




def 			lowerCamelCase_		(       UpperCamelCase__				:      int ,     UpperCamelCase__				:      int      )     ->       int:





				"""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(UpperCamelCase__      ):
								result *= n - i
								result //= i + 1
				return result







def 			lowerCamelCase_		(       UpperCamelCase__				:      int      )     ->       int:





				"""simple docstring"""


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







def 			lowerCamelCase_		(       UpperCamelCase__				:      int      )     ->       int:





				"""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__				:      int      )     ->       int:





				"""simple docstring"""


				return catalan_number(UpperCamelCase__      ) * factorial(UpperCamelCase__      )


if __name__ == "__main__":
					__A        =    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 Optional

import pyspark

from .. import Features, NamedSplit
from ..download import DownloadMode
from ..packaged_modules.spark.spark import Spark
from .abc import AbstractDatasetReader





class 	snake_case_   (		__A					):







			'''simple docstring'''

			def __init__(     self :				int							,   _UpperCamelCase :				pyspark.sql.DataFrame							,   _UpperCamelCase :				Optional[NamedSplit] = None							,   _UpperCamelCase :				Optional[Features] = None							,   _UpperCamelCase :				bool = True							,   _UpperCamelCase :				str = None							,   _UpperCamelCase :				bool = False							,   _UpperCamelCase :				str = None							,   _UpperCamelCase :				bool = True							,   _UpperCamelCase :				str = "arrow"							,   **_UpperCamelCase :				Tuple							,   )      ->str:
									super().__init__(
									    split=_UpperCamelCase							,   features=_UpperCamelCase							,   cache_dir=_UpperCamelCase							,   keep_in_memory=_UpperCamelCase							,   streaming=_UpperCamelCase							,   **_UpperCamelCase							,   )
									snake_case_   =	load_from_cache_file
									snake_case_   =	file_format
									snake_case_   =	Spark(
									    df=_UpperCamelCase							,   features=_UpperCamelCase							,   cache_dir=_UpperCamelCase							,   working_dir=_UpperCamelCase							,   **_UpperCamelCase							,   )







			def 				snake_case__(     self :				int							)      ->Tuple:
									if self.streaming:
															return self.builder.as_streaming_dataset(split=self.split							)
									snake_case_   =	None if self._load_from_cache_file else DownloadMode.FORCE_REDOWNLOAD
									self.builder.download_and_prepare(
									    download_mode=_UpperCamelCase							,   file_format=self._file_format							,   )
									return self.builder.as_dataset(split=self.split							)