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;

class Program
{
    static void Main()
    {
        Solve();
        return;

    }

    public static string Solve()
    {
        int N = ReadInt();
        int[] b = ReadInts();
        List<int> bList = new List<int>(N);
        bList.AddRange(b);
        List<int> ans = new List<int>(N);
        for(int i=0;i<N;i++)
        {
            for(int j=N-1-i;j>=0;j--)
            {
                if(bList[j]==j+1)
                {
                    ans.Add(j+1);
                    bList.RemoveAt(j);
                    break;
                }
                if(j==0)
                {
                    Console.WriteLine(-1);
                    return "-1";
                }
            }
        }
        for(int i=N-1;i>=0;i--)
        {
            Console.WriteLine(ans[i]);
        }
        return "";
    }

    private static string Read() { return Console.ReadLine(); }
    private static int ReadInt() { return int.Parse(Read()); }
    private static long ReadLong() { return long.Parse(Read()); }
    private static double ReadDouble() { return double.Parse(Read()); }
    private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
    private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
    private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
}