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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

public class Main {

    void solve() {
        int n = in.nextInt();
        long a = 2;
        long b = 1;
        if (n == 1) {
            out.println(a);
            return;
        }
        if (n == 2) {
            out.println(b);
            return;
        }
        for (int i = 2; i <= n; i++) {
            long c = a + b;
            a = b;
            b = c;
            if (i == n) {
                out.println(c);
            }
        }
    }

    Scanner in;
    PrintWriter out;

    void run() {
        try {
            in = new Scanner(new File("Main.in"));
            out = new PrintWriter(new File("Main.out"));

            solve();

            out.close();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }

    void runIO() {

        in = new Scanner(System.in);
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }

    class Scanner {
        BufferedReader br;
        StringTokenizer st;

        public Scanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public Scanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

        private boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        private int skip() {
            int b;
            while ((b = read()) != -1 && isSpaceChar(b)) ;
            return b;
        }

        private int read() {
            int res = -1;
            try {
                res = br.read();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return res;
        }

        char[] nextCharArray(int size) {
            char[] buf = new char[size];
            int b = skip(), p = 0;
            while (p < size && !(isSpaceChar(b))) {
                buf[p++] = (char) b;
                b = read();
            }
            return size == p ? buf : Arrays.copyOf(buf, p);
        }

        char[][] nextCharMap(int n, int m) {
            char[][] map = new char[n][];
            for (int i = 0; i < n; i++) {
                map[i] = nextCharArray(m);
            }
            return map;
        }

        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }

    public static void main(String[] args) {
        new Main().runIO();
    }
}