There are N dogs in a pet store. The pet store wants to keep the N dogs in cages.
There can be two dogs in each cage. A dog can be eitheir passive or aggressive.
If the dog is passive, it can be clubed with another passive dog.
If the dog is aggressive, it has to be alone in a cage.
The program must print the number ways W to put the N dogs in the cages as the output.

Note: The number of cages in the pet store is sufficient to keep N dogs according to the given condition.

Example Input/Output 1:
Input:
2
Output:
2

Example Input/Output 2:
Input:
3
Output:
4

Example Input/Output 3:
Input: 10
Output: 9496

import math

def calculate_ways(n):
    # Calculate the factorial of N
    b = math.factorial(n)
    # Initialize the sum variable to 1 (at least one way to arrange the dogs)
    sum_ways = 1

    # Iterate from 1 to N/2 (inclusive) to calculate the number of ways
    for i in range(1, (n // 2) + 1):
        # Calculate the number of ways for each i using the formula
        k = b // (1 << i) // math.factorial(n - (i * 2)) // math.factorial(i)
        # Add the number of ways for this i to the total sum
        sum_ways += k

    return sum_ways

a = int(input())
result = calculate_ways(a)
print(result)
#include <iostream>
#include <cmath>
using namespace std;

long double f(long double a) {
    if (a <= 1)
        return 1;
    return a * f(a - 1);
}

long double calculate_ways(long double a) {
    long double sum = 1;
    long double val = f(a);

    for (int i = 1; i <= a / 2; i++) {
        long double k = val;
        k /= pow(2, i);
        k /= f(a - (2 * i));
        k /= f(i);
        sum += k;
    }

    return sum;
}

int main() {
    long double a;
    cin >> a;
    long double result = calculate_ways(a);
    cout << result;
    return 0;
}
#include <stdio.h>
#include <math.h>

long double f(long double a) {
    if (a <= 1)
        return 1;
    return a * f(a - 1);
}

long double calculate_ways(long double a) {
    long double sum = 1;
    long double val = f(a);

    for (int i = 1; i <= a / 2; i++) {
        long double k = val;
        k /= pow(2, i);
        k /= f(a - (2 * i));
        k /= f(i);
        sum += k;
    }

    return sum;
}

int main() {
    long double a;
    scanf("%Lf", &a);
    long double result = calculate_ways(a);
    printf("%.Lf", result);
    return 0;
}
import java.util.*;
import java.math.*;
public class Main {
    public static void main(String[] args) {
//Your Code Here
        Scanner scan=new Scanner(System.in);
        int n=scan.nextInt();
        BigInteger bigie[]=new BigInteger[n+1];
        for(int i=1;i<=n;++i){
            if(i<=2){
                bigie[i]=new BigInteger(i+"");
            }
            else{
                bigie[i]=new BigInteger((i-1)+"");
                bigie[i]=bigie[i].multiply(bigie[i-2]);
                bigie[i]=bigie[i].add(bigie[i-1]);
            }
        }
        System.out.print(bigie[n]);
}
}
using System;
using System.Numerics;

public class Program {
    public static BigInteger CalculateWays(int n) {
        BigInteger[] bigie = new BigInteger[n + 1];
        for (int i = 1; i <= n; ++i) {
            if (i <= 2) {
                bigie[i] = new BigInteger(i);
            } else {
                bigie[i] = new BigInteger(i - 1);
                bigie[i] = bigie[i].Multiply(bigie[i - 2]);
                bigie[i] = bigie[i].Add(bigie[i - 1]);
            }
        }
        return bigie[n];
    }

    public static void Main() {
        int n = Convert.ToInt32(Console.ReadLine());
        BigInteger result = CalculateWays(n);
        Console.Write(result);
    }
}
const readline = require('readline');
const rl = readline.createInterface({
    input: process.stdin,
    output: process.stdout
});

function calculateWays(n) {
    // Array to store the number of ways for each N (using BigInt to handle large values)
    const bigie = new Array(n + 1).fill(0).map((_, i) => i <= 2 ? BigInt(i) : null);

    // Calculate the number of ways for each N using the formula
    for (let i = 3; i <= n; i++) {
        bigie[i] = bigie[i - 1] * bigie[i - 2] + bigie[i - 1];
    }

    return bigie[n];
}

function main() {
    rl.question("Enter the number of dogs (N): ", input => {
        const n = parseInt(input);
        const result = calculateWays(n);
        console.log(result.toString());
        rl.close();
    });
}

main();

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