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.Collections.Generic;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;

using System;
using System.Linq;

namespace ConsoleApp1
{
    class Program
    {
        public class Button
        {
            public int Index { get; set; }
            public int Next { get; set; }
            public bool Flashed { get; set; }
        }

        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var buttons = new List<Button>();
            for(var i =0;i<N;i++)
            {
                buttons.Add(new Button() { Index = i, Next = int.Parse(Console.ReadLine()), Flashed = false });
            }
            var next = 0;
            var result = 0;
            while(!buttons[next].Flashed)
            {
                if(next==1)
                {
                    Console.WriteLine(result);
                    return;
                }
                buttons[next].Flashed = true;
                result++;
                next = buttons[next].Next-1;
            }
            Console.WriteLine(-1);
        }
    }
}