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)

#pragma warning disable IDE0011
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using static System.Math;
using static Extentions;

class IO
{
    int idx;
    string[] line;

    public void R(params char[] sep) { line = Console.ReadLine().Split(sep); idx = 0; }
    public string S => line[idx++];
    public string[] Ss => line.Skip(idx++).ToArray();
    public char C => char.Parse(line[idx++]);
    public char[] Cs => line.Skip(idx++).Select(char.Parse).ToArray();
    public int I => int.Parse(line[idx++]);
    public int[] Is => line.Skip(idx++).Select(int.Parse).ToArray();
    public long L => long.Parse(line[idx++]);
    public long[] Ls => line.Skip(idx++).Select(long.Parse).ToArray();
    public double F => double.Parse(line[idx++]);
    public double[] Fs => line.Skip(idx++).Select(double.Parse).ToArray();
    public decimal D => decimal.Parse(line[idx++]);
    public decimal[] Ds => line.Skip(idx++).Select(decimal.Parse).ToArray();
    public BigInteger B => BigInteger.Parse(line[idx++]);
    public BigInteger[] Bs => line.Skip(idx++).Select(BigInteger.Parse).ToArray();

    public void Write(params object[] xs)
    {
        Console.Write(xs.First());
        foreach (var x in xs.Skip(1)) Console.Write(" " + x);
        Console.WriteLine();
    }
}

static class Extentions
{
}

static class Program
{
    static void Main()
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        Solve(new IO());
        Console.Out.Flush();
    }

    static void Solve(IO io)
    {
        io.R(); var n = io.I;
        var a = new int[n + 1];
        for (var i = 1; i <= n; i++) { io.R(); a[i] = io.I; }

        var set = new HashSet<int> { 1 };
        var next = 1;
        var cnt = 0;

        while (true)
        {
            cnt++;
            next = a[next];

            if (next == 2)
            {
                io.Write(cnt);
                return;
            }
            if (!set.Add(next))
            {
                io.Write(-1);
                return;
            }
        }
    }
}