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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
#if !DEBUG
    using System.IO;
#endif

public class Program {
    public static void Main() {
        #region SetAutoFlushIsFalse
#if !DEBUG
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
#endif
        #endregion
        n = ReadLib.ReadAsInt();
        aArr = ReadLib.ReadNTimesAsInt(n);

        var val = CalcVal(n, aArr);
        Console.WriteLine(val);
        #region Flush
#if !DEBUG
        Console.Out.Flush();
        sw.Close();
#endif
        #endregion

    }

    static int n;
    static int[] aArr;
    static int[] resultLog;

    private static int CalcVal(int n, int[] aArr) {
        resultLog = new int[n];

        // self loop is error
        aArr.Where((i, a) => a == i - 1)
            .ToList()
            .ForEach(i => resultLog[i - 1] = -1);

        return canPush(2, 0, new HashSet<int>());

        
    }

    private static int canPush(int current, int cnt, HashSet<int> prevHistory) {
        if (current == 1) {
            resultLog[current - 1] = cnt;
            return cnt;
        }

        var memo = resultLog[current - 1];
        if (memo != 0) {
            return memo == -1 ? -1 : cnt + resultLog[current - 1];
        }

        var currentHistory = new HashSet<int>(prevHistory);
        if (!currentHistory.Add(current)) {
            // loop
            resultLog[current - 1] = -1;
            return -1;
        }

        var nextNumbers = Enumerable.Range(0, n).Where(i => aArr[i] == current).Select(i => i + 1);
        var results = nextNumbers
            .Select(f => canPush(f, cnt + 1, currentHistory))
            .Where(v => v != -1)
            .ToArray();

        if (results.Count() == 0) {
            resultLog[current - 1] = -1;
            return -1;
        }

        var result = results.Min();
        resultLog[current - 1] = result;
        return result;
    }
}

static class ReadLib {
    public static long ReadAsLong() {
        return long.Parse(Console.ReadLine());
    }

    public static int ReadAsInt() {
        return int.Parse(Console.ReadLine());
    }

    public static int[] ReadAsIntArray() {
        return Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
    }

    public static long[] ReadAsLongArray() {
        return Console.ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
    }

    public static ulong[] ReadAsULongArray() {
        return Console.ReadLine().Split(' ').Select(s => ulong.Parse(s)).ToArray();
    }

    public static string[] ReadAsStringArray() {
        return Console.ReadLine().Split(' ');
    }

    public static int[] ReadNTimesAsInt(int n) {
        return Enumerable.Range(1, n).Select(s => int.Parse(Console.ReadLine())).ToArray();
    }

    public static int[][] ReadNTimesAsIntArray(int n) {
        return Enumerable.Range(1, n).Select(s => ReadAsIntArray()).ToArray();
    }

}