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.Generic;
using System.Linq;

namespace ConsoleApp1
{
    public static class MyExtensions
    {
        public static string Slice(this string str, int start = 0, int stop = 0)
        {
            if (start > str.Length || stop > str.Length || start < 0 || stop < 0)
                return "";

            if (stop == 0) stop = str.Length;
            return str.Substring(start, stop - start);
        }
    }

    class Program
    {
        static void Main(string[] args)
        {
            B();
        }

        static void B()
        {
            var N = ReadInt();
            Func<long, long> func = null;
            var memo = new Dictionary<long, long>();
            func = (i) =>
            {
                if (i == 0)
                    return 2;
                if (i == 1)
                    return 1;

                if (memo.ContainsKey(i))
                {
                    return memo[i];
                }

                memo[i] = func(i - 1) + func(i - 2);
                return memo[i];
            };
            Console.WriteLine(func(N)); 
        }

        public static IEnumerable<int> Range(int start, int stop)
        {
            if (start < 0 || stop < 0)
                throw new Exception("0未満");

            if (start > stop || (start == 0 && stop == 0))
                return new List<int>();

            return Enumerable.Range(start, stop - start);
        }

        public static bool IsDigit(string str)
        {
            var i = 0;
            return int.TryParse(str, out i);
        }

        public static int DigitsSum(long num)
        {
            return num.ToString().Select(x => x.ToString()).Sum(int.Parse);
        }

        public static int[] ToIntArray(string str)
        {
            return str.Select(x => x.ToString()).Select(int.Parse).ToArray();
        }

        public static string Read()
        {
            return Console.ReadLine();
        }

        public static IList<int> ReadIntInputs()
        {
            return Read().Split(' ').Select(int.Parse).ToList();
        }

        public static int ReadInt()
        {
            return int.Parse(Read());
        }

        public static IList<string> ReadInputs()
        {
            return Read().Split(' ').ToList();
        }
    }
}