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: Accepted)

use std::io::{stdin, Read};
use std::str::FromStr;
use std::collections::HashSet;

fn read<T: FromStr>() -> Option<T> {
    let stdin = stdin();
    let s = stdin
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect::<String>();
    s.parse::<T>().ok()
}
 
fn main() {
    let n: usize = read().unwrap();
    let mut a: Vec<usize> = Vec::new();
    for _i in 0..n {
        let x: usize = read().unwrap();
        a.push(x);
    }
    let mut touched: HashSet<usize> = HashSet::new();
    let mut counter: i64 = 0;
    let mut t: usize = 1;
    while {
        counter += 1;
        touched.insert(t);
        t = a[t - 1];
        t != 2 && !touched.contains(&t)
    } {}
    if t == 2 {
        println!("{}", counter);
    } else {
        println!("-1");
    }
}