Problem:
Score : 200 points

Problem Statement

It is November 18 now in Japan. By the way, 11 and 18 are adjacent Lucas numbers.

You are given an integer N. Find the N-th Lucas number.

Here, the i-th Lucas number L_i is defined as follows:

L_0=2

L_1=1

L_i=L_{i-1}+L_{i-2} (i≥2)

Constraints

1≤N≤86

It is guaranteed that the answer is less than 10^{18}.

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the N-th Lucas number.

Sample Input 1

5

Sample Output 1

11

L_0=2

L_1=1

L_2=L_0+L_1=3

L_3=L_1+L_2=4

L_4=L_2+L_3=7

L_5=L_3+L_4=11

Thus, the 5-th Lucas number is 11.

Sample Input 2

86

Sample Output 2

939587134549734843

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.Threading.Tasks;
using System.IO;
using System.Diagnostics;
class Program
{
    public static Scanner input;
    static void Main()
    {
        input = new Scanner();
        int n = input.Int();
        var arr = new long[n+1];
        for (int a = 0; a <= n; a++)
        {
            if (a == 0)
            {
                arr[a] = 2;
            }
            else if (a == 1)
            {
                arr[a] = 1;
            }
            else
            {
                arr[a] = arr[a - 2] + arr[a - 1];
            }
        }
        WriteLine(arr[n]);
    }
}

class Scanner
{

    public Scanner()
    {
    }

    public void skip()
    {
        ReadLine();
        return;
    }
    public string String()
    {
        return ReadLine();
    }
    public string[] splitString()
    {
        return ReadLine().Split();
    }
    public string[] linesString(int len)
    {
        var arr = new string[len];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine();
        }
        return arr;
    }
    public string[][] jaggedArrayString(int len)
    {
        var arr = new string[len][];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine().Split();
        }
        return arr;
    }
    public int Int()
    {
        return int.Parse(ReadLine());
    }
    public int[] splitInt()
    {
        return ReadLine().Split().Select(i => int.Parse(i)).ToArray();
    }
    public int[] linesInt(int len)
    {
        var arr = new int[len];
        for (int a = 0; a < len; a++)
        {
            arr[a] = int.Parse(ReadLine());
        }
        return arr;
    }
    public int[][] jaggedArrayInt(int len)
    {
        var arr = new int[len][];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine().Split().Select(i => int.Parse(i)).ToArray();
        }
        return arr;
    }
    public long Long()
    {
        return long.Parse(ReadLine());
    }
    public long[] splitLong()
    {
        return ReadLine().Split().Select(i => long.Parse(i)).ToArray();
    }
    public long[] linesLong(int len)
    {
        var arr = new long[len];
        for (int a = 0; a < len; a++)
        {
            arr[a] = long.Parse(ReadLine());
        }
        return arr;
    }
    public long[][] jaggedArrayLong(int len)
    {
        var arr = new long[len][];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine().Split().Select(i => long.Parse(i)).ToArray();
        }
        return arr;
    }
    public double Double()
    {
        return double.Parse(ReadLine());
    }
    public double[] splitDouble()
    {
        return ReadLine().Split().Select(i => double.Parse(i)).ToArray();
    }
    public double[] linesDouble(int len)
    {
        var arr = new double[len];
        for (int a = 0; a < len; a++)
        {
            arr[a] = double.Parse(ReadLine());
        }
        return arr;
    }
    public double[][] jaggedArrayDouble(int len)
    {
        var arr = new double[len][];
        for (int a = 0; a < len; a++)
        {
            arr[a] = ReadLine().Split().Select(i => double.Parse(i)).ToArray();
        }
        return arr;
    }
}