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.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            new Program().Solve(new MyInputStream(Console.In, ' '));
            Console.Out.Flush();
        }

        public void Solve(MyInputStream cin)
        {
            var N = cin.ReadInt();
            if (N == 0) { WriteLine(2); return; }
            if (N == 1) { WriteLine(1); return; }
            var L0 = 2L;
            var L1 = 1L;
            var L = 0L;
            for (int i = 1; i < N; ++i)
            {
                L = L0 + L1;
                L0 = L1;
                L1 = L;
            }
            WriteLine(L);
        }
    }

    public class MyInputStream
    {
        private readonly System.IO.TextReader _stream;
        private char separator = ' ';
        private Queue<string> inputStream;
        public MyInputStream(System.IO.TextReader s, char separator = ' ')
        {
            this.separator = separator;
            this._stream = s;
            inputStream = new Queue<string>();
        }
        public string Read()
        {
            if (inputStream.Count != 0) return inputStream.Dequeue();
            string[] tmp = _stream.ReadLine().Split(separator);
            for (int i = 0; i < tmp.Length; ++i)
                inputStream.Enqueue(tmp[i]);
            return inputStream.Dequeue();
        }
        public string ReadLine() { return _stream.ReadLine(); }
        public int ReadInt() { return int.Parse(Read()); }
        public long ReadLong() { return long.Parse(Read()); }
        public double ReadDouble() { return double.Parse(Read()); }
        public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read(); return ret;}
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt(); return ret;}
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong(); return ret;}
    }
}