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: Runtime Error)

import scala.collection.mutable.ArrayBuffer

object Main extends App {
  val n = readInt
  val arr = readLine.split(" ").map(_.toInt).toBuffer
  val outBuf = ArrayBuffer.fill(n)(0)
  var i = 0
  
  var arraySize = n
  while(i < n) {
    var j = arraySize
    var found = false
    while (found == false) {
      j -= 1
      val num = arr(j)
      
      if (num == j + 1) {
        outBuf(arraySize - 1) = num
        arr.remove(j)
        found = true
      }
      
      if (j == 0 && found == false) {
        println(-1)
        sys.exit(-1)
      }
    }
    arraySize -= 1
    i += 1
  }
  
  outBuf.foreach(println)
}