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)

#define _USE_MATH_DEFINES
#include<bits/stdc++.h>
#define int long long
#define rep(i,n) for(int i=0;i<n;i++)
#define Rep(i,a,b) for(int i=0;i<b;i++)
#define REP(i,a,b) for(int i=0;i<=b;i++)
#define rev(i,n) for(int i=n-1;i>=0;i--)
#define vi vector<int>
#define vvi vector<vi>
#define pb push_back
#define pi pair<int,int>
#define vp vector<pair<int,int>>
#define mp make_pair
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second
#define MEMSET(a) memset(a,0,sizeof(a))
#define inf (1ll<<60)
#define Yes(f) cout <<(f?"Yes":"No")<<endl//fが真の場合Yesを出力、偽の場合Noを出力
#define yes(f) cout <<(f?"yes":"no")<<endl
#define YES(f) cout <<(f?"YES":"NO")<<endl
#define SORT(v) sort(all(v))
#define RSORT(v) sort(all(v),greater<int>())

using namespace std;

const int mod=1e9+7;

int last_two=2;
int last_one=1;
signed main(){
    int n;
    cin >> n;
    int ans=1;
    rep(i,n-1)
    {
        ans=last_one+last_two;
        last_two=last_one;
        last_one=ans;
    }

    cout << ans << endl;
}