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 Python (3.4.3) (judge verdict: Wrong Answer)

N=int(input())


a = []

for i in range(N):
    a.append(int(input()) - 1)
# a=[0]*N
# for i in range(N):
#   a[i]=int(input())
count=0

#loopの定義→同じインデックスを使用したらloop判定
#in の処理を爆速で実行するためにsetを使用する
#loop=[]
loop=set()

tmp=1
while True:  
  tmp=a[tmp-1]
  count+=1
  if tmp==2:
    print(count)
    exit()
  if tmp-1 in loop:
    print(-1)
    exit()
  #loop.append(tmp-1)
  loop.add(tmp-1)