
"""simple docstring"""

def 							A						(    snake_case				:List[Any]    , snake_case				:Optional[int]		)				->     Any:
	_enforce_args(__UpperCAmelCase    , __UpperCAmelCase		)
	if n == 0:
		return 0
	__UpperCamelCase      =	float('-inf'		)
	for i in range(1    , n + 1		):
		__UpperCamelCase      =	max(
		    __UpperCAmelCase    , prices[i - 1] + naive_cut_rod_recursive(n - i    , __UpperCAmelCase		)		)

	return max_revue






def 							A						(    snake_case				:str    , snake_case				:str		)				->     Any:
	_enforce_args(__UpperCAmelCase    , __UpperCAmelCase		)
	__UpperCamelCase      =	[float('-inf'		) for _ in range(n + 1		)]
	return _top_down_cut_rod_recursive(__UpperCAmelCase    , __UpperCAmelCase    , __UpperCAmelCase		)






def 							A						(    snake_case				:Tuple    , snake_case				:Tuple    , snake_case				:Any		)				->     Union[str, Any]:

	if max_rev[n] >= 0:
		return max_rev[n]
	elif n == 0:
		return 0
	else:
		__UpperCamelCase      =	float('-inf'		)
		for i in range(1    , n + 1		):
			__UpperCamelCase      =	max(
			    __UpperCAmelCase    , prices[i - 1] + _top_down_cut_rod_recursive(n - i    , __UpperCAmelCase    , __UpperCAmelCase		)    , )

		__UpperCamelCase      =	max_revenue

	return max_rev[n]






def 							A						(    snake_case				:Optional[Any]    , snake_case				:Optional[int]		)				->     Any:
	_enforce_args(__UpperCAmelCase    , __UpperCAmelCase		)

	# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
	# length 0.
	__UpperCamelCase      =	[float('-inf'		) for _ in range(n + 1		)]
	__UpperCamelCase      =	0

	for i in range(1    , n + 1		):
		__UpperCamelCase      =	max_rev[i]
		for j in range(1    , i + 1		):
			__UpperCamelCase      =	max(__UpperCAmelCase    , prices[j - 1] + max_rev[i - j]		)

		__UpperCamelCase      =	max_revenue_i

	return max_rev[n]






def 							A						(    snake_case				:Optional[int]    , snake_case				:List[str]		)				->     int:

	if n < 0:
		__UpperCamelCase      =	f'n must be greater than or equal to 0. Got n = {n}'
		raise ValueError(__UpperCAmelCase		)

	if n > len(__UpperCAmelCase		):
		__UpperCamelCase      =	(
		    'Each integral piece of rod must have a corresponding price. '
		    f'Got n = {n} but length of prices = {len(__UpperCAmelCase		)}'
		)
		raise ValueError(__UpperCAmelCase		)






def 							A						(    )				->     Optional[int]:
	__UpperCamelCase      =	[6, 1_0, 1_2, 1_5, 2_0, 2_3]
	__UpperCamelCase      =	len(__UpperCAmelCase		)

	# the best revenue comes from cutting the rod into 6 pieces, each
	# of length 1 resulting in a revenue of 6 * 6 = 36.
	__UpperCamelCase      =	3_6

	__UpperCamelCase      =	top_down_cut_rod(__UpperCAmelCase    , __UpperCAmelCase		)
	__UpperCamelCase      =	bottom_up_cut_rod(__UpperCAmelCase    , __UpperCAmelCase		)
	__UpperCamelCase      =	naive_cut_rod_recursive(__UpperCAmelCase    , __UpperCAmelCase		)

	assert expected_max_revenue == max_rev_top_down
	assert max_rev_top_down == max_rev_bottom_up
	assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
						main()





"""simple docstring"""

from math import factorial

UpperCamelCase     :    List[Any]       =			{str(d): factorial(d) for d in range(1_0)}






def 							A						(    snake_case				:int		)				->     int:
 return sum(DIGIT_FACTORIAL[d] for d in str(snake_case		)		)






def 							A						(    )				->     int:
 __UpperCamelCase      =	7 * factorial(9		) + 1
 return sum(i for i in range(3    , snake_case		) if sum_of_digit_factorial(snake_case		) == i		)


if __name__ == "__main__":
      print(f'''{solution() = }''')



