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 hiding (log)
import Control.Monad
-- import Control.Arrow ((&&&))
import Data.Array
-- import Data.List (nub, sort, group)
-- import Data.Maybe (fromMaybe)
-- import qualified Data.IntMap as M
type Lights = Array Int Int

main :: IO ()
main = do
    n <- readLn
    as <- replicateM n readLn
    print $ solve (conv n as, 0, []) 1

-- |
--
-- >>> solve (conv 3 [3,1,2],0,[]) 1
-- 2
--
-- >>> solve (conv 4 [3,4,1,2],0,[]) 1
-- -1
--
-- >>> solve (conv 5 [3,3,4,2,4],0,[]) 1
-- 3
solve :: (Lights, Int, [Int]) -> Int -> Int
solve (as, cnt, log) x
  | y == 2       = cnt + 1
  | y `elem` log = -1
  | otherwise    = solve (as, cnt + 1, x : log) y
  where y = as ! x

conv :: Int -> [Int] -> Lights
conv n as = array (1, n) (zip [1 .. n] as)