



"""simple docstring"""





from __future__ import annotations

from dataclasses import dataclass



@dataclass
class  _lowerCAmelCase     :





		"""simple docstring"""






		_lowerCamelCase      	=							42
		_lowerCamelCase      	=							None
		_lowerCamelCase      	=							None




def 						__lowerCAmelCase    (		__UpperCamelCase   :      TreeNode | None     ):


						'''simple docstring'''






						def is_valid_tree(__UpperCamelCase   :      TreeNode | None     ) -> bool:
												if node is None:
																		return True

												if not isinstance(__UpperCamelCase       ,			__UpperCamelCase     ):
																		return False

												try:
																		float(node.data     )
												except (TypeError, ValueError):
																		return False

												return is_valid_tree(node.left     ) and is_valid_tree(node.right     )

						if not is_valid_tree(__UpperCamelCase     ):
												raise ValueError(
												    """Each node should be type of TreeNode and data should be float."""     )

						def is_binary_search_tree_recursive_check(
						    __UpperCamelCase   :      TreeNode | None       ,			__UpperCamelCase   :      float       ,			__UpperCamelCase   :      float     ) -> bool:

												if node is None:
																		return True

												return (
												    left_bound < node.data < right_bound
												    and is_binary_search_tree_recursive_check(node.left       ,			__UpperCamelCase       ,			node.data     )
												    and is_binary_search_tree_recursive_check(
												        node.right       ,			node.data       ,			__UpperCamelCase     )
												)

						return is_binary_search_tree_recursive_check(__UpperCamelCase       ,			-float("""inf"""     )       ,			float("""inf"""     )     )


if __name__ == "__main__":
					import doctest

					doctest.testmod()








def 		lowerCAmelCase  (	UpperCamelCase__   :   list       ,			UpperCamelCase__   :   list       ,			UpperCamelCase__   :   int					)      ->    list:

						"""simple docstring"""





						__SCREAMING_SNAKE_CASE:				Tuple           =   len(UpperCamelCase__					)
						__SCREAMING_SNAKE_CASE:				Optional[int]           =   [[0] * n for i in range(UpperCamelCase__					)]
						for i in range(UpperCamelCase__					):
												__SCREAMING_SNAKE_CASE:				str           =   y_points[i]

						for i in range(2       ,			UpperCamelCase__					):
												for j in range(UpperCamelCase__       ,			UpperCamelCase__					):
																		__SCREAMING_SNAKE_CASE:				Optional[int]           =   (
																		    (xa - x_points[j - i + 1]) * q[j][i - 1]
																		    - (xa - x_points[j]) * q[j - 1][i - 1]
																		) / (x_points[j] - x_points[j - i + 1])

						return [q[n - 1][n - 1], q]


if __name__ == "__main__":
							import doctest

							doctest.testmod()



