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.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder.ABC
{
    class QuestionB
    {
        public static void Main(string[] args)
        {
            long n = int.Parse(Console.ReadLine());

            var a = new int[n];

            for (int i = 0; i < n; i++) {
                a[i] = int.Parse(Console.ReadLine()) - 1;
            }

            var hash = new HashSet<int>();

            var last = a[0];

            var result = -1;

			for (int i = 1; ; i++) {
                if (last == 1) {
                    result = i;
                    break;
                }

                if (hash.Contains(last)) {
                    break;
				}

                hash.Add(last);
                last = a[last];
            }

            Console.WriteLine(result);
        }

        public static long Pow(long a, long b, long mod = 0L)
        {
            var temp = a;
            var ans = 1L;

            for(int i = 1; i <= b;i <<= 1) {
                if((b & i) != 0) {
                    ans *= temp;
                    if (mod != 0) {
                        ans %= mod;
                    }
                }

                temp *= temp;
                if(mod != 0) {
                    temp %= mod;
                }
            }

            return ans;
        }
    }
}