




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





def 				A__ (snake_case   :		int				)     ->						int:
					return binomial_coefficient(2 * node_count		,	snake_case				) // (node_count + 1)





def 				A__ (snake_case   :		int				)     ->						int:
					if n < 0:
										raise ValueError("""factorial() not defined for negative values"""				)
					__UpperCamelCase					:	Optional[Any]             =      1
					for i in range(1		,	n + 1				):
										result *= i
					return result





def 				A__ (snake_case   :		int				)     ->						int:
					return catalan_number(snake_case				) * factorial(snake_case				)


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."
	)












import copy
from dataclasses import dataclass, field
from typing import ClassVar, Dict

from ..features import ClassLabel, Features, Image
from .base import TaskTemplate


@dataclass(frozen=_UpperCamelCase   )
class    SCREAMING_SNAKE_CASE_				(       _UpperCamelCase   ):



	"""simple docstring"""


	__magic_name__   :       str      	=		field(default='image-classification'	,  metadata={'include_in_asdict_even_if_is_default': True}   )
	__magic_name__   :       ClassVar[Features]      	=		Features({'image': Image()}   )
	__magic_name__   :       ClassVar[Features]      	=		Features({'labels': ClassLabel}   )
	__magic_name__   :       str      	=		"image"
	__magic_name__   :       str      	=		"labels"






	def 					lowerCamelCase__     (					self		:						Any					,     lowerCAmelCase		:						Optional[Any]	)	->       Union[str, Any]:







						"""simple docstring"""







						if self.label_column not in features:
											raise ValueError(F'''Column {self.label_column} is not present in features.'''	)
						if not isinstance(features[self.label_column]					,     lowerCAmelCase	):
											raise ValueError(F'''Column {self.label_column} is not a ClassLabel.'''	)
						__UpperCamelCase					:	List[str]             =      copy.deepcopy(self	)
						__UpperCamelCase					:	List[Any]             =      self.label_schema.copy()
						__UpperCamelCase					:	List[str]             =      features[self.label_column]
						__UpperCamelCase					:	List[str]             =      label_schema
						return task_template






	@property
	def 					lowerCamelCase__     (					self		:						List[Any]	)	->       Dict[str, str]:







						"""simple docstring"""







						return {
						    self.image_column: "image",
						    self.label_column: "labels",
						}






