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: Accepted)

# https://beta.atcoder.jp/contests/abc065/tasks/abc065_b

import sys


def model():
    e = list(map(int, sys.stdin))
    cur = e[1]
    for i in range(e[0]):
        if cur == 2:
            print(i + 1)
            break
        cur = e[cur]
    else:
        print(-1)


def input_lines():
    """hell?"""
    lines = sys.stdin.readlines()
    for i in range(1, int(lines[0])+1):
        yield i, int(lines[i].strip())


def solve():
    d = {i: button for i, button in input_lines()}
    count = 1
    index = 1

    while True:
        try:
            prev = index
            index = d[index]

            if index is None:
                print(-1)
                exit()
            elif index == 2:
                print(count)
                exit()
            d[prev] = None
            count += 1
        except KeyError:
            print(-1)
            exit()


if __name__ == '__main__':
    solve()
    # model()