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.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

public class Program
{
    #region Standard I/O
    readonly TextReader input;
    readonly TextWriter output;

    X[] ReadLine<X>(Func<string, X> func)
    {
        return input.ReadLine().Split(' ').Select(func).ToArray();
    }

    void WriteLineOne(object obj)
    {
        output.WriteLine("{0}", obj);
    }

    void WriteLineMany(params object[] objects)
    {
        output.WriteLine(string.Join(" ", objects.Select(obj => obj.ToString())));
    }
    #endregion

    int n;
    int[] js;

    void Read()
    {
        var l = ReadLine(int.Parse);
        n = l[0];
        js = Enumerable.Range(0, n).Select(_ => int.Parse(input.ReadLine()) - 1).ToArray();
    }

    int Solve()
    {
        var done = new bool[n];

        var i = 0;
        var d = 1;

        while (true)
        {
            if (done[i]) return -1;
            done[i] = true;

            var j = js[i];
            if (j == 1) return d;

            i = j;
            d++;
        }
    }

    public void Run()
    {
        Read();
        WriteLineOne(Solve());
    }

    public Program(TextReader input, TextWriter output)
    {
        this.input = input;
        this.output = output;
    }

    public static void Main(string[] args)
    {
        new Program(Console.In, Console.Out).Run();
    }
}