
def   lowerCAmelCase_						(					_snake_case      :  int      ,   _snake_case      :  int   )				->		int:







	'''simple docstring'''


	__magic_name__		:		Dict	   =     1  # To kept the Calculated Value
	# Since C(n, k) = C(n, n-k)
	if k > (n - k):
		__magic_name__		:		Any	   =     n - k
	# Calculate C(n,k)
	for i in range(_snake_case   ):
		result *= n - i
		result //= i + 1
	return result






def   lowerCAmelCase_						(					_snake_case      :  int   )				->		int:







	'''simple docstring'''


	return binomial_coefficient(2 * node_count      ,   _snake_case   ) // (node_count + 1)






def   lowerCAmelCase_						(					_snake_case      :  int   )				->		int:







	'''simple docstring'''


	if n < 0:
		raise ValueError("factorial() not defined for negative values"   )
	__magic_name__		:		Optional[Any]	   =     1
	for i in range(1      ,   n + 1   ):
		result *= i
	return result






def   lowerCAmelCase_						(					_snake_case      :  int   )				->		int:







	'''simple docstring'''


	return catalan_number(_snake_case   ) * factorial(_snake_case   )


if __name__ == "__main__":
				snake_case :		Dict							      =  int(input("Enter the number of nodes: ").strip() or 0)
				if node_count <= 0:
								raise ValueError("We need some nodes to work with.")
				print(
				    F"Given {node_count} nodes, there are {binary_tree_count(node_count)} "
				    F"binary trees and {catalan_number(node_count)} binary search trees."
				)


snake_case :		Optional[int]							      =  "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"






def   lowerCAmelCase_						(					_snake_case      :  bytes   )				->		bytes:







	'''simple docstring'''


	if not isinstance(_snake_case      ,   _snake_case   ):
		__magic_name__		:		Tuple	   =     F'''a bytes-like object is required, not \'{data.__class__.__name__}\''''
		raise TypeError(_snake_case   )

	__magic_name__		:		Optional[int]	   =     "".join(bin(_snake_case   )[2:].zfill(8   ) for byte in data   )

	__magic_name__		:		List[Any]	   =     len(_snake_case   ) % 6 != 0

	if padding_needed:
		# The padding that will be added later
		__magic_name__		:		List[str]	   =     B"=" * ((6 - len(_snake_case   ) % 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(_snake_case   ) % 6)
	else:
		__magic_name__		:		List[str]	   =     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(_snake_case   )      ,   6   )   ).encode()
	    + padding
	)






def   lowerCAmelCase_						(					_snake_case      :  str   )				->		bytes:







	'''simple docstring'''


	if not isinstance(_snake_case      ,   _snake_case   ) and not isinstance(_snake_case      ,   _snake_case   ):
		__magic_name__		:		List[str]	   =     (
		    "argument should be a bytes-like object or ASCII string, "
		    F'''not \'{encoded_data.__class__.__name__}\''''
		)
		raise TypeError(_snake_case   )

	# 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(_snake_case      ,   _snake_case   ):
		try:
			__magic_name__		:		List[Any]	   =     encoded_data.decode("utf-8"   )
		except UnicodeDecodeError:
			raise ValueError("base64 encoded data should only contain ASCII characters"   )

	__magic_name__		:		List[str]	   =     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(_snake_case   ) % 4 == 0 and padding < 3, "Incorrect padding"

	if padding:
		# Remove padding if there is one
		__magic_name__		:		Optional[int]	   =     encoded_data[:-padding]

		__magic_name__		:		Dict	   =     "".join(
		    bin(B64_CHARSET.index(_snake_case   )   )[2:].zfill(6   ) for char in encoded_data   )[: -padding * 2]
	else:
		__magic_name__		:		Union[str, Any]	   =     "".join(
		    bin(B64_CHARSET.index(_snake_case   )   )[2:].zfill(6   ) for char in encoded_data   )

	__magic_name__		:		List[Any]	   =     [
	    int(binary_stream[index : index + 8]      ,   2   )
	    for index in range(0      ,   len(_snake_case   )      ,   8   )
	]

	return bytes(_snake_case   )


if __name__ == "__main__":
				import doctest

				doctest.testmod()
