


"""simple docstring"""


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase      ):

			'''simple docstring'''




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


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




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


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




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


def _lowerCamelCase	(		_UpperCamelCase      ):

			'''simple docstring'''




			return catalan_number(A_      ) * factorial(A_      )


if __name__ == "__main__":
	A     :   int			    =			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 ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


__lowercase    					=      {
    """configuration_rag""": ["""RagConfig"""],
    """retrieval_rag""": ["""RagRetriever"""],
    """tokenization_rag""": ["""RagTokenizer"""],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __lowercase    					=      [
     """RagModel""",
     """RagPreTrainedModel""",
     """RagSequenceForGeneration""",
     """RagTokenForGeneration""",
 ]

try:
 if not is_tf_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __lowercase    					=      [
     """TFRagModel""",
     """TFRagPreTrainedModel""",
     """TFRagSequenceForGeneration""",
     """TFRagTokenForGeneration""",
 ]


if TYPE_CHECKING:
 from .configuration_rag import RagConfig
 from .retrieval_rag import RagRetriever
 from .tokenization_rag import RagTokenizer

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_rag import RagModel, RagPreTrainedModel, RagSequenceForGeneration, RagTokenForGeneration

 try:
  if not is_tf_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_tf_rag import (
      TFRagModel,
      TFRagPreTrainedModel,
      TFRagSequenceForGeneration,
      TFRagTokenForGeneration,
  )

else:
 import sys

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






