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 (1.42.0) (judge verdict: Accepted)

use std::collections::HashSet;
use whiteread::parse_line;

fn main() {
    let n: usize = parse_line().unwrap();
    let mut a: Vec<u32> = Vec::new();
    let mut button: HashSet<u32> = HashSet::new();
    let mut idx = 0;

    for _ in 0..n {
        a.push(parse_line().unwrap());
    }
    button.insert(1);
    println!(
        "{}",
        loop {
            if a[idx] == 2 {
                break button.len() as isize;
            } else {
                if !button.insert(a[idx]) {
                    break -1;
                }
                idx = (a[idx] - 1) as usize;
            }
        }
    );
}