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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics.CodeAnalysis;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine()); 
            List<int> button = new List<int>();
            for (int i = 0; i < N; i++) 
            {
                button.Add(int.Parse(Console.ReadLine()));
            }

            int p = 0;
            int count = 0;
            while (true) 
            {
                count++;
                if (button[p] == 2) 
                {
                    Console.WriteLine(count);
                    break;
                }
                int b = button[p] - 1;
                if (button[button[p] -1] - 1 == p) 
                {
                    Console.WriteLine(-1);
                    break;
                }
                p = button[p] -1 ;
            }
        }
    }
}