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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ABC065_B_Trained
{
	internal class Program
	{
		public static void Main(string[] args)
		{
			int n = int.Parse(Console.ReadLine());
			List<int> aList = new List<int>(n);
			for(int i = 0; i < n; i++)
				aList.Add(int.Parse(Console.ReadLine()));

			int index = 1;
			List<int> pushedButtonIndex = new List<int>();
			int count = 0;
			while (index != 2)
			{
				if (pushedButtonIndex.Any(value => value == index))
				{
					Console.WriteLine(-1);
					return;
				}
				
				pushedButtonIndex.Add(index);
				index = aList[index - 1];
				count++;
			}
			
			Console.WriteLine(count);
		}
	}
}