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.

Examples

Input

3
3
1
2


Output

2


Input

4
3
4
1
2


Output

-1


Input

5
3
3
4
2
4


Output

3


import java.util.Scanner;

public class Main{

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		new Main().start();
	}
	void start(){
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int[] a = new int[n];
		for(int i = 0; i < n; i++){
			a[i] = in.nextInt();
		}
		int count = 0;
		int i = 0;
		while(true){
			if(i == 1){
				break;
			}else if(count > 100000){
				break;
			}
			i = a[i]-1;
			count++;
		}
		if(count != 100001){
			System.out.println(count);
		}else{
			System.out.println(-1);
		}
		in.close();
	}
}
