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 Rust (1.15.1) (judge verdict: Time Limit Exceeded)

use std::io::stdin;

fn main() {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    let len = buf.trim().parse::<usize>().unwrap();
    let mut input: Vec<usize> = Vec::new();
    for _ in 0..len {
        let mut buf = String::new();
        stdin().read_line(&mut buf).unwrap();
        input.push(buf.trim().parse::<usize>().unwrap());
    }
    println!("{}", solve(input));
}

fn solve(input: Vec<usize>) -> i32{
    let mut used_button: Vec<usize> = vec![1];
    let mut counter = 1;
    let mut current = input[0];
    loop {
        if current == 2 {
            return counter;
        }
        if used_button.contains(&input[current-1]) || input.len() <= counter as usize {
            return -1;
        }
        used_button.push(current);
        current = input[current-1];
        counter += 1;
    }
}