"""
145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

Note: As 1!=1 and 2!=2 are not sums they are not included.
"""

import time
from functools import lru_cache


def timer(func):
    def wrapper(*args, **kwargs):
        start_time = time.time()
        result = func(*args, **kwargs)
        end_time = time.time()
        print(f"{func.__name__} time: {end_time - start_time:.6f} seconds")
        return result

    return wrapper


@lru_cache(maxsize=None)
def factorial(n: int) -> int:
    if n == 0:
        return 1
    elif n == 1:
        return 1
    elif n == 2:
        return 2
    elif n == 3:
        return 6
    elif n == 4:
        return 24
    elif n == 5:
        return 120
    elif n == 6:
        return 720
    elif n == 7:
        return 5040
    elif n == 8:
        return 40320
    elif n == 9:
        return 362880
    elif n == 10:
        return 3628800
    else:
        return n * factorial(n - 1)


def sum_digits(n: int) -> int:
    tmp = str(n)
    return sum(factorial(int(digit)) for digit in tmp)


@timer
def main() -> None:
    res = list()
    for i in range(12, 9999999):
        if sum_digits(i) == i:
            res.append(i)
    print(sum(res))


if __name__ == "__main__":
    main()