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;

namespace AGC032A
{
    internal class Program
    {
        public static void Main(string[] args)
        {
            long[] NN = Console.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();
            long N = NN[0];
            long[] B = Console.ReadLine().Split(' ').Select(a => long.Parse(a)).ToArray();

            long[] Rev = new long[N];
            List<long> BB = B.ToList();

            for (int i = 0; i < N; i++)
            {
                int stat = -1;
                for (int j = 0; j < BB.Count; j++)
                {
                    if (j + 1 == BB[j])
                    {
                        stat = Math.Max(stat, j);
                    }
                }

                if (stat == -1)
                {
                    Console.WriteLine(-1);
                    return;
                }

                Rev[i] = stat;
                BB.RemoveAt(stat);
            }

            Array.Reverse(Rev);
            for (int i = 0; i < N; i++)
            {
                Console.WriteLine(Rev[i] + 1);
            }
        }
    }
}