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: Wrong Answer)

    import java.util.Scanner;
    
    class Main {
     
        public static void main(String[] args) {
            Scanner sc = new Scanner(System.in);
            int N = sc.nextInt();
            boolean[] n = new boolean[N+1];
            boolean isEnd = false;
            for(int i = 1; i <=N; i++) {
            	n[i] = false;
            }
            int[] a = new int[N+1];
            for(int i = 1; i <= N; i++) {
            	a[i] = sc.nextInt();
            }
            sc.close();
            
            int count = 0;
            int i = 1;
            
            while(i < 100000 ) {
            	if( n[i] == false ) {
            		n[i] = true;
            		count ++;
            		if( a[i] == 2 ) {
            			break;
            		}
            		i = a[i];
     			}else {
     				count = -1;
     				break;
             	}
            }
	         System.out.println(count);
;        }
    }