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 OCaml (4.02.3) (judge verdict: Time Limit Exceeded)

open Batteries
open Printf
let () =
  let n = Scanf.scanf "%d " (fun a -> a) in
  let a_lst = Array.to_list @@ Array.init n (fun i -> (Scanf.scanf "%d " (fun a -> a))) in

  let rec aux visited i cnt =
    let next = (List.nth a_lst i)-1 in
    if List.mem i visited then -1 else
    if i = 1 then cnt else
      aux (i::visited) next (cnt+1)
  in

  Printf.printf "%d\n" @@
  aux [] 0 0