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 Control.Monad.Primitive (PrimState)
import qualified Data.Vector.Unboxed.Mutable as MV
import qualified Data.ByteString.Char8 as B
import Data.Maybe (fromJust)

type Vec = MV.MVector (PrimState IO)

solve :: Vec Int -> Vec Bool -> Int -> Int -> IO (Int, Int)
solve mva mvb i count = do
    next <- MV.unsafeRead mva i
    if next == 1
        then return (next, count)
        else do
            b <- MV.unsafeRead mvb next
            if b
                then return (next, count)
                else do
                    MV.unsafeWrite mvb next True
                    solve mva mvb next (count + 1)
main :: IO ()
main = do
    n <- fst . fromJust . B.readInt <$> B.getLine
    mva <- MV.unsafeNew n :: IO (Vec Int)
    mvb <- MV.replicate n False :: IO (Vec Bool)
    forM_ [0..(n - 1)] $ \i -> do
        a <- fst . fromJust . B.readInt <$> B.getLine
        MV.write mva i (a - 1)
    (stop, count) <- solve mva mvb 0 1
    print $ if stop == 1 then count else -1