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

class TEST
{
    static void Main()
    {
        Sol mySol = new Sol();
        mySol.Solve();
    }
}

class Sol
{

    public Sol()
    {

        int N = int.Parse(Console.ReadLine());
        int[] a = new int[N+1];
        bool[] idxI = new bool[N + 1];
        int index = 1;
        for (int i = 1; i <= N; i++) {
            a[i] = int.Parse(Console.ReadLine());
            idxI[i] = false;
        }

        int step =0;
        idxI[1] = true;
        while (index != 2)
        {
            // press index button
            
            step++;
            index = a[index];
            if (idxI[index])
            {
                Console.WriteLine(-1); return;
            }
            else if (index == 2)
            {
                Console.WriteLine(step); return;
            }
            else
            {
                idxI[index] = true;
            }
        }

    }


    public void Solve()
    {

    }

    static String rs() { return Console.ReadLine(); }
    static int ri() { return int.Parse(Console.ReadLine()); }
    static long rl() { return long.Parse(Console.ReadLine()); }
    static double rd() { return double.Parse(Console.ReadLine()); }
    static String[] rsa(char sep = ' ') { return Console.ReadLine().Split(sep); }
    static int[] ria(char sep = ' ') { return Array.ConvertAll(Console.ReadLine().Trim().Split(sep), e => int.Parse(e)); }
    static long[] rla(char sep = ' ') { return Array.ConvertAll(Console.ReadLine().Trim().Split(sep), e => long.Parse(e)); }
    static double[] rda(char sep = ' ') { return Array.ConvertAll(Console.ReadLine().Trim().Split(sep), e => double.Parse(e)); }


}