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: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class Main {
    public static void main(String[] args) {
        try {
            // 標準入力
            InputStreamReader isr = new InputStreamReader(System.in);
            BufferedReader br = new BufferedReader(isr);
            int n = Integer.parseInt(br.readLine());
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = Integer.parseInt(br.readLine());
            }
            int now = a[0];
            int count = 1;
            ArrayList<Integer> list = new ArrayList<Integer>();
            while (true) {
                if (now == 2) {
                    System.out.println(count);
                    break;
                } else {
                    boolean flag = false;
                    for (int i = 0; i < list.size(); i++) {
                        if (now == list.get(i)) {
                            flag = true;
                            break;
                        }
                    }
                    if (flag) {
                        System.out.println(-1);
                        break;
                    } else {
                        list.add(now);
                    }
                }
                now = a[now - 1];
                count++;
            }
        } catch (IOException e) {
            e.printStackTrace();
           }
    }
}