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)

#[allow(unused_imports)]
use std::io::{stdin, Read, StdinLock};
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::str::FromStr;
#[allow(unused_imports)]
use std::collections::{HashSet, HashMap, BinaryHeap};
#[allow(unused_imports)]
use std::vec::Vec;

#[allow(dead_code)]
const INF: i32 = 1000_000_000;
#[allow(dead_code)]
const INFLL: i64 = 1000_000_000_000_000_000;
#[allow(dead_code)]
const EPS: f64 = 1.0e-10;

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

impl<'a> Scanner<'a> {
    #[allow(dead_code)]
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner {cin: cin}
    }

    #[allow(dead_code)]
    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin.by_ref().bytes().map(|c| c.unwrap() as char)
                    .skip_while(|c| c.is_whitespace())
                    .take_while(|c| !c.is_whitespace())
                    .collect::<String>();
        token.parse::<T>().ok()
    }

    #[allow(dead_code)]
    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }
}

fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin);
    let n: usize = sc.read();
    let mut a: Vec<i32> = vec![0; n];
    for i in 0..n {
        a[i] = sc.read();
    }
    let mut now: usize = 0;
    let mut ans = 0;
    loop {
        ans += 1;
        match a[now] {
            0 => {
                ans = -1;
                break;
            },
            2 => {
                break;
            },
            nxt => {
                a[now] = 0;
                now = (nxt - 1) as usize;
            }
        }
    }
    println!("{}", ans);
}