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: Time Limit Exceeded)

import Prelude
import Control.Monad
import Control.Applicative


takahashi ::[Int]-> [Int]-> Int -> Int
takahashi as his now |now==2 = length his
                     |elem now his = -1
                     |otherwise = as `seq` his `seq` now `seq` takahashi as (now:his) $as!!(now-1)

takahashi2 :: [Int]->[Int]->Int->Int
takahashi2 as his now
  |(not$elem 2 as) = -1
  |otherwise = (takahashi as his now)

takahashi3 ::[Int]-> Int-> Int -> Int
takahashi3 as l now |now==2 = l
                    |l==length(as)+1 = -1
                    |otherwise = as `seq` l `seq` now `seq` takahashi3 as (l+1) $as!!(now-1)
main :: IO ()
main = do
	n <- readLn
	l <- replicateM n readLn
        putStrLn $ show $ takahashi3 l 0 1