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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
using namespace std;

typedef long long ll;

ll memo[10000] = {0};

ll lucas(int x) {
    if (x == 0) return 2;
    else if (x == 1) return 1;
    else if (memo[x] != 0) return memo[x];
    return memo[x] = lucas(x - 2) + lucas(x - 1);
}

int main() {
    // input
    int N;
    cin >> N;

    // solve
    ll ans = lucas(N);

    // output
    cout << ans << endl;

    return 0;
}