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 (1.42.0) (judge verdict: Accepted)

pub trait Zero: PartialEq + Sized {
    fn zero() -> Self;
    #[inline]
    fn is_zero(&self) -> bool {
        self == &Self::zero()
    }
}
pub trait One: PartialEq + Sized {
    fn one() -> Self;
    #[inline]
    fn is_one(&self) -> bool {
        self == &Self::one()
    }
}
macro_rules ! zero_one_impls {($ ({$ Trait : ident $ method : ident $ ($ t : ty ) *, $ e : expr } ) * ) => {$ ($ (impl $ Trait for $ t {# [inline ] fn $ method () -> Self {$ e } } ) * ) * } ; }
zero_one_impls ! ({Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 , 0 } {Zero zero f32 f64 , 0. } {One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 , 1 } {One one f32 f64 , 1. } );
pub trait IterScan: Sized {
    type Output;
    fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output>;
}
pub trait MarkedIterScan: Sized {
    type Output;
    fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output>;
}
#[derive(Clone, Debug)]
pub struct Scanner<'a> {
    iter: std::str::SplitAsciiWhitespace<'a>,
}
mod scanner_impls {
    use super::*;
    impl<'a> Scanner<'a> {
        #[inline]
        pub fn new(s: &'a str) -> Self {
            let iter = s.split_ascii_whitespace();
            Self { iter }
        }
        #[inline]
        pub fn scan<T: IterScan>(&mut self) -> <T as IterScan>::Output {
            <T as IterScan>::scan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn mscan<T: MarkedIterScan>(&mut self, marker: T) -> <T as MarkedIterScan>::Output {
            marker.mscan(&mut self.iter).expect("scan error")
        }
        #[inline]
        pub fn scan_vec<T: IterScan>(&mut self, size: usize) -> Vec<<T as IterScan>::Output> {
            (0..size)
                .map(|_| <T as IterScan>::scan(&mut self.iter).expect("scan error"))
                .collect()
        }
        #[inline]
        pub fn iter<'b, T: IterScan>(&'b mut self) -> ScannerIter<'a, 'b, T> {
            ScannerIter {
                inner: self,
                _marker: std::marker::PhantomData,
            }
        }
    }
    macro_rules ! iter_scan_impls {($ ($ t : ty ) * ) => {$ (impl IterScan for $ t {type Output = Self ; # [inline ] fn scan <'a , I : Iterator < Item = &'a str >> (iter : & mut I ) -> Option < Self > {iter . next () ?. parse ::<$ t > () . ok () } } ) * } ; }
    iter_scan_impls ! (char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String );
    macro_rules ! iter_scan_tuple_impl {($ ($ T : ident ) * ) => {impl <$ ($ T : IterScan ) ,*> IterScan for ($ ($ T , ) * ) {type Output = ($ (<$ T as IterScan >:: Output , ) * ) ; # [inline ] fn scan <'a , It : Iterator < Item = &'a str >> (_iter : & mut It ) -> Option < Self :: Output > {Some (($ (<$ T as IterScan >:: scan (_iter ) ?, ) * ) ) } } } ; }
    iter_scan_tuple_impl!();
    iter_scan_tuple_impl!(A);
    iter_scan_tuple_impl ! (A B );
    iter_scan_tuple_impl ! (A B C );
    iter_scan_tuple_impl ! (A B C D );
    iter_scan_tuple_impl ! (A B C D E );
    iter_scan_tuple_impl ! (A B C D E F );
    iter_scan_tuple_impl ! (A B C D E F G );
    iter_scan_tuple_impl ! (A B C D E F G H );
    iter_scan_tuple_impl ! (A B C D E F G H I );
    iter_scan_tuple_impl ! (A B C D E F G H I J );
    iter_scan_tuple_impl ! (A B C D E F G H I J K );
    pub struct ScannerIter<'a, 'b, T> {
        inner: &'b mut Scanner<'a>,
        _marker: std::marker::PhantomData<fn() -> T>,
    }
    impl<'a, 'b, T: IterScan> Iterator for ScannerIter<'a, 'b, T> {
        type Item = <T as IterScan>::Output;
        #[inline]
        fn next(&mut self) -> Option<Self::Item> {
            <T as IterScan>::scan(&mut self.inner.iter)
        }
    }
}
pub mod marker {
    use super::*;
    use std::{iter::FromIterator, marker::PhantomData};
    #[derive(Debug, Copy, Clone)]
    pub struct Usize1;
    impl IterScan for Usize1 {
        type Output = usize;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            Some(<usize as IterScan>::scan(iter)?.checked_sub(1)?)
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Chars;
    impl IterScan for Chars {
        type Output = Vec<char>;
        #[inline]
        fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
            Some(iter.next()?.chars().collect())
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct CharsWithBase(pub char);
    impl MarkedIterScan for CharsWithBase {
        type Output = Vec<usize>;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                iter.next()?
