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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Math;

class MainClass : Scanner
{
    static void Main()
    {
        int N = RInt();
        var b = RInts();
        if (b[0] == 1)
        {
            for (int i = 0; i < N; i++)
            {
                WriteLine(1);
            }
        }
        else
        {
            WriteLine(-1);
        }
    }
}

class Scanner
{
    public static int RInt() => int.Parse(Console.ReadLine());
    public static long RLong() => long.Parse(Console.ReadLine());
    public static string RString() => Console.ReadLine();
    public static double RDouble() => double.Parse(Console.ReadLine());

    public static int[] RInts() => Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
    public static int[] RInts(Func<string, int> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static long[] RLongs() => Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
    public static long[] RLongs(Func<string, long> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static double[] RDoubles() => Array.ConvertAll(Console.ReadLine().Split(), double.Parse);
    public static double[] RDoubles(Func<string, double> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static string[] RStrings() => Console.ReadLine().Split();
    //public static string[] RStrings(Func<string, string> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static T1 ReadStream<T1>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        return r1;
    }
    public static (T1, T2) ReadStream<T1, T2>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        var r2 = (T2)Convert.ChangeType(r[1], typeof(T2));
        return (r1, r2);
    }
    public static (T1, T2, T3) ReadStream<T1, T2, T3>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        var r2 = (T2)Convert.ChangeType(r[1], typeof(T2));
        var r3 = (T3)Convert.ChangeType(r[2], typeof(T3));
        return (r1, r2, r3);
    }
    public static (T1, T2, T3, T4) ReadStream<T1, T2, T3, T4>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        var r2 = (T2)Convert.ChangeType(r[1], typeof(T2));
        var r3 = (T3)Convert.ChangeType(r[0], typeof(T3));
        var r4 = (T4)Convert.ChangeType(r[0], typeof(T4));
        return (r1, r2, r3, r4);
    }
}