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(unused_macros)]
#![allow(dead_code)]
#![allow(unused_imports)]

use itertools::Itertools;

const U_INF: usize = 1 << 60;
const I_INF: isize = 1 << 60;

fn main() {
    let mut sc = Scanner::new();
    let n = sc.next_usize();
    let mut a = Vec::with_capacity(n);
    for _ in 0..n {
        let ai = sc.next_usize();
        a.push(ai);
    }

    let mut now = 0;
    for i in 0..n {
        now = a[now] - 1;

        if now == 1 {
            println!("{}", i + 1);
            return;
        }
    }

    println!("{}", -1);
}

pub struct Scanner {
    buf: std::collections::VecDeque<String>,
}

impl Scanner {
    pub fn new() -> Self {
        Self {
            buf: std::collections::VecDeque::new(),
        }
    }

    fn scan_line(&mut self) {
        let mut flag = 0;
        while self.buf.is_empty() {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).unwrap();
            let mut iter = s.split_whitespace().peekable();
            if iter.peek().is_none() {
                if flag >= 5 {
                    panic!("There is no input!");
                }
                flag += 1;
                continue;
            }

            for si in iter {
                self.buf.push_back(si.to_string());
            }
        }
    }

    pub fn next<T: std::str::FromStr>(&mut self) -> T {
        self.scan_line();
        self.buf
            .pop_front()
            .unwrap()
            .parse()
            .unwrap_or_else(|_| panic!("Couldn't parse!"))
    }

    pub fn next_usize(&mut self) -> usize {
        self.next()
    }

    pub fn next_isize(&mut self) -> isize {
        self.next()
    }

    pub fn next_chars(&mut self) -> Vec<char> {
        self.next::<String>().chars().collect()
    }

    pub fn next_string(&mut self) -> String {
        self.next()
    }

    pub fn next_char(&mut self) -> char {
        self.next()
    }

    pub fn next_float(&mut self) -> f64 {
        self.next()
    }
}