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;

class Program
{
 static void Main(string[] args)
 {
   int total = int.Parse(Console.ReadLine());
   string[] numStrArray = Console.ReadLine().Split(' ');
   int[] numArray = new int[total];
   int cnt = 0;
   int buff;
   bool no_error = true;
   List<int> listValue = new List<int>();
   
   for( cnt = 0; cnt < total; cnt++ )
   {
     buff = int.Parse(numStrArray[cnt]);
     numArray[cnt] = buff;
     
     if( buff > (cnt+1) )
     {
       no_error = false;
       break;
     }
   }

   if(no_error)
   {
     for( cnt = 0; cnt < total; cnt++ )
     {
       if( cnt == 0 )
       {
          listValue.Add(numArray[cnt]);
       }
       else
       {  
         buff = (listValue.Count - (numArray[cnt] - 1));
         if( buff == listValue.Count)
         {
          listValue.Add(numArray[cnt]);
         }
         else
         {
           listValue.Insert(buff, numArray[cnt]);
         }
       }
     } 
   }
   
   if(no_error)
   {
     listValue.Reverse();
     foreach( int i in listValue )
     {
       Console.WriteLine(i);
     }
   }
   else
   {
     Console.WriteLine(-1);
   }
 }
}