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.Collections;
using System.Collections.Generic;
using System.ComponentModel;
using System.ComponentModel.Design;
using System.IO.Compression;
using System.Linq;
using System.Numerics;
using System.Text;

namespace Atcoder
{
    class Program
    {
        private const long COMDIV = 1000000007;
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            Console.WriteLine(Cal(n));
        }
        static Dictionary<int,long> memo = new Dictionary<int, long>();
        static long Cal(int val)
        {
            if (val == 0) return 2;
            if (val == 1) return 1;
            long left;
            long right;
            if (memo.ContainsKey(val - 1))
            {
                left = memo[val - 1];
            }
            else
            {
                left = Cal(val - 1);
                memo.Add(val - 1,left);
            }
            if (memo.ContainsKey(val - 2))
            {
                right = memo[val - 2];
            }
            else
            {
                right = Cal(val - 2);
                memo.Add(val - 2, right);
            }
            return left + right;
        }
        
    }
}