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 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE BangPatterns #-}
module Main where

import qualified Data.Array as A
import qualified Data.IntSet as S
import Data.Bool

main :: IO ()
main = do
  { n:as <- map read . words <$> getContents
  ; print $ solve $! A.listArray (1, n) as
  }

{- |
>>> solve $ A.listArray (1,3) [3,1,2]
2
-}
solve :: A.Array Int Int -> Int
solve bs = iter S.empty 1 1
  where
    iter s b c = bool (bool (iter (S.insert b s) b' (succ c)) c  (b' == 2)) (-1) (S.member b s)
      where
        b' = bs A.! b

readLineInputs :: Read a => IO [a]
readLineInputs = map read . words <$> getLine