№23 — #23148

from functools import lru_cache
import math
def cube_root_int(n):
    r = round(n ** (1 / 3))
    while (r + 1) ** 3 <= n:
        r += 1
    while r ** 3 > n:
        r -= 1
    return r if r ** 3 == n else None
def sum_digits(n):
    return sum(map(int, str(n)))
@lru_cache(None)
def f(n, has99=False, has31=False):
    if n == 4:
        return 1 if (has99 or has31) else 0
    if n < 4 or n == 24:
        return 0
ans = 0
x = n - 3
    ans += f(x, has99 or x == 99, has31 or x == 31)
x = int(math.isqrt(n))
    if x < n:
        ans += f(x, has99 or x == 99, has31 or x == 31)
if n > 9:
        x = n // 10
        ans += f(x, has99 or x == 99, has31 or x == 31)
x = n // 2 if n % 2 == 0 else n - 5
    if x < n and x >= 1:
        ans += f(x, has99 or x == 99, has31 or x == 31)
r = cube_root_int(n)
    if r is not None and r < n:
        ans += f(r, has99 or r == 99, has31 or r == 31)
return ans
raw = f(999)
print(sum_digits(raw) ** 2)