






'''simple docstring'''







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





def 		_UpperCAmelCase   (							__A							:   int      ):
				return binomial_coefficient(2 * node_count						,		__A      ) // (node_count + 1)





def 		_UpperCAmelCase   (							__A							:   int      ):
				if n < 0:
								raise ValueError('''factorial() not defined for negative values'''      )
				a_		:  Dict											=      1
				for i in range(1						,		n + 1      ):
								result *= i
				return result





def 		_UpperCAmelCase   (							__A							:   int      ):
				return catalan_number(__A      ) * factorial(__A      )


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."""
		)












'''simple docstring'''







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

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





@dataclass(frozen=SCREAMING_SNAKE_CASE_       )
class 	SCREAMING_SNAKE_CASE					(					SCREAMING_SNAKE_CASE_       ):
			snake_case__  =				field(default="image-classification"	,   metadata={"include_in_asdict_even_if_is_default": True}       )
			snake_case__  =				Features({"image": Image()}       )
			snake_case__  =				Features({"labels": ClassLabel}       )
			snake_case__  =				"image"
			snake_case__  =				"labels"






			def 			SCREAMING_SNAKE_CASE      ( self      :			List[str]  ,						__SCREAMING_SNAKE_CASE      :			List[Any]					)			->			Any:
							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]  ,						__SCREAMING_SNAKE_CASE					):
											raise ValueError(f'Column {self.label_column} is not a ClassLabel.'					)
							a_		:  Optional[int]											=      copy.deepcopy(self					)
							a_		:  int											=      self.label_schema.copy()
							a_		:  Tuple											=      features[self.label_column]
							a_		:  str											=      label_schema
							return task_template







			@property
			def 			SCREAMING_SNAKE_CASE      ( self      :			Tuple					)			->			Dict[str, str]:
							return {
							    self.image_column: "image",
							    self.label_column: "labels",
							}




