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 Scala (2.11.7) (judge verdict: Accepted)

object Main extends App {
  val in = scala.io.Source.stdin.getLines.toSeq
  val B = in.tail.head.split(' ').map(_.toInt.toChar).toArray
  
  private def func(b:Array[Char]):Seq[Int] = {
    if(b.isEmpty) return Seq()
    //println(b)
    var i=b.size - 1
    val sz=b.size
    while(i >= 0){
      if((i+1) < b(i)) return null
      if((i+1) == b(i)){ 
        val sub = func(b.take(i) ++ b.drop(i+1) )
        //println(sub)
        if(sub != null) return sub :+ (i+1)
      }
      i -= 1
    }
    return null
  }
  val ret = func(B)
  if(ret == null) println(-1) else println(ret.mkString("\n"))
}