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 (GCC 9.2.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#define rep(i,n) for(int i=0;i<n;i++)
int gcd(int a, int b){
    int r=1;
    while(r!=0){
        r=a%b;
        a=b;
        b=r;
    }
    return a;
}
typedef long long ll;
void revStr(char* str){
    int size = strlen(str);
    int i,j;
    char tmp = {0};
    for(i = 0, j = size - 1; i < size / 2; i++, j--){
        tmp = str[i];
        str[i] = str[j];
        str[j] = tmp;
    }return;
}
typedef struct{
    int a,b;
}data;

//昇順
int compare_int(const void *a, const void *b)
{
    return *(int*)a - *(int*)b;
}
//構造体降順
int comp( const void *c1, const void *c2 )
{
  data test1 = *(data *)c1;
  data test2 = *(data *)c2;
  int tmp1 = test1.b;   /* b を基準とする */
  int tmp2 = test2.b;
  return tmp2 - tmp1;
}


int kai(int n){
    if(n==0){
        return 1;
    }
    int sum=1;
    for(int i=1;i<=n;i++){
        sum*=i;
    }
    return sum;
}

int main(){
    int N;
    scanf("%d",&N);
    long long at[100];
    at[0]=2;at[1]=1;
    for(int i=2;i<=N;i++){
        at[i]=at[i-1]+at[i-2];
    }
    printf("%lld",at[N]);
}