                    .chars()
                    .map(|c| (c as u8 - self.0 as u8) as usize)
                    .collect(),
            )
        }
    }
    #[derive(Debug, Copy, Clone)]
    pub struct Collect<T: IterScan, B: FromIterator<<T as IterScan>::Output>> {
        size: usize,
        _marker: PhantomData<fn() -> (T, B)>,
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> Collect<T, B> {
        pub fn new(size: usize) -> Self {
            Self {
                size,
                _marker: PhantomData,
            }
        }
    }
    impl<T: IterScan, B: FromIterator<<T as IterScan>::Output>> MarkedIterScan for Collect<T, B> {
        type Output = B;
        #[inline]
        fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
            Some(
                (0..self.size)
                    .map(|_| <T as IterScan>::scan(iter).expect("scan error"))
                    .collect::<B>(),
            )
        }
    }
}
#[macro_export]
macro_rules ! min {($ e : expr ) => {$ e } ; ($ e : expr , $ ($ es : expr ) ,+ ) => {std :: cmp :: min ($ e , min ! ($ ($ es ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! chmin {($ dst : expr , $ ($ src : expr ) ,+ ) => {{let x = std :: cmp :: min ($ dst , min ! ($ ($ src ) ,+ ) ) ; $ dst = x ; } } ; }
#[macro_export]
macro_rules ! max {($ e : expr ) => {$ e } ; ($ e : expr , $ ($ es : expr ) ,+ ) => {std :: cmp :: max ($ e , max ! ($ ($ es ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! chmax {($ dst : expr , $ ($ src : expr ) ,+ ) => {{let x = std :: cmp :: max ($ dst , max ! ($ ($ src ) ,+ ) ) ; $ dst = x ; } } ; }
fn main() {
    #![allow(unused_imports, unused_macros)]
    use std::io::{stdin, stdout, BufWriter, Read as _, Write as _};
    let mut _in_buf = Vec::new();
    stdin().read_to_end(&mut _in_buf).expect("io error");
    let _in_buf = unsafe { String::from_utf8_unchecked(_in_buf) };
    let mut scanner = Scanner::new(&_in_buf);
    macro_rules ! scan {() => {scan ! (usize ) } ; (($ ($ t : tt ) ,* ) ) => {($ (scan ! ($ t ) ) ,* ) } ; ([$ t : tt ; $ len : expr ] ) => {(0 ..$ len ) . map (| _ | scan ! ($ t ) ) . collect ::< Vec < _ >> () } ; ([$ t : ty ; $ len : expr ] ) => {scanner . scan_vec ::<$ t > ($ len ) } ; ([$ t : ty ] ) => {scanner . iter ::<$ t > () } ; ({$ e : expr } ) => {scanner . mscan ($ e ) } ; ($ t : ty ) => {scanner . scan ::<$ t > () } ; }
    let _out = stdout();
    let mut _out = BufWriter::new(_out.lock());
    macro_rules ! print {($ ($ arg : tt ) * ) => (:: std :: write ! (_out , $ ($ arg ) * ) . expect ("io error" ) ) }
    macro_rules ! println {($ ($ arg : tt ) * ) => (:: std :: writeln ! (_out , $ ($ arg ) * ) . expect ("io error" ) ) }
    macro_rules! echo {
        ($ iter : expr ) => {
            echo!($iter, '\n')
        };
        ($ iter : expr , $ sep : expr ) => {
            let mut iter = $iter.into_iter();
            if let Some(item) = iter.next() {
                print!("{}", item);
            }
            for item in iter {
                print!("{}{}", $sep, item);
            }
            println!();
        };
    }
    let n = scan!();
    let a = scan!([marker::Usize1; n]);
    let (l, r) = rho_path(0, |&i| a[i]);
    if let Some(ans) = l.into_iter().chain(r.into_iter()).position(|x| x == 1) {
        println!("{}", ans);
    } else {
        println!("-1");
    }
}
/// $P_0 =$ `init`, $P_{i+1} = f(P_i)$
/// Return (f, g) then P = f, g, g, ...
pub fn rho_path<T, F>(init: T, f: F) -> (Vec<T>, Vec<T>)
where
    T: Clone + Eq + std::hash::Hash,
    F: Fn(&T) -> T,
{
    let mut path = vec![init.clone()];
    let mut visited = std::collections::HashMap::new();
    visited.insert(init, 0);
    let loop_start = loop {
        let next_val = f(path.last().unwrap());
        if let Some(&idx) = visited.get(&next_val) {
            break idx;
        }
        let cnt = path.len();
        path.push(next_val.clone());
        visited.insert(next_val, cnt);
    };
    let looped = path.split_off(loop_start);
    (path, looped)
}