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.BufferedReader;
import java.io.InputStreamReader;

public class Main {
    public static void main(String[] args) throws Exception {
        // Here your code !
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        
        int n = Integer.parseInt(br.readLine());
        
        int[] data = new int[n+1];
        for(int i = 1; i < n+1; i ++){
            data[i] = Integer.parseInt(br.readLine());
        }
        
        int[] light = new int[n+1];
        int[] pushed = new int[n+1];
        light[1] = 1;
        pushed[1] = 0;
        for(int i = 2; i <= n ; i++){
            light[i] = 0;
            pushed[i] = 0;
        }
        
        int count = 0;
        boolean achieve = false;
        //光っているボタンを探す
        int next = 1;
        while(true){
            boolean breakFlag = false;
            
            
            //System.out.println("count = "+count);
            for(int i = next; i <= n; i++){
                //System.out.println("i = "+i);
                if(light[i] == 1){
                    //System.out.println(i + " was pushed next is "+data[i]);
                    light[i] = 0;
                    light[data[i]] = 1;
                    next = data[i];
                    pushed[i] = 1;
                    count++;
                    
                    if(data[i] == 2){
                        //System.out.println("clear");
                        achieve = true;
                        breakFlag = true;
                    }
                    
                    else if(pushed[data[i]] == 1){
                        breakFlag = true;
                    }
                    
                    break;
                }
                /*
                else if(light[i] > 1 && count > 1){
                    //System.out.println("i = "+i+" failed");
                    breakFlag = true;
                }*/
            }
            
            //System.out.println(breakFlag);
            if(breakFlag){
                break;
            }
        }
        
        if(achieve){
            System.out.println(count);
        }
        else {
            System.out.println(-1);
        }
        
    }
}