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.Linq;
using System.Collections.Generic;

namespace AGC032
{
    class Program
    {
        static void Main(string[] args)
        {
            // input, N ,List<int> b 
            //for N -> 1 
            //各処理時点において、1 <= j <= i を満たす要素が存在するのか確認する
            //添字と要素の数が一致しているかどうか

            int N = int.Parse(Console.ReadLine());
            List<int> b = Console.ReadLine().Split().Select(int.Parse).ToList();

            if (b[0] != 1) { Console.WriteLine(-1); return; }

            int[] Res = new int[N];
            int index = 0;
            for (int i = N; i >= 1; i--)
            {
                bool isOK = false;
                for (int j = 0; j < b.Count; j++)
                {
                    //条件を満たすものが複数ある場合は、一番大きいものを選ぶ

                    if (b[j] == j + 1)
                    {
                        isOK = true;
                        index = Math.Max(index, j);
                    }
                }
                if (!isOK) { Console.WriteLine(-1); return; }

                Res[i - 1] = index + 1;
                b.RemoveAt(index);
                index = 0;
            }

            foreach (var i in Res)
            {
                Console.WriteLine(i);
            }
        }
    }
}