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::collections::HashSet;
use std::io;

fn read_lines() -> Vec<i32> {
    let mut line = String::new();
    let mut inputs = Vec::<i32>::new();
    io::stdin().read_line(&mut line).unwrap();
    let n_num = line.trim().parse::<i32>().unwrap();
    line.clear();
    for _ in 0..n_num {
        io::stdin().read_line(&mut line).unwrap();
        let line_num = line.trim().parse::<i32>().unwrap();
        inputs.push(line_num);
        line.clear();
    }
    inputs
}

fn solve(inputs: Vec<i32>) -> i32 {
    let mut past_set = HashSet::new();
    let mut curr_i = inputs[0];
    let mut count = 1;
    for _ in 0..(inputs.len()) {
        if curr_i == 2 {
            return count;
        }
        let next_i = inputs[(curr_i - 1) as usize];
        past_set.insert(curr_i);
        if past_set.contains(&next_i) {
            return -1;
        }
        curr_i = next_i;
        count += 1;
    }
    -1
}

fn main() {
    let inputs = read_lines();
    let res = solve(inputs);
    println!("{}", res);
}