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)
			{   
			    Scanner scanner = new Scanner(System.in);
			    int N = scanner.nextInt();
			    int[] a = new int[N];
			    int count = 0;
			    int v = 1;
			    int flg = 0;
			    
			    for (int i = 0; i < N; i++) {
			    	a[i] = scanner.nextInt();
			    } 
			    
			    for (int i = 0; i < N; i++) {
			    	v = a[v-1];
			    	
			    	count ++;
			    	if (v == 2) {
			    		System.out.println(count);
			    		count = 0;
			    		break;
			    	}
			    	
			    }
			    
			    if (count == N) {
			    	System.out.println(-1);
			    }
		}
		}