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.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		try {
			int n = Integer.parseInt(sc.nextLine());

			Map<Integer, String> map = new HashMap<Integer, String>();
			int next = 1;
			int count = 0;
			for (int i = 1; i <= n; i++) {
				String s = sc.nextLine();
				if (i == next) {
					next = Integer.parseInt(s);
					count++;
					while (next < i) {
						if (next == 2) {
							System.out.println(count);
							return;
						}
						if (!map.containsKey(next)) {
							// すでに押したことがあるボタンに戻ってしまった場合は到達不可
							System.out.println(-1);
							return;
						}
						next = Integer.parseInt(map.get(next));
						count++;
					}
				} else {
					map.put(i, s);
				}
			}
		} finally {
			sc.close();
		}
	}
}