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::fmt;
use std::io::stdin;
use std::io::BufRead;
use std::str;
use std::str::FromStr;

fn main() {
	let stdin = stdin();
	let mut scan = InputScanner::new(stdin.lock(),256);

	let n:usize = scan.next();
	let a:Vec<usize> = (0..n).map(|_| scan.next()).collect::<Vec<usize>>();

	let mut history = (0..n).map(|_| false).collect::<Vec<bool>>();

	let mut i = 1;
	let mut count = 1;

	history[0] = true;

	while !history[a[i-1]-1] {
		if a[i-1] == 2 {
			println!("{}",count);
			return;
		}
		i = a[i-1];

		count += 1;

		history[i-1] = true;
	}

	println!("-1");
}
struct InputScanner<R: BufRead> {
	reader: R,
	buf: Vec<u8>, // Should never be empty
	pos: usize,   // Should never be out of bounds as long as the input ends with '\n'
}
impl<R: BufRead> InputScanner<R> {
	fn new(reader: R, capacity: usize) -> Self {
		InputScanner {
			reader: reader,
			buf: Vec::with_capacity(capacity),
			pos: 0,
		}
	}

	#[inline]
	fn next<T: FromStr>(&mut self) -> T
	where
		T::Err: fmt::Debug,
	{
		if self.buf.is_empty() {
			self._read_next_line();
		}
		let mut start = None;
		loop {
			match (self.buf[self.pos], start.is_some()) {
				(b' ', true) | (b'\n', true) | (b'\r', true) => break,
				(_, true) | (b' ', false) => self.pos += 1,
				(b'\n', false) | (b'\r', false) => self._read_next_line(),
				(_, false) => start = Some(self.pos),
			}
		}
		let target = &self.buf[start.unwrap()..self.pos];
		unsafe { str::from_utf8_unchecked(target) }.parse().unwrap()
	}

	#[inline]
	fn _read_next_line(&mut self) {
		self.pos = 0;
		self.buf.clear();
		if self.reader.read_until(b'\n', &mut self.buf).unwrap() == 0 {
			panic!("Reached EOF");
		}
	}
}