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.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		final long n = sc.nextInt();

		List<Integer> a = new ArrayList<>();

		for (int i = 0; i < n; i++) {
			a.add(sc.nextInt());
		}

		sc.close();

		boolean continueFlag = true;
		int count = 0;
		int previ = 0;
		int prevp = 0;
		while (continueFlag) {

			if (count == 0) {
				previ = a.get(0);
				count++;
				continue;
			}

			if (previ == 2) {
				continueFlag = false;
				continue;
			} else if ((prevp + 1) == a.get(previ - 1)) {
				count = -1;
				continueFlag = false;
				continue;
			} else {
				prevp = previ - 1;
				previ = a.get(previ - 1);
				count++;
			}

		}

		System.out.print(count);

	}

}