"""
A googol (10^100) is a massive number: one followed by one-hundred zeros;
100^100 is almost unimaginably large: one followed by two-hundred zeros.
Despite their size, the sum of the digits in each number is only 1 .

Considering natural numbers of the form, a^b , where a,b < 100 , what is the maximum digital sum?
"""

import time
from decimal import MAX_EMAX
from functools import wraps
from typing import Any, Callable, TypeVar

F = TypeVar("F", bound=Callable[..., Any])


def benchmark(repeat: int = 1) -> Callable[[F], F]:
    if repeat < 1:
        raise ValueError("repeat must >= 1")

    def decorator(func: F) -> F:
        @wraps(func)
        def wrapper(*args: Any, **kwargs: Any) -> Any:
            total = 0.0
            result = None

            for _ in range(repeat):
                start = time.perf_counter()
                result = func(*args, **kwargs)
                end = time.perf_counter()
                total += end - start

            wrapper.avg_time = total / repeat  # type: ignore[attr-defined]
            wrapper.total_time = total  # type: ignore[attr-defined]

            print(
                f"[Benchmark] {func.__name__} | repeated {repeat} times | "
                f"average: {wrapper.avg_time:.6f}s | total: {wrapper.total_time:.6f}s"  # type: ignore[attr-defined]
            )
            return result

        wrapper.avg_time = 0.0  # type: ignore[attr-defined]
        wrapper.total_time = 0.0  # type: ignore[attr-defined]
        return wrapper  # type: ignore[return-value]

    return decorator


def powtodigit(a: int, b: int) -> tuple[int, str]:
    res = pow(a, b)
    return res, str(res)


@benchmark(repeat=15)
def main() -> None:
    max_digit_sum = 0
    for a in range(2, 101):
        for b in range(2, 101):
            digit_sum = sum(int(d) for d in powtodigit(a, b)[1])
            max_digit_sum = max(max_digit_sum, digit_sum)
    print(f"Maximum digit sum: {max_digit_sum}")


@benchmark(repeat=15)
def main_inone() -> None:
    max_digit_sum = 0
    abp = 1
    a = 99
    for b in range(100, 2, -1):
        abp = abp * a
        max_digit_sum = max(max_digit_sum, sum(int(d) for d in str(abp)))
    print(f"Maximum digit sum: {max_digit_sum}")


if __name__ == "__main__":
    main()
    main_inone()