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 5.4.1) (judge verdict: Accepted)

/*
cat <<EOF >mistaken-paste
*/

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
 
#define BIG 2000000007
 
#define MOD 1000000007
typedef unsigned long long ull;
typedef   signed long long sll;

#define N_MAX 200000
#define M_MAX 100000
 
typedef struct {
	int a;
	int b;
} hw;

typedef struct {
	sll a;
	sll b;
} hwll;
 

typedef struct {
	ull a;
	int i;
} struct_a;

typedef struct {
	ull cost;
	int left;
	int right;
} struct_b;


const hw vector8[8] = {
	{-1, -1},
	{-1,  0},
	{-1, +1},
	{ 0, -1},
	{ 0, +1},
	{+1, -1},
	{+1,  0},
	{+1, +1}
};
 
ull n, m;
ull h, w;
ull k;
sll va, vb, vc, vd, ve, vf;
ull a[N_MAX];
// sll a[N_MAX];
ull b[N_MAX];
// sll b[M_MAX];
// char s[N_MAX + 1];
// char t[N_MAX + 1];
// char s[N_MAX][M_MAX + 1];

ull dp[N_MAX];
// ull dp[N_MAX + 1][N_MAX + 1];
// ull dp[N_MAX][M_MAX + 1];

// hw arr[N_MAX];
// hwll arr[N_MAX];
// hw brr[M_MAX];

// struct_a arr[N_MAX * 2];
// struct_b brr[N_MAX * 2];

// ull digitdp[102][   2][    2];
//          pos  less  carry
 
void swap_adj(ull *a, ull *b){
	ull tmp = *b;
	*b = *a;
	*a = tmp;
	return;
}
 
ull divide(ull a, ull b){
	ull x = MOD - 2;
	ull ans = 1;
	while (x) {
		if (x & 1) ans = (ans * b) % MOD;
		b = (b * b) % MOD;
		x /= 2;
	}
	return (a * ans) % MOD;
}
 
int digits(ull x){
	int i = 1;
	while (x >= 10) {
		x /= 10;
		i++;
	}
	return i;
}
 
ull min(ull x, ull y){
	return (x < y) ? x : y;
}

ull max(ull x, ull y){
	return (x > y) ? x : y;
}

ull gcd(ull x, ull y){
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}
 
ull bitpow(ull a, ull x){
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= MOD;
		}
		x /= 2;
		a = (a * a) % MOD;
	}
	return result;
}
 
// int nextroute(int arr[]){
// 	int i = n - 1;
// 	int j, x;
// 	while (arr[i - 1] > arr[i]) i--;
 
// 	x = n;
// 	for (j = i; j < n; j++) {
// 		if (arr[j] < arr[i - 1]) continue;
// 		if (x == n || arr[x] > arr[j]) x = j;
// 	}
// 	arr[i - 1] ^= arr[x];
// 	arr[x] ^= arr[i - 1];
// 	arr[i - 1] ^= arr[x];
 
// 	qsort(&arr[i], n - i, sizeof(int), comp);
// 	return 0;
// }
 
int targetdig(ull x, int index /* 1-indexed */){
	// static...?
	int posmax = digits(x);
	if (posmax < index) return -1;
	while (posmax > index) {
		posmax--;
		x /= 10;
	}
	return x % 10;
}
 
int intcomp(const void *left, const void *right){
	if ((*(int*)left) < (*(int*)right)) {
		return -1;
	} else if ((*(int*)left) > (*(int*)right)) {
		return +1;
	} else {
		return 0;
	}
}

int ullcomp(const void *left, const void *right){
	if ((*(ull*)left) < (*(ull*)right)) {
		return -1;
	} else if ((*(ull*)left) > (*(ull*)right)) {
		return +1;
	} else {
		return 0;
	}
}

int sllcomp(const void *left, const void *right){
	if ((*(sll*)left) < (*(sll*)right)) {
		return -1;
	} else if ((*(sll*)left) > (*(sll*)right)) {
		return +1;
	} else {
		return 0;
	}
}

