def isprime(n):
    prime = [True for i in range(n + 1)]
    p = 2
    while p * p <= n:
        if prime[p]:
            for i in range(p * 2, n + 1, p):
                prime[i] = False
        p += 1
    prime_numbers = []
    for p in range(2, n):
        if prime[p]:
            prime_numbers.append(p)
    return len(prime_numbers)

def redJohn(n):
    m = 0
    for i in range(n // 4 + 1):
        pl = n - (i * 3)
        m += int(math.factorial(pl) / (math.factorial(i) * math.factorial(pl - i)))
    return isprime(m+1)

public static int redJohn(int n) {
        int countWays = numberOfWays(n);
        int totalPrimes = sieve(countWays);
        
        return totalPrimes;
    }
		
public static int numberOfWays(int N){
    if (N<=3) return 1;
    if (N==4) return 2;
    return numberOfWays(N-1) + numberOfWays(N-4);
}

public static int sieve(int n) {
    int count = 0;
    boolean prime[] = new boolean[n + 1];
    for (int i = 0; i <= n; i++)
        prime[i] = true;

    for (int p = 2; p * p <= n; p++)
        if (prime[p] == true)
            for (int i = p * 2; i <= n; i += p)
                prime[i] = false;

    for (int i = 2; i <= n; i++)
        if (prime[i] == true)
            count++;

    return count;

function redJohn(n) {
    const r = x => Math.round(x)
    const s = x => Math.sqrt(x)
    
    const fact = (n) => n <= 1 ? 1 : fact(n - 1) * n
    
    const prime = (n) => { 
        if (n % 2 == 0 && n > 2) 
            return false
        for (let i=3; i <= r(s(n)); i+=2)
            if (n % i == 0)
                return false
        return true
    }
    
    let M = 0
    for (let i=0; i <= n/4; i++) {
        M += r(fact(n-i*3) / (fact(i) * fact(n-i*4)))
    }
    let res = 0
    for (let i=2; i <= M; i++)
        if (prime(i))
            res++
    return res
}