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::io::Read;

fn solve(i : usize, n : usize, a : Vec<usize>, d : usize) -> i32 {
    if d > n { return -1 }
    else if i == 2 { return d as i32 }
    else { return solve(a[i-1], n, a, d+1) }
}


fn main() {
    let mut input = String::new();
    std::io::stdin().read_to_string(&mut input).unwrap();
    use std::iter::FromIterator;
    let mut iter = input.split_whitespace();
    let n : usize = iter.next().unwrap().parse().unwrap();
    let a : Vec<usize> = Vec::from_iter(iter.map(|s| s.parse().unwrap()));

    println!("{}", solve(1, n, a, 0))
}