int hwAcomp(const void *left, const void *right){
	return intcomp(&(((hw*)left)->a), &(((hw*)right)->a));
}
 
int hwBcomp(const void *left, const void *right){
	return intcomp(&(((hw*)left)->b), &(((hw*)right)->b));
}
 
int hwABcomp(const void *left, const void *right){
	int x = hwAcomp(left, right);
	if (x) return x;
	return hwBcomp(left, right);
}

int hwllAcomp(const void *left, const void *right){
	return sllcomp(&(((hw*)left)->a), &(((hw*)right)->a));
}
 
int hwllBcomp(const void *left, const void *right){
	return sllcomp(&(((hw*)left)->b), &(((hw*)right)->b));
}
 
int hwllABcomp(const void *left, const void *right){
	int x = hwllAcomp(left, right);
	if (x) return x;
	return hwllBcomp(left, right);
}

int strAcomp(const struct_a *left, const struct_a *right){
	return ullcomp(&(left->a), &(right->a));
}

int strBcomp(const struct_b *left, const struct_b *right){
	return ullcomp(&(left->cost), &(right->cost));
}

int bitlet(char c){
	return (1 << (c - 'a'));
}


// ull seg[262144];
// ull baseIndex;

// int initSeg(ull a[], int num) {
// 	int i;

// 	baseIndex = 1;
// 	while (baseIndex < num) baseIndex *= 2;

// 	for (i = 0; i < baseIndex; i++) {
// 		seg[baseIndex + i] = (i < num ? a[i] : 0);
// 	}
// 	for (i = baseIndex - 1; i >= 1; i--) {
// 		seg[i] = seg[i * 2] + seg[i * 2 + 1];
// 	}

// }

// ull plainAnswerSeg(int num) {
// 	ull lookIndex = baseIndex;
// 	ull result = 0;

// 	while (num) {
// 		if (num % 2 == 1) {
// 			result += seg[lookIndex + num - 1];
// 		}

// 		lookIndex /= 2;
// 		num /= 2;
// 	}

// 	return result;
// }

// ull gapAnswerSeg(int start, int end){
// 	if (start > end) return gapAnswerSeg(end, start);
// 	return plainAnswerSeg(end) - plainAnswerSeg(start - 1);
// }


// int parent[N_MAX];
// int rank[N_MAX];

// void uf_init(int n){
// 	int i;
// 	for (i = 0; i < n; i++) {
// 		parent[i] = i;
// 		rank[i] = 0;
// 	}
// }

// int uf_find(int x){
// 	if (parent[x] == x) {
// 		return x;
// 	} else {
// 		return parent[x] = uf_find(parent[x]);
// 	}
// }

// int uf_unite(int x, int y){
// 	x = uf_find(x);
// 	y = uf_find(y);
// 	if (x == y) return 1;

// 	if (rank[x] < rank[y]) {
// 		parent[x] = y;
// 	} else {
// 		parent[y] = x;
// 		if (rank[x] == rank[y]) rank[x]++;
// 	}
// }

// bool uf_same(int x, int y){
// 	return uf_find(x) == uf_find(y);
// }


ull ulldiff(ull a, ull b){
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

ull ullkaijo(ull a){
	ull i;
	ull result = 1;
	for (i = 1; i <= a; i++) {
		result *= i;
		result %= MOD;
	}
	return result;
}

ull solve(){
	int i, j, ki;
	ull result = 0;

	dp[0] = 2;
	dp[1] = 1;
	for (i = 2; i <= n; i++) dp[i] = dp[i - 1] + dp[i - 2];

	printf("%llu\n", dp[n]);

	return 0;
}
 
int main(void){
	int i, j;
	int x, y;

	scanf("%llu", &n, &m);
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu%llu", &a[i], &b[i]);
	// }

	solve();

	return 0;
}