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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)


def read_input():
    n = int(input())
    alist = [-1]

    for i in range(n):
        alist.append(int(input()))


    return n, alist

def submit():
    n, alist = read_input()

    through = {}
    curr_button = 1
    steps = 0
    while curr_button not in through.keys():
        through[curr_button] = 1
        curr_button = alist[curr_button]
        steps += 1

        if curr_button == 2:
            break

    if curr_button == 2:
        print(steps)
    else:
        print(-1)



if __name__ == '__main__':
    submit()