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 Haskell (GHC 8.8.3) (judge verdict: Wrong Answer)

import Control.Monad
import Data.List

solve :: Int -> [Int] -> (Int, Int)
solve n as =
  (\(x, y, _) -> (x, y)) $
    foldl'
      ( \(cnt, state, a) i ->
          if state == 2
            then (cnt, state, tail a)
            else
              if not (null a) && state == i
                then (cnt + 1, head a, tail a)
                else (cnt, state, tail a)
      )
      (0, 1, as)
      [1 .. n]

main = do
  n <- readLn
  as <- replicateM n readLn
  let ans = solve n as
  print $ if snd ans == 2 then fst ans else -1