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::collections::HashSet;
use std::io::prelude::*;
use std::string::String;

fn main() {
    let mut s = String::new();
    let stdin = std::io::stdin();
    let mut stdin = stdin.lock();
    stdin.read_line(&mut s).expect("line");
    let _: u32 = s.trim().parse().expect("parsing N");
    let a_s: Vec<u32> = stdin
        .lines()
        .map(|l| l.unwrap().trim().parse().expect("error reading line"))
        .collect();
    println!("{}", solve(&a_s).map(|i| i as i32).unwrap_or(-1));
}

fn solve(a_s: &[u32]) -> Option<usize> {
    let mut current = 0;
    let mut history: HashSet<u32> = HashSet::new();
    while history.insert(current) {
        current = a_s[current as usize] - 1;
        if current == 1 {
            return Some(history.len());
        }
    }
    None
}