from functools import lru_cache


@lru_cache(maxsize=10)
def fac(n):
    r = 1
    if n <= 1:
        return 1
    for i in range(2, n + 1):
        r *= i
    return r


@lru_cache(maxsize=1000000)
def get_factorial_sum(n):
    s = 0
    for d in get_digits(n):
        s += fac(d)
    return s


current_numbers_set = set()


@lru_cache(maxsize=10000000)
def get_chain_length(n):
    """ Could be further optimized by caching all permutations
    of the given number. All permutations of a number
    have the same factorial sum because they consist of the
    same digits. """
    global current_numbers_set
    next_value = get_factorial_sum(n)
    if next_value in current_numbers_set:
        return 1
    else:
        current_numbers_set.add(next_value)
        return 1 + get_chain_length(next_value)


def get_digits(n):
    return map(int, str(n))


def euler_074():
    c = 0
    for n in range(10**6):
        global current_numbers_set
        current_numbers_set = set([n])
        chain_len = get_chain_length(n)
        if chain_len == 60:
            # print("n: {} length: {}".format(n, chain_len))
            c += 1
    return c


if __name__ == "__main__":
    print("e074.py: " + str(euler_074()))
    assert(euler_074() == 402)