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)

#[allow(dead_code)]
fn primes(num: i64) -> Vec<i64> {
    let mut ans = vec![1];
    let mut cur = num;
    for i in 2.. {
        if i * i > num { break; }
        if cur % i == 0 {
            while cur % i == 0 {
                ans.push(i);
                cur /= i;
            }
        }
    }
    if cur > 1 {
        ans.push(cur);
    }
    return ans;
}

#[test]
fn test_primes() {
    assert_eq!(primes(1), vec![1]);
    assert_eq!(primes(140), vec![1, 2, 2, 5, 7])
}

// https://techracho.bpsinc.jp/jhonda/2019_08_05/78537
macro_rules! test {
    ($($input:expr => $output:expr),* $(,)*) => {
        #[test]
        fn solve_test() {
            $(
                assert_eq!(solve($input), $output);
            )*
        }
    };
}
test! {
r"3
3
1
2
" => r"2",

r"4
3
4
1
2
" => r"-1",

r"5
3
3
4
2
4
" => r"3"
}

use proconio::{input, fastout};
use proconio::source::auto::AutoSource;
use im_rc::HashSet;

fn do_solve(a: &Vec<usize>, i: usize, cnt: i64, cache: &mut HashSet<usize>) -> i64 {
    return match a[i] {
        2 => cnt + 1,
        x => {
            if cache.contains(&x) {
                return -1;
            }

            cache.insert(x);

            do_solve(a, a[i] - 1, cnt + 1, cache)
        }
    };
}

fn solve(src: &str) -> String {
    let source = AutoSource::from(src);
    input! {
       from source,
       n:i64,
       a:[usize; n]
    }
    let a: Vec<usize> = a;
    let mut cache = HashSet::new();


    let ans = do_solve(&a, 0, 0, &mut cache);
    format!("{}", ans)
}


#[fastout]
fn main() {
    use std::io::Read;
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();

    println!("{}", solve(&*s));
}