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: Runtime Error)

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

namespace ConsoleApplication
{
    class Program
    {
        static void Main()
        {
            new Solution().answer();
        }
    }
    class Solution
    {
        string n;
        string[] input;
        public Solution()
        {
            n = Console.ReadLine();
            input = Console.ReadLine().Split(' ');
        }
        public void answer()
        {
            int i = 1;
            int j = 0;
            int a = 0;
            int b = 0;
            int answer = 0;
            int k = 0;
            int test=0;

            for (a = 2; a <= Convert.ToInt32(n) - 1; a++)
            {
                test = test + Convert.ToInt32(input[a]) - (a + 1);
            }

            if (test>=0)
            {
                Console.WriteLine("-1");
            }
            else
            {
                while (i != 2)
                {
                    i = Convert.ToInt32(input[i - 1]);  ///第i-1個項目
                    k = Convert.ToInt32(input[i - 1]) - 1;
                    if ((Convert.ToInt32(input[k]) == i) || answer >= Convert.ToInt32(n))
                    {
                        Console.WriteLine("-1");
                        i = 2;
                        j = 1;
                    }
                    else
                    {
                        answer = answer + 1;
                    }
                }

                if (j == 0)
                {
                    Console.WriteLine(answer.ToString());
                }
            }
        }
    }
}