


def 					UpperCamelCase   (      __magic_name__	:				int       ,       __magic_name__	:				list	)  ->    str:
		"""simple docstring"""




		_enforce_args(__magic_name__       ,       __magic_name__	)
		if n == 0:
				return 0
		lowercase__	     =						float("""-inf"""	)
		for i in range(1       ,       n + 1	):
				lowercase__	     =						max(
				    __magic_name__       ,       prices[i - 1] + naive_cut_rod_recursive(n - i       ,       __magic_name__	)	)

		return max_revue






def 					UpperCamelCase   (      __magic_name__	:				int       ,       __magic_name__	:				list	)  ->    Optional[int]:
		"""simple docstring"""




		_enforce_args(__magic_name__       ,       __magic_name__	)
		lowercase__	     =						[float("""-inf"""	) for _ in range(n + 1	)]
		return _top_down_cut_rod_recursive(__magic_name__       ,       __magic_name__       ,       __magic_name__	)






def 					UpperCamelCase   (      __magic_name__	:				int       ,       __magic_name__	:				list       ,       __magic_name__	:				list	)  ->    int:
		"""simple docstring"""




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

				lowercase__	     =						max_revenue

		return max_rev[n]






def 					UpperCamelCase   (      __magic_name__	:				int       ,       __magic_name__	:				list	)  ->    Tuple:
		"""simple docstring"""




		_enforce_args(__magic_name__       ,       __magic_name__	)

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

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

				lowercase__	     =						max_revenue_i

		return max_rev[n]






def 					UpperCamelCase   (      __magic_name__	:				int       ,       __magic_name__	:				list	)  ->    Union[str, Any]:
		"""simple docstring"""




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

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






def 					UpperCamelCase   (      )  ->    List[Any]:
		"""simple docstring"""




		lowercase__	     =						[6, 10, 12, 15, 20, 23]
		lowercase__	     =						len(__magic_name__	)

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

		lowercase__	     =						top_down_cut_rod(__magic_name__       ,       __magic_name__	)
		lowercase__	     =						bottom_up_cut_rod(__magic_name__       ,       __magic_name__	)
		lowercase__	     =						naive_cut_rod_recursive(__magic_name__       ,       __magic_name__	)

		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"""





def 					__A  (_SCREAMING_SNAKE_CASE     )   ->str:





  """simple docstring"""


  lowerCAmelCase__     :List[Any]											=				int(_SCREAMING_SNAKE_CASE     )
  if decimal in (0, 1):  # Exit cases for the recursion
    return str(_SCREAMING_SNAKE_CASE     )
  lowerCAmelCase__				,							lowerCAmelCase__     :int											=				divmod(_SCREAMING_SNAKE_CASE	,  2     )
  return binary_recursive(_SCREAMING_SNAKE_CASE     ) + str(_SCREAMING_SNAKE_CASE     )
def 					__A  (_SCREAMING_SNAKE_CASE     )   ->str:





  """simple docstring"""


  lowerCAmelCase__     :str											=				str(_SCREAMING_SNAKE_CASE     ).strip()
  if not number:
    raise ValueError('No input value was provided'     )
  lowerCAmelCase__     :Dict											=				'-' if number.startswith('-'     ) else ''
  lowerCAmelCase__     :int											=				number.lstrip('-'     )
  if not number.isnumeric():
    raise ValueError('Input value is not an integer'     )
  return F"{negative}0b{binary_recursive(int(_SCREAMING_SNAKE_CASE     )     )}"


if __name__ == "__main__":
  from doctest import testmod

  testmod()
