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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.Scanner;
import java.util.*;


public class Main {
	public static void main(String[] args) {

		Scanner sc=new Scanner(System.in);

		int n=sc.nextInt();
		
		Map<Integer,Integer> data=new TreeMap<Integer,Integer>();
		
		for(int i=1;i<=n;i++) {
			data.put(i,sc.nextInt());
		}
		
		int counter=1;
		int firstkey=data.get(1);
		int key=0;
		int buf=0;
		while(true) {
			
			
			
			if(counter==0) {
				key=firstkey;
			}
			
			
			
			
			buf=data.get(key);
			counter++;
			key=buf;
			
			
			if(buf==2) {
				System.out.println(counter);
				break;
			}
			
			if(counter>=n) {
				System.out.println("-1");
				break;
				
			}
			
		}
		
		
		sc.close();


	}


}