





'''simple docstring'''




def 		__A		(  lowerCamelCase_			,			lowerCamelCase_	):


		"""simple docstring"""



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



def 		__A		(  lowerCamelCase_	):


		"""simple docstring"""



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



def 		__A		(  lowerCamelCase_	):


		"""simple docstring"""



		if n < 0:
				raise ValueError("""factorial() not defined for negative values"""	)
		SCREAMING_SNAKE_CASE :				Dict		=			1
		for i in range(1			,			n + 1	):
				result *= i
		return result



def 		__A		(  lowerCamelCase_	):


		"""simple docstring"""



		return catalan_number(lowerCamelCase_	) * factorial(lowerCamelCase_	)


if __name__ == "__main__":
							__UpperCAmelCase            =       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.'''
							)










'''simple docstring'''




from typing import TYPE_CHECKING

from ...file_utils import _LazyModule, is_tokenizers_available, is_torch_available
from ...utils import OptionalDependencyNotAvailable


__UpperCAmelCase            =       {"""configuration_gpt_neox""": ["""GPT_NEOX_PRETRAINED_CONFIG_ARCHIVE_MAP""", """GPTNeoXConfig"""]}

try:
							if not is_tokenizers_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__UpperCAmelCase            =       ["""GPTNeoXTokenizerFast"""]

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__UpperCAmelCase            =       [
							    """GPT_NEOX_PRETRAINED_MODEL_ARCHIVE_LIST""",
							    """GPTNeoXForCausalLM""",
							    """GPTNeoXForQuestionAnswering""",
							    """GPTNeoXForSequenceClassification""",
							    """GPTNeoXForTokenClassification""",
							    """GPTNeoXLayer""",
							    """GPTNeoXModel""",
							    """GPTNeoXPreTrainedModel""",
							]


if TYPE_CHECKING:
							from .configuration_gpt_neox import GPT_NEOX_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTNeoXConfig

							try:
														if not is_tokenizers_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .tokenization_gpt_neox_fast import GPTNeoXTokenizerFast

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_gpt_neox import (
														    GPT_NEOX_PRETRAINED_MODEL_ARCHIVE_LIST,
														    GPTNeoXForCausalLM,
														    GPTNeoXForQuestionAnswering,
														    GPTNeoXForSequenceClassification,
														    GPTNeoXForTokenClassification,
														    GPTNeoXLayer,
														    GPTNeoXModel,
														    GPTNeoXPreTrainedModel,
														)


else:
							import sys

							__UpperCAmelCase            =       _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



