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 System.Text;
using System.Threading.Tasks;

namespace Contest
{
	class Program
	{
		static void Main()
		{
            int N = int.Parse(Console.ReadLine());
            var a = new int[N];
            var flag = new bool[N];
            flag[0] = true;
            for (int x = 0; x < N; x++)
            {
                a[x] = int.Parse(Console.ReadLine()) - 1;
            }
            int ans = 0, i = 0;
            for (; i != 1; ans++)
            {
                if (flag[a[i]])
                {
                    break;
                }
                else
                {
                    flag[a[i]] = true;
                }
                i = a[i];
            }
            Console.WriteLine(i == 1 ? ans : -1);
#if DEBUG
            Console.ReadKey();
#endif
		}
	}
}