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)

#[cfg(test)]
#[macro_use]
extern crate contest;

use std::fmt::Debug;
use std::io::{self, Bytes, Read, Stdin, StdinLock};
use std::str::{self, FromStr};

fn main() {
    let stdin = io::stdin();
    let mut sc = StdinScanner::new(&stdin);
    let n = sc.next();
    println!("{}", solve(sc.vec(n)).map(|v| v as i32).unwrap_or(-1));
}


fn solve(a: Vec<usize>) -> Option<usize> {
    let mut result = 0;
    let mut visited = vec![false; a.len()];
    let mut current = 0;

    while current != 1 {
        if visited[current] {
            return None;
        } else {
            visited[current] = true;
            current = a[current] - 1;
            result += 1;
        }
    }
    Some(result)
}


#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test() {
        assert_eq_in_time!(1000, "", "");
    }
}


struct StdinScanner<'a> {
    buf: Vec<u8>,
    bytes: Bytes<StdinLock<'a>>,
}


#[allow(dead_code)]
impl<'a> StdinScanner<'a> {
    fn new(stdin: &'a Stdin) -> Self {
        StdinScanner {
            buf: Vec::with_capacity(256),
            bytes: stdin.lock().bytes(),
        }
    }

    fn next<T: FromStr>(&mut self) -> T
        where <T as FromStr>::Err: Debug
    {
        self.buf.clear();
        let mut c = self.bytes.next().unwrap().unwrap();
        while c == ' ' as u8 || c == '\n' as u8 {
            c = self.bytes.next().unwrap().unwrap();
        }
        while !(c == ' ' as u8 || c == '\n' as u8) {
            self.buf.push(c);
            c = self.bytes.next().unwrap().unwrap();
        }
        str::from_utf8(&self.buf).unwrap().parse().unwrap()
    }

    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T>
        where <T as FromStr>::Err: Debug
    {
        (0..n).map(|_| self.next()).collect()
    }

    fn pairs<A: FromStr, B: FromStr>(&mut self, n: usize) -> Vec<(A, B)>
        where <A as FromStr>::Err: Debug,
              <B as FromStr>::Err: Debug
    {
        (0..n).map(|_| (self.next(), self.next())).collect()
    }

    fn trios<A: FromStr, B: FromStr, C: FromStr>(&mut self, n: usize) -> Vec<(A, B, C)>
        where <A as FromStr>::Err: Debug,
              <B as FromStr>::Err: Debug,
              <C as FromStr>::Err: Debug
    {
        (0..n)
            .map(|_| (self.next(), self.next(), self.next()))
            .collect()
    }

    fn mat<T: FromStr>(&mut self, m: usize, n: usize) -> Vec<Vec<T>>
        where <T as FromStr>::Err: Debug
    {
        (0..n).map(|_| self.vec(m)).collect()
    }
}


trait PrintYn {
    fn print_yn(self, yes: &str, no: &str);
}

impl PrintYn for bool {
    fn print_yn(self, yes: &str, no: &str) {
        println!("{}", if self { yes } else { no });
    }
}