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::cmp::*;
use std::collections::HashSet;
use std::io::*;
use std::num::*;
use std::str::*;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let s = stdin
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect::<String>();
    s.parse::<T>().ok().unwrap()
}

fn string() -> String {
    read()
}

fn int() -> i64 {
    read()
}

fn char() -> char {
    read::<String>().pop().unwrap()
}

fn vecchar() -> Vec<char> {
    string().chars().collect()
}

fn vecint(n: i64) -> Vec<i64> {
    let mut vec = Vec::new();
    for i in 0..n {
        vec.push(int())
    }
    vec
}

fn main() {
    let n = int() as usize;
    let mut a = Vec::new();
    a.push(0usize);
    for _ in 0..n {
        a.push(int() as usize)
    }

    let mut memo = HashSet::new();
    let mut cur = 1;
    let mut ans = 1;
    memo.insert(1 as usize);
    loop {
        if memo.contains(&a[cur]) {
            println!("-1");
            return;
        } else {
            let target = a[cur];
            if target == 2 {
                println!("{}", ans);
                return;
            }

            memo.insert(target);
            cur = target;
            ans += 1;
        }
    }
}