



def   lowerCAmelCase__						(			_SCREAMING_SNAKE_CASE       :			int				,     _SCREAMING_SNAKE_CASE       :			int    ):
				"""simple docstring"""







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

def   lowerCAmelCase__						(			_SCREAMING_SNAKE_CASE       :			int    ):
				"""simple docstring"""







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

def   lowerCAmelCase__						(			_SCREAMING_SNAKE_CASE       :			int    ):
				"""simple docstring"""







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

def   lowerCAmelCase__						(			_SCREAMING_SNAKE_CASE       :			int    ):
				"""simple docstring"""







				return catalan_number(_SCREAMING_SNAKE_CASE    ) * factorial(_SCREAMING_SNAKE_CASE    )


if __name__ == "__main__":
						lowerCamelCase__			= 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."""
						)





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


lowerCamelCase__			= {"""configuration_mbart""": ["""MBART_PRETRAINED_CONFIG_ARCHIVE_MAP""", """MBartConfig""", """MBartOnnxConfig"""]}

try:
						if not is_sentencepiece_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCamelCase__			= ["""MBartTokenizer"""]

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

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCamelCase__			= [
						    """MBART_PRETRAINED_MODEL_ARCHIVE_LIST""",
						    """MBartForCausalLM""",
						    """MBartForConditionalGeneration""",
						    """MBartForQuestionAnswering""",
						    """MBartForSequenceClassification""",
						    """MBartModel""",
						    """MBartPreTrainedModel""",
						]

try:
						if not is_tf_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCamelCase__			= [
						    """TFMBartForConditionalGeneration""",
						    """TFMBartModel""",
						    """TFMBartPreTrainedModel""",
						]

try:
						if not is_flax_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCamelCase__			= [
						    """FlaxMBartForConditionalGeneration""",
						    """FlaxMBartForQuestionAnswering""",
						    """FlaxMBartForSequenceClassification""",
						    """FlaxMBartModel""",
						    """FlaxMBartPreTrainedModel""",
						]


if TYPE_CHECKING:
						from .configuration_mbart import MBART_PRETRAINED_CONFIG_ARCHIVE_MAP, MBartConfig, MBartOnnxConfig

						try:
												if not is_sentencepiece_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_mbart import MBartTokenizer

						try:
												if not is_tokenizers_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_mbart_fast import MBartTokenizerFast

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_mbart import (
												    MBART_PRETRAINED_MODEL_ARCHIVE_LIST,
												    MBartForCausalLM,
												    MBartForConditionalGeneration,
												    MBartForQuestionAnswering,
												    MBartForSequenceClassification,
												    MBartModel,
												    MBartPreTrainedModel,
												)

						try:
												if not is_tf_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_tf_mbart import TFMBartForConditionalGeneration, TFMBartModel, TFMBartPreTrainedModel

						try:
												if not is_flax_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_flax_mbart import (
												    FlaxMBartForConditionalGeneration,
												    FlaxMBartForQuestionAnswering,
												    FlaxMBartForSequenceClassification,
												    FlaxMBartModel,
												    FlaxMBartPreTrainedModel,
												)

else:
						import sys

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