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.Linq;
using System.Collections.Generic;
using System.IO;
using System.Diagnostics;
using System.Text;

public class Program{
    public static void Main(){
        var watch = new Stopwatch();
        watch.Start();
        var isTest = false;
        var stream = new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false};
        Console.SetOut(stream);
        TextReader reader;
        string filename="";

        if(filename.Length!=0){
            reader = new StreamReader(filename);
        }else{
            reader = Console.In;
        }

        var n = int.Parse(reader.ReadLine());
        var lis = new int[n];
        for(var i=0; i<n; i++){
            lis[i] = int.Parse(reader.ReadLine())-1;
        }

        var passed = new bool[n];
        var now = 0;
        var cnt = 0;
        while(now!=1){
            if(passed[now]){
                cnt = -1;
                break;
            }
            passed[now] = true;
            now = lis[now];
            cnt++;
        }
        Console.WriteLine(cnt);

        watch.Stop();
        if(isTest){
            Console.WriteLine($"実行時間{watch.ElapsedMilliseconds}ミリ秒");
        }
        Console.Out.Flush();
    }
}