def 						__lowerCamelCase				(UpperCAmelCase__  :				int   ,			UpperCAmelCase__  :				List[Any]	):
					SCREAMING_SNAKE_CASE           =							1  # To kept the Calculated Value
					# Since C(n, k) = C(n, n-k)
					if k > (n - k):
										SCREAMING_SNAKE_CASE           =							n - k
					# Calculate C(n,k)
					for i in range(UpperCAmelCase__	):
										result *= n - i
										result //= i + 1
					return result





def 						__lowerCamelCase				(UpperCAmelCase__  :				List[str]	):
					return binomial_coefficient(2 * node_count   ,			UpperCAmelCase__	) // (node_count + 1)





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





def 						__lowerCamelCase				(UpperCAmelCase__  :				Optional[Any]	):
					return catalan_number(UpperCAmelCase__	) * factorial(UpperCAmelCase__	)


if __name__ == "__main__":
							_lowerCamelCase       : Union[str, Any]      					=		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 dataclasses import dataclass, field
from typing import TYPE_CHECKING, Any, ClassVar, Dict, List, Optional, Union

import pyarrow as pa


if TYPE_CHECKING:
							from .features import FeatureType




@dataclass
class 		__A   :
						UpperCamelCase      =       42
						UpperCamelCase      =       None
						# Automatically constructed
						UpperCamelCase      =       "dict"
						UpperCamelCase      =       None
						UpperCamelCase      =       field(default="""Translation"""       ,    init=UpperCamelCase__       ,    repr=UpperCamelCase__      )

						def __call__(		self :Union[str, Any]			):
										'''simple docstring'''

										return pa.struct({lang: pa.string() for lang in sorted(self.languages			)}			)


						def      A__    (		self :List[Any]			):
										'''simple docstring'''

										from .features import Value

										return {k: Value("""string"""			) for k in sorted(self.languages			)}




@dataclass
class 		__A   :
						UpperCamelCase      =       None
						UpperCamelCase      =       None
						UpperCamelCase      =       None
						# Automatically constructed
						UpperCamelCase      =       "dict"
						UpperCamelCase      =       None
						UpperCamelCase      =       field(default="""TranslationVariableLanguages"""       ,    init=UpperCamelCase__       ,    repr=UpperCamelCase__      )

						def      A__    (		self :Optional[Any]			):
										'''simple docstring'''

										__magic_name__						:						List[Any]										=sorted(set(self.languages			)			) if self.languages else None
										__magic_name__						:						Optional[int]										=len(self.languages			) if self.languages else None

						def __call__(		self :List[str]			):
										'''simple docstring'''

										return pa.struct({"""language""": pa.list_(pa.string()			), """translation""": pa.list_(pa.string()			)}			)

						def      A__    (		self :str     ,			__snake_case :str			):
										'''simple docstring'''

										__magic_name__						:						Optional[int]										=set(self.languages			)
										if self.languages and set(__snake_case			) - lang_set:
														raise ValueError(
														    f"Some languages in example ({', '.join(sorted(set(__snake_case			) - lang_set			)			)}) are not in valid set ({', '.join(__snake_case			)})."			)

										# Convert dictionary into tuples, splitting out cases where there are
										# multiple translations for a single language.
										__magic_name__						:						Any										=[]
										for lang, text in translation_dict.items():
														if isinstance(__snake_case     ,			__snake_case			):
																		translation_tuples.append((lang, text)			)
														else:
																		translation_tuples.extend([(lang, el) for el in text]			)

        # Ensure translations are in ascending order by language code.
										__magic_name__					,			__magic_name__						:						List[str]										=zip(*sorted(__snake_case			)			)

										return {"language": languages, "translation": translations}


						def      A__    (		self :List[Any]			):
										'''simple docstring'''

										from .features import Sequence, Value

										return {
										    "language": Sequence(Value("""string"""			)			),
										    "translation": Sequence(Value("""string"""			)			),
										}




