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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Math;

class Program{
  public static void Main(){

    int n = int.Parse(Console.ReadLine());
    int[] a = new int[n];
    for(int i=0; i<n; i++){
      a[i] = int.Parse(Console.ReadLine());
    }
    int cnt = 0;
    var b = Enumerable.Repeat(false,n).ToArray();
    
    var prg = new Program();
    int ans = prg.button(a,b,cnt,0);
    Console.WriteLine(ans);
  }
  
  public int button(int[] a,bool[] b,int cnt,int index){
    
    if(b[index] == true) return -1;
    if(index == 1) return cnt;
    
    b[index] = true;
    cnt++;
    return button(a,b,cnt,a[index]-1);
  }
}