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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.ComponentModel.DataAnnotations;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            long N = long.Parse(Console.ReadLine());
            long[] btnNum = new long[N];
            for (int i = 0; i < N; i++)
            {
                btnNum[i] = long.Parse(Console.ReadLine());
            }
            long num = 0;
            int cnt = 0;
            List<long> oldNum = new List<long>();
            while (true)
            {
                //該当ボタンとその先を見る
                //num == numはたどり着けないのでbreak
                if (num == btnNum[num] - 1)
                {
                    Console.WriteLine(-1);
                    return;
                }
                if (oldNum.Contains(num))
                {
                    Console.WriteLine(-1);
                    return;
                }

                // 該当番号が2なら終わり
                if (btnNum[num] == 2)
                {
                    Console.WriteLine(cnt + 1/*最初のbtn1の分*/);
                    return;
                }
                else
                {
                    oldNum.Add(num);
                    //該当の番号取得
                    num = btnNum[num] - 1;
                    //掛かった回数
                    cnt++;
                }
            }
        }
    }
}
// 文字列の入力
//string s = Console.ReadLine();

// 整数の入力
//long n = long.Parse(Console.ReadLine());

// 文字列配列の入力
//string[] inputStrArray = Console.ReadLine().Split(' ');

// 整数配列の入力
//long[] inputLongArray = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();


//Console.WriteLine(ans);