from itertools import combinations, permutations
from lib_prime import is_prime_rabin_miller as is_prime


def as_number(xs) -> int:
    return int("".join(map(str, xs)))


def list_diff(xs, ys):
    xs = list(xs)
    for y in ys:
        xs.remove(y)
    return xs


def combs(xs, size):
    return sorted([p
        for cs in combinations(xs, size)
        for p in permutations(cs)])


def count(min_set_size: int, min_num: int, remaining: list[int]) -> int:
    if not remaining:
        return 1

    result = 0
    # There are no pandigital primes with 9 digits, so we only check till 8.
    for set_size in range(min_set_size, 9):
        for subset in combs(remaining, set_size):
            n = as_number(subset)
            if n > min_num and is_prime(n):
                new_remaining = list_diff(remaining, subset)
                result += count(set_size, n, new_remaining)
    return result


def euler_118():
    return count(1, 0, [1, 2, 3, 4, 5, 6, 7, 8, 9])


if __name__ == "__main__":
    solution = euler_118()
    print("e118.py: " + str(solution))
    assert(solution == 44680)