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: Accepted)

import java.io.*;
import java.lang.*;
import java.util.*;
import java.math.*;

class Solver extends Main{
	Solver(){
		
	}
}//Solver_end

@SuppressWarnings("unchecked")
class Main{
	static int imax=Integer.MAX_VALUE;
	static long lmax=Long.MAX_VALUE;
	
	public static void main(String[] args) throws FileNotFoundException{
		
		Scanner sc=new Scanner(System.in);
		
		int n=readI(sc);
		int[] num=new int[n];
		
		for(int i=0;i<n; i++){
			num[i]=readI(sc)-1;
		}
		
		int prev=0;
		int cur=num[0];
		int cnt=1;
		
		
		while(cur!=1 && num[cur]!=-1){
			prev=cur;
			cur=num[cur];
			num[prev]=-1;
			cnt+=1;
		}
		
		puts(cur==1 ? cnt : -1);
		
		new Solver();
	}//main_end
	
//---------------------------------------------------------------------------
	static int readI(Scanner sc){
		return Integer.parseInt(sc.nextLine().trim());
	}
	static long readL(Scanner sc){
		return Long.parseLong(sc.nextLine().trim());
	}
	static String readS(Scanner sc){
		return sc.nextLine().trim();
	}
	static int[] readlnI(Scanner sc, String dl){
		return Arrays.stream(sc.nextLine().trim().split(dl)).mapToInt(Integer::parseInt).toArray();
	}
	static long[] readlnL(Scanner sc, String dl){
		return Arrays.stream(sc.nextLine().trim().split(dl)).mapToLong(Long::parseLong).toArray();
	}
	static String[] readlnS(Scanner sc, String dl){
		return sc.nextLine().trim().split(dl);
	}
	@SuppressWarnings("unchecked")
	static <T> void puts(T... args){
		for(int i=0; i<args.length-1; i++){
			System.out.printf("%s ",args[i]);
		}
		System.out.println(args[args.length-1]);
	}
	static void puts(int[] ary){
		for(int i=0; i<ary.length-1; i++){
			System.out.printf("%d ",ary[i]);
		}
		System.out.println(ary[ary.length-1]);
	}
	static void puts(long[] ary){
		for(int i=0; i<ary.length-1; i++){
			System.out.printf("%d ",ary[i]);
		}
		System.out.println(ary[ary.length-1]);
	}
	static void bs(){
		System.out.println("");
	}
	static int sum(int[] ary){
		int sum=0;
		for(int i=0; i<ary.length; i++) sum+=ary[i];
		return sum;
	}
	static long sum(long[] ary){
		long sum=0;
		for(int i=0; i<ary.length; i++) sum+=ary[i];
		return sum;
	}
	static void tblSort(int[][] tbl){
		Arrays.sort(tbl, new Comparator<int[]>(){
			@Override
			public int compare(int[] a, int[] b){
				if(a[0]==b[0]){
					return b[1]-a[1];
				}else{
					return b[0]-a[0];
				}
			}
		});
	}
}