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.

Examples

Input

3
3
1
2


Output

2


Input

4
3
4
1
2


Output

-1


Input

5
3
3
4
2
4


Output

3
import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);

    int N = sc.nextInt();
    int[] a = new int[N + 1];

    for (int i =1; i < N+1; i++) {
      a[i] = sc.nextInt();
    }

    boolean b = true;
    int sq = 0;
    int cr = 1;

    while (b) {
      sq++;
      cr = a[cr];

      if (cr == 2) b = false;
      if (sq == N) {
        sq = 0;
        b = false;
      }
    }

    System.out.println(sq == 0 ? -1 : sq);

  }

}
