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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

// Born Sinner
// old but im not that old
// fuck all you hoes get a grip
import java.util.*;
import java.lang.*;
import java.io.*;

public class Main
{
    static class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next(){
            while(st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt(){
            return Integer.parseInt(next());
        }
        long nextLong(){
            return Long.parseLong(next());
        }
        double nextDouble(){
            return Double.parseDouble(next());
        }
        String nextLine(){
            String str = "";
            try{
                str = br.readLine();
            } catch (Exception e){
                e.printStackTrace();
            }
            return str;
        }
    }
    static int modPower(int x, int y, int mod){
        int res = 1;
        x %= mod;
        if(x==0) return 0;
        while(y>0){
            if(y%2==1){
                res = (res*x)%mod;
            }
            y = y>>1;
            x = (x*x)%mod;
        }
        return res;
    }
    static class pair<T1, T2>{
        T1 first;
        T2 second;
        pair(T1 first, T2 second){
            this.first = first;
            this.second = second;
        }
    }
    
    public static void main (String[] args) throws java.lang.Exception
    {
        FastReader in = new FastReader();
        int n = in.nextInt();
        int[] a = new int[n+1];
        for(int i =1 ;i <= n; i++){
            a[i] = in.nextInt();
        }
        int ans = 0;
        int cur = 1;
        while(a[cur] != 2){
            if(a[cur] == a[a[a[cur]]]){ //3 == 3
                ans = -2;
                break;
            }
            cur = a[cur];
            ans++;
        }
        System.out.println(ans+1);
    }
}