Problem:
Score : 200 points

Problem Statement

Takahashi wants to gain muscle, and decides to work out at AtCoder Gym.

The exercise machine at the gym has N buttons, and exactly one of the buttons is lighten up.
These buttons are numbered 1 through N.
When Button i is lighten up and you press it, the light is turned off, and then Button a_i will be lighten up. It is possible that i=a_i.
When Button i is not lighten up, nothing will happen by pressing it.

Initially, Button 1 is lighten up. Takahashi wants to quit pressing buttons when Button 2 is lighten up.

Determine whether this is possible. If the answer is positive, find the minimum number of times he needs to press buttons.

Constraints

2 ≤ N ≤ 10^5

1 ≤ a_i ≤ N

Input

Input is given from Standard Input in the following format:

N
a_1
a_2
:
a_N

Output

Print -1 if it is impossible to lighten up Button 2.
Otherwise, print the minimum number of times we need to press buttons in order to lighten up Button 2.

Sample Input 1

3
3
1
2

Sample Output 1

2

Press Button 1, then Button 3.

Sample Input 2

4
3
4
1
2

Sample Output 2

-1

Pressing Button 1 lightens up Button 3, and vice versa, so Button 2 will never be lighten up.

Sample Input 3

5
3
3
4
2
4

Sample Output 3

3

Solution in Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import io.StdIn.readInt
import annotation.tailrec
import collection.mutable.ListBuffer
import collection.Searching._

object Main extends App {
  val n = readInt
  val as = Seq.fill(n)(readInt)
  val vs = ListBuffer.empty[Int]

  println(solve(0, 0, as, vs))

  @tailrec def solve(pos: Int, res: Int, as: Seq[Int], vs: ListBuffer[Int]): Int = {
    if (pos == 1) res
    else vs.search(pos) match {
      case Found(_) => -1
      case InsertionPoint(i) => {
        vs.insert(i, pos)
        solve(as(pos) - 1, res + 1, as, vs)
      }
    }
  }
}