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.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		int count = 0;
		Scanner sc = new Scanner(System.in);
		count = sc.nextInt();
		sc.nextLine();
		int[] array = new int[count];
		int[] array2 = new int[count];
		int number = 0;
		int number2 = 0;
		boolean flag = false;
		for (int i = 0; i < count; i++) {
			array[i] = Integer.valueOf(sc.nextLine());
			array2[i] = array[i];
			if (array[i] == 1) {
				number = i;
				flag = true;
			}
			if (array[i] == 2) {
				number2 = i;
			}
		}
		sc.close();
		boolean stopFlag = false;
		int result = 0;
		boolean flag2 = false;
		while(!stopFlag) {
			
			if (!flag && !flag2) {
				Arrays.sort(array2);
				if (array2[0] == 2) {
					result++;
					number = array2[1] - 1;
				} else {
					result = -1;
					break;
				}
				flag2 = true;
			}
			if (array[number] == 2) {
				break;
			} else {
				result++;
				number = array[number] - 1;
			}
			if (result > count) {
				result = -1;
				break;
			}
		}
		
		if (!flag) {
			result = result + 1;
		}
		
		System.out.println(result);
	}
}