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.Collections.Generic;
using static System.Console;

class Program {
	static void Main() {
		var N = NextInt();
		var a = new int[N];
		for (var i = 0; i < N; i++) {
			a[i] = NextInt();
		}
		var j = 1;
		for (var i = 1; i <= N; i++) {
			j = a[j - 1];
			if (j == 2) {
				WriteLine(i);
				return;
			}
		}
		WriteLine(-1);
	}

	static int NextInt() {
		return int.Parse(NextString());
	}

	static string NextString() {
		var result = new List<char>();
		while (true) {
			int next = Read();
			if (next < 0)
				break;
			var nextChar = (char)next;
			if (!char.IsWhiteSpace(nextChar))
				result.Add(nextChar);
			else if (nextChar != '\r')
				break;
		}
		return string.Join("", result);
	}
}