№23 — #23155

from functools import lru_cache
def sum_digits(n):
    return sum(map(int, str(n)))
@lru_cache(None)
def f(n, acount=0, has20=False, has54=False):
    if n == 100:
        return 1 if (has20 ^ has54) and acount % 2 == 1 else 0
    if n > 100:
        return 0
ans = 0
    ans += f(n + 2, acount + 1, has20 or n + 2 == 20, has54 or n + 2 == 54)
    ans += f(n + 7, acount, has20 or n + 7 == 20, has54 or n + 7 == 54)
    ans += f(n * 2, acount, has20 or n * 2 == 20, has54 or n * 2 == 54)
    ans += f(n * 3, acount, has20 or n * 3 == 20, has54 or n * 3 == 54)
x = n + sum_digits(n)
    if x <= 100:
        ans += f(x, acount, has20 or x == 20, has54 or x == 54)
return ans
raw = f(4)
print(sum_digits(raw) % 17)