



'''simple docstring'''

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

	return max_revue







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







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

		_lowercase					:       List[str]       =		max_revenue

	return max_rev[n]







def 						__UpperCamelCase				(							_lowercase,				_lowercase					) ->			str:
	_enforce_args(_lowercase,				_lowercase					)

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

	for i in range(1,				n + 1					):
		_lowercase					:       Tuple       =		max_rev[i]
		for j in range(1,				i + 1					):
			_lowercase					:       Optional[int]       =		max(_lowercase,				prices[j - 1] + max_rev[i - j]					)

		_lowercase					:       Union[str, Any]       =		max_revenue_i

	return max_rev[n]







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

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







def 						__UpperCamelCase				(							) ->			List[str]:
	_lowercase					:       Optional[Any]       =		[6, 10, 12, 15, 20, 23]
	_lowercase					:       Optional[int]       =		len(_lowercase					)

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

	_lowercase					:       Optional[int]       =		top_down_cut_rod(_lowercase,				_lowercase					)
	_lowercase					:       List[Any]       =		bottom_up_cut_rod(_lowercase,				_lowercase					)
	_lowercase					:       List[str]       =		naive_cut_rod_recursive(_lowercase,				_lowercase					)

	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'''

_A				:    Optional[Any]     						='''ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/'''







def 						__UpperCamelCase				(							_lowercase					) ->			bytes:
	# Make sure the supplied data is a bytes-like object
	if not isinstance(_lowercase,				_lowercase					):
		_lowercase					:       Union[str, Any]       =		f'''a bytes-like object is required, not \'{data.__class__.__name__}\''''
		raise TypeError(_lowercase					)

	_lowercase					:       int       =		''.join(bin(_lowercase					)[2:].zfill(8					) for byte in data					)

	_lowercase					:       Dict       =		len(_lowercase					) % 6 != 0

	if padding_needed:
		# The padding that will be added later
		_lowercase					:       Optional[Any]       =		B'=' * ((6 - len(_lowercase					) % 6) // 2)

		# Append binary_stream with arbitrary binary digits (0's by default) to make its
		# length a multiple of 6.
		binary_stream += "0" * (6 - len(_lowercase					) % 6)
	else:
		_lowercase					:       Optional[int]       =		B''

	# Encode every 6 binary digits to their corresponding Base64 character
	return (
	    "".join(
	        B64_CHARSET[int(binary_stream[index : index + 6],				2					)]
	        for index in range(0,				len(_lowercase					),				6					)					).encode()
	    + padding
	)







def 						__UpperCamelCase				(							_lowercase					) ->			bytes:
	# Make sure encoded_data is either a string or a bytes-like object
	if not isinstance(_lowercase,				_lowercase					) and not isinstance(_lowercase,				_lowercase					):
		_lowercase					:       int       =		(
		    'argument should be a bytes-like object or ASCII string, '
		    f'''not \'{encoded_data.__class__.__name__}\''''
		)
		raise TypeError(_lowercase					)

	# In case encoded_data is a bytes-like object, make sure it contains only
	# ASCII characters so we convert it to a string object
	if isinstance(_lowercase,				_lowercase					):
		try:
			_lowercase					:       Optional[int]       =		encoded_data.decode('utf-8'					)
		except UnicodeDecodeError:
			raise ValueError('base64 encoded data should only contain ASCII characters'					)

	_lowercase					:       Optional[int]       =		encoded_data.count('='					)

	# Check if the encoded string contains non base64 characters
	if padding:
		assert all(
		    char in B64_CHARSET for char in encoded_data[:-padding]					), "Invalid base64 character(s) found."
	else:
		assert all(
		    char in B64_CHARSET for char in encoded_data					), "Invalid base64 character(s) found."

	# Check the padding
	assert len(_lowercase					) % 4 == 0 and padding < 3, "Incorrect padding"

	if padding:
		# Remove padding if there is one
		_lowercase					:       str       =		encoded_data[:-padding]

		_lowercase					:       Tuple       =		''.join(
		    bin(B64_CHARSET.index(_lowercase					)					)[2:].zfill(6					) for char in encoded_data					)[: -padding * 2]
	else:
		_lowercase					:       Union[str, Any]       =		''.join(
		    bin(B64_CHARSET.index(_lowercase					)					)[2:].zfill(6					) for char in encoded_data					)

	_lowercase					:       List[str]       =		[
	    int(binary_stream[index : index + 8],				2					)
	    for index in range(0,				len(_lowercase					),				8					)
	]

	return bytes(_lowercase					)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
