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;
using System.Text;

namespace atcorder_GrandContest_032
{
    class Program
    {

        public const int MOD = 1000000000 + 7;

        static void Main(string[] args)
        {

            int cnt = int.Parse(Console.ReadLine());
            int[] numArr = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
          
            List<int> numList = new List<int>();
            for(int i = cnt - 1; 0 <= i; i--)
            {
                numList.Add(numArr[i]);
            }

            Stack<int> retStack = new Stack<int>();
            int idx = 0;
            while (idx < numList.Count)
            {
                if (numList.Count - idx == numList[idx])
                {
                    retStack.Push(numList[idx]);
                    numList.RemoveAt(idx);
                    idx = 0;
                }
                else
                {
                    idx++;
                }
            }

            if (cnt == retStack.Count)
            {
                for (int i = 0; i < cnt; i++)
                {
                    Console.WriteLine(retStack.Pop());
                }
            }
            else
            {
                Console.WriteLine(-1);
            }
        }

    }
}