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 <bits/stdc++.h>

using namespace std;

typedef long long lli;
typedef vector<lli> vll;
typedef vector<bool> vbl;
typedef vector<vector<lli>> mat;

lli n;
vll dp;

lli l(lli n){
	if(n == 0) return 2;
	if(n == 1) return 1;
	if(dp[n]) return dp[n];
	return dp[n] = l(n-1)+l(n-2);
}

int main(){
	cin >> n;
	dp = vll(100);
	cout << l(n) << endl;
	return 0;
}