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 Control.Monad
import Control.Applicative
import Data.List
import qualified Data.Map as Map
import Data.Array
import qualified Data.ByteString.Char8 as BC
import Data.Maybe
import qualified Data.Set as Set
import qualified Data.Sequence as Sq
import Data.Sequence (ViewL(..),ViewR(..),(><),(<|),(|>),Seq)

bsreadInt :: BC.ByteString -> Int
bsreadInt = fst . fromJust . BC.readInt
strToInt s = (read :: String -> Int) s

main = do
    n <- readLn :: IO Int
    an <- (map bsreadInt) <$> replicateM n BC.getLine
    let a = array (1,n) [(k,an !! (k-1)) | k <- [1..n] ]
    print $ solve 1 0 n a
 
solve :: Int -> Int -> Int -> (Array Int Int) -> Int
solve 2 x n a = x
solve i x n a = if x > n + 1
                         then -1
                         else solve (a ! i) (x+1) n a