count, List<int> tmp,List<int> tmp2)
        {
            if(count == N + 1)
            {

                for (int i = 0; i < N; i++)
                {
                    if(tmp[i] != B[i])
                    {
                        return;
                    }
                }
                ans = tmp2;
                possible = true;
            }
            else
            {
                for (int i = 1; i <= count; i++)
                {
                    var tmp3 = new List<int>(tmp);
                    var tmp4 = new List<int>(tmp2);
                    tmp3.Insert(i - 1, i);
                    tmp4.Add(i);
                    Solve(count+1,tmp3,tmp4);
                }
            }
        }

    }
}