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)

import Control.Monad
import Data.Array
import qualified Data.ByteString.Char8 as BS
import Data.Maybe
import qualified Data.Vector.Unboxed.Mutable as VUM

readInt = fst . fromJust . BS.readInt

getInt = readInt <$> BS.getLine
getIntListN n = map readInt <$> replicateM (fromIntegral n) BS.getLine

play table n as count = do
  let index = as ! n
  if index == 2
    then return count
    else do
      entry <- VUM.read table (index - 1)
      if entry == -1
        then do
          VUM.write table (index - 1) 1
          play table index as (count + 1)
        else return (-1)

main = do
  n <- getInt
  as <- getIntListN n
  let as' = listArray (1, length as) as
  table <- VUM.replicate n (-1) :: IO (VUM.IOVector Int)
  result <- play table 1 as' 1
  print result