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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static Input;

public class Prog
{
    private const int INF = 1000000007;
    private const long INFINITY = 9223372036854775807;
    private static int[] make_cost = { 0, 2, 5, 5, 4, 5, 6, 3, 7, 6 };
    public static void Main()
    {
        int N = NextInt();
        int[] b = LineInt();
        bool f = true;
        for (int i = 0; i < N; i++) if (b[i] > (i + 1)) f = false;
        List<int> ans = new List<int>();
        if (f)
        {
            for (int i = N - 1; i >= 0; i--)
            {
                //必要digit
                int bi = b[i];
                int li = bi;
                List<int> l = new List<int>();
                List<int> r = new List<int>();
                l.Add(bi);
                while (true)
                {
                    if (bi == 1 && li == 1) break;
                    i--;
                    li--;
                    //1個前見る
                    int bi2 = b[i];
                     if (bi2 == li || bi2 == 1)
                    {
                        l.Insert(0, bi2);
                    }
                    else
                    {
                        r.Add(bi2);
                        li = Math.Max(li, bi2);
                    }
                    bi = bi2;
                }
                l.ForEach(ans.Add);
                r.Reverse();
                r.ForEach(ans.Add);
            }
        }
        else ans.Add(-1);
        ans.ForEach(Console.WriteLine);
    }
}

public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}