from lib_prime import is_prime_rabin_miller as is_prime


def get_permutations(number: str, number_permutations: int, start_index = 0):
    """ Returns number permutated at number_permutations locations. """
    if number_permutations == 0:
        yield int(number)
    else:
        numbers = list("0123456789")
        base = list(str(number))
        for i in range(start_index, len(base)):
            digit_stored = base[i]
            for n in numbers:
                if n == digit_stored:
                    continue
                base[i] = n
                if base[0] == "0":
                    continue
                for p in get_permutations("".join(base), number_permutations - 1, i):
                    yield p
            base[i] = digit_stored


def euler_111():
    result = 0
    n = 10
    for d in range(10):
        subresult = 0
        base = "".join([str(d) for _ in range(n)])
        for p in get_permutations(base, 1):
            if is_prime(p):
                subresult += p
        if subresult == 0:
            # d in [0, 2, 8] requires two permutations to yield at least one prime
            for p in get_permutations(base, 2):
                if is_prime(p):
                    subresult += p
        assert subresult > 0, "More than two permutations required to yield prime"
        result += subresult
    return result


if __name__ == "__main__":
    solution = euler_111()
    print("e111.py: " + str(solution))
    assert(solution == 612407567715)