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: Wrong Answer)


#![allow(unused)]

use std::cmp;
use std::io::{self, BufRead};
use std::iter;

macro_rules! destruct_ {
  ($e: expr, ()) => (
    assert!($e.next().is_none())
  );
  ($e: expr, ($arg: ident, $( $args: ident, )*)) => (
    $arg = $e.next().unwrap();
    destruct_!($e, ($($args,)*))
  );
  ($e: expr, ($arg: ident $(, $args: ident )*)) => (
    $arg = $e.next().unwrap();
    destruct_!($e, ($($args,)*))
  );
}

macro_rules! into {
  ($e: expr, $($name: ident)*) => {
    let mut iter = $e.into_iter();
    destruct_!(iter, ($($name)*));
  }
}

macro_rules! get {
  ($i: ident) => (
    let stdin = io::stdin();
    let mut $i = Vec::new();
    for line in stdin.lock().lines() {
      $i.push(
        line
          .unwrap()
          .split_whitespace()
          .map(|a| a.parse().unwrap())
          .collect()
      );
    }
  )
}

macro_rules! p {
  ($a: expr) => (
    println!("{}", $a);
  )
}

fn main() {
  let stdin = io::stdin();
  let mut args: Vec<usize> = Vec::new();
  for line in stdin.lock().lines() {
    args.push(line.unwrap().parse::<usize>().unwrap());
  }

  let mut b = args[1];
  let mut n = 0;
  while args[0].pow(2) >= n {
    b = args[b];
    n += 1;
    if b == args[2] {
      p!(n);
      return;
    }
  }

  p!(-1);
}