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 (2.13.1) (judge verdict: Time Limit Exceeded)

import scala.collection.mutable.ListBuffer
import scala.io.StdIn.readInt
import scala.util.control.Breaks.break

object Main {
  def main(args: Array[String]): Unit = {
    val n = readInt()
    val list: ListBuffer[Int] = scala.collection.mutable.ListBuffer.empty[Int]
    list += 0

    for(i <- 1.to(n)) {
      list += readInt()
    }

    var pos = 1
    var cnt = 0

    while (pos != 2) {
      if(list(pos) == -1) {
        println(-1)
        return
      }
      val next = list(pos)
      list(pos) = -1
      pos = next
      cnt.+=(1)
    }

    print(cnt)
  }
}