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"""
Problem 34: https://projecteuler.net/problem=34
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.
"""
from math import factorial
DIGIT_FACTORIAL = {str(d): factorial(d) for d in range(10)}
def sum_of_digit_factorial(n: int) -> int:
"""
Returns the sum of the factorial of digits in n
>>> sum_of_digit_factorial(15)
121
>>> sum_of_digit_factorial(0)
1
"""
return sum(DIGIT_FACTORIAL[d] for d in str(n))
def solution() -> int:
"""
Returns the sum of all numbers whose
sum of the factorials of all digits
add up to the number itself.
>>> solution()
40730
"""
limit = 7 * factorial(9) + 1
return sum(i for i in range(3, limit) if sum_of_digit_factorial(i) == i)
if __name__ == "__main__":
print(f"{solution() = }")
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