№23 — #23151

from functools import lru_cache
def sum_digits(n):
    return sum(map(int, str(n)))
@lru_cache(None)
def f(n, ccount=0, has18=False, has54=False):
    if n == 96:
        return 1 if (has18 or has54) and ccount == 1 else 0
    if n > 96:
        return 0
ans = 0
    ans += f(n + 2, ccount, has18 or n + 2 == 18, has54 or n + 2 == 54)
    ans += f(n * 2, ccount, has18 or n * 2 == 18, has54 or n * 2 == 54)
if ccount < 1:
        ans += f(n * 3, ccount + 1, has18 or n * 3 == 18, has54 or n * 3 == 54)
ans += f(n + 5, ccount, has18 or n + 5 == 18, has54 or n + 5 == 54)
x = n + sum_digits(n)
    if x <= 96:
        ans += f(x, ccount, has18 or x == 18, has54 or x == 54)
return ans
raw = f(2)
print(sum_digits(raw) % 19)