from functools import lru_cache
from itertools import product

from tqdm import tqdm


@lru_cache(maxsize=None)
def per(n, base=10):
    if n < base:
        return 0

    new_n = 1
    while n:
        new_n *= n % base
        # remove last digit from number (as integer)
        n //= base

    return 1 + per(new_n, base)


BASE = 10

added_digits = [n for n in [2, 3, 5, 7, 11, 13, 17, 19] if n < BASE]
options = added_digits

max_found = 0

f = open("out.txt", "a")

i = 0
while True:
    i += 1
    print("------")
    print("So far, we found max", max_found, "persistance")
    print("With", i, "digits")
    print("Number of options", len(options))
    for p in tqdm(options):
        x = per(p, base=BASE)
        if x > max_found:
            print()
            print("Found", x, p)
            f.write("\nFound " + str(x) + " " + str(p))

            max_found = x
    print()

    options = [a * BASE + b for a, b in product(options, added_digits) if a % BASE <= b]