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-csc 3.5.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using System.IO;
using static System.Console;


namespace atcorder2
{
    class Program
    {
        public static long Read()
        {

            return long.Parse(Console.ReadLine());
        }

        public static long[] Reads()
        {
            return Console.ReadLine().Split().Select(long.Parse).ToArray();
        }

       
       
        public static long gcd(long x,long y)
        {
            if (x < y) gcd(y, x);
            
            while (y > 0)
            {
                var z = x % y;
                x = y;
                y = z;
            }
            return x;
        }

        public static long lcm(long x,long y)
        {
            return x * y / gcd(x, y);
        }



        static void Main(string[] args)
        {
            var sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);


            var n = Read();
            var a = new long[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = Read();
            }
            var s = a[0];
            var ans = 1;
            bool f = false;
            for (int i = 1; i < n; i++)
            {
                if (s == 2)
                {
                    f = true;
                    break;
                }
                ans++;
                s = a[s-1];
            }

            WriteLine(f?ans:-1);

          
          
            Out.Flush();
        }
    }
}