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)

import scala.io.{StdIn => in}
import scala.collection.{mutable => mu}

object Main extends App {
  val out = new java.io.PrintWriter(System.out)
  val n = in.readInt
  var b = in.readLine.split(" ").map(_.toInt).toBuffer
  val a = mu.ListBuffer.empty[Int]

  for(i <- 0 until n) {
    var isFind = false
    for(j <- b.size-1 to 0 by -1 if !isFind) {
      if(b(j) == j+1) {
        a += b(j)
        isFind = true
        debug(j, b(j))
      }
    }
    if(isFind && a.nonEmpty && a.last <= b.size) b.remove(a.last-1)
  }

  if(b.isEmpty) {
    println(a.reverse.mkString("\n"))
  }
  else {
    println(-1)
  }

  def debug(any:Any*):Unit = {
    if(this.getClass.toString == "class Main$") return
    println(any.mkString(" "))
  }
}