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 {
	static Scanner sc = new Scanner(System.in);

	public static void main(String[] args) {
		int N = sc.nextInt();
		int[] a = new int[N];
		for (int i = 0; i < N; i++) {
			a[i] = sc.nextInt();
		}
		boolean[] dist = new boolean[N];

		int btn = 0;
		int ans = -1;
		int cnt = 0;
		for (int i = 0; i < N; i++) {
			if (dist[btn]) break;
			dist[btn] = true;
			
			if (a[btn] == 2) {
				ans = cnt + 1;
				break;
			}
			btn = a[btn] - 1;
			cnt++;
		}
		
		System.out.println(ans);
	}
}