
"""simple docstring"""

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

 return max_revue






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






def 							A						(    snake_case				:int    , snake_case				:list    , snake_case				:list		)				->     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(
       snake_case    , prices[i - 1] + _top_down_cut_rod_recursive(n - i    , snake_case    , snake_case		)    , )

  __UpperCamelCase      =	max_revenue

 return max_rev[n]






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

 # 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(snake_case    , prices[j - 1] + max_rev[i - j]		)

  __UpperCamelCase      =	max_revenue_i

 return max_rev[n]






def 							A						(    snake_case				:int    , snake_case				:list		)				->     List[str]:
 if n < 0:
  __UpperCamelCase      =	f'n must be greater than or equal to 0. Got n = {n}'
  raise ValueError(snake_case		)

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






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

 # 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(snake_case    , snake_case		)
 __UpperCamelCase      =	bottom_up_cut_rod(snake_case    , snake_case		)
 __UpperCamelCase      =	naive_cut_rod_recursive(snake_case    , snake_case		)

 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() = }''')



