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;

namespace atcoder_ABC065B
{
    class MainClass
    {
        public static void Main(string[] args)
        {
			int buttonCount = int.Parse(Console.ReadLine());
			Dictionary<string, string> lightPatterns = new Dictionary<string, string>();
			for (int i = 0; i < buttonCount; i++)
			{
				lightPatterns[(i + 1).ToString()] = Console.ReadLine();
			}

			int pushCount = 0;
			string lightingButton = "1";
            while (true)
			{
				if (!lightPatterns.ContainsKey(lightingButton)) {
					Console.WriteLine("-1"); 
					return;	
				}

				string pushedButton = lightingButton;

				lightingButton = lightPatterns[lightingButton];
				lightPatterns.Remove(pushedButton);

				pushCount++;

				if (lightingButton == "2") {
					Console.WriteLine(pushCount); 
					return;	
				}
			}
        }
    }
}