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.Linq;
using System.Text;

class Program
{
    static void Main(string[] args)
    {
        string str = Console.ReadLine();
        int N = int.Parse(str);
        int[] a = new int[N+1];
        bool[] b = new bool[N+1];
        int current;
        int cnt = 1;

        for(int i = 1; i < N+1; i++){
            str = Console.ReadLine();
            a[i] = int.Parse(str);
        }

        current = a[1];
        b[1] = true;
        for(int i = 1; i < N; i++){
            if(!b[current]){
                if(current == 2){
                    Console.WriteLine(cnt);
                    return;
                }
                cnt++;
                current = a[current];
            }else{
                Console.WriteLine(-1);
                break;
            }
        }
        if(cnt == N){
            Console.WriteLine(-1);
        }
    }
}