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.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner scan = new Scanner(System.in);
        int N = scan.nextInt();
        int[] num = new int[N];
        
        for(int i = 0; i < N; i++) {
            num[i] = scan.nextInt();
        }
        
        boolean[] lightON = new boolean[N];
        int buttonNum = num[0];
        lightON[0] = true;

        int count = 0;
        int answer = -1;
        
        while(true) {
            lightON[buttonNum-1] = true;
            count++;
            
            if(lightON[1] == true) {
                answer = count;
                break;
            }
            
            buttonNum = num[buttonNum-1];
            if(lightON[buttonNum-1] == true) {
                break; 
            }
        }
        System.out.println(answer);
    }
}