
from __future__ import annotations

from dataclasses import dataclass

@dataclass
class       a		:
							lowercase_		:						float
							lowercase_		:						TreeNode | None   							=  None
							lowercase_		:						TreeNode | None   							=  None






def 		_UpperCAmelCase   (	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()








from __future__ import annotations

UpperCamelCase_   	=	[True] * 1_0_0_0_0_0_1
UpperCamelCase_   	=	2
while i * i <= 1_0_0_0_0_0_0:
					if seive[i]:
										for j in range(i * i, 1_0_0_0_0_0_1, i):
															UpperCamelCase_   	=	False
					i += 1






def 		_UpperCAmelCase   (	UpperCamelCase:     int  ):






	"""simple docstring"""


	return seive[n]






def 		_UpperCAmelCase   (	UpperCamelCase:     int  ):






	"""simple docstring"""


	return any(digit in "02468" for digit in str(UpperCamelCase  )  )






def 		_UpperCAmelCase   (	UpperCamelCase:     int = 1_0_0_0_0_0_0  ):






	"""simple docstring"""


	__lowerCAmelCase         =							[2]  # result already includes the number 2.
	for num in range(3			,							limit + 1			,							2  ):
		if is_prime(UpperCamelCase  ) and not contains_an_even_digit(UpperCamelCase  ):
			__lowerCAmelCase         =							str(UpperCamelCase  )
			__lowerCAmelCase         =							[int(str_num[j:] + str_num[:j]  ) for j in range(len(UpperCamelCase  )  )]
			if all(is_prime(UpperCamelCase  ) for i in list_nums  ):
				result.append(UpperCamelCase  )
	return result






def 		_UpperCAmelCase   (	):






	"""simple docstring"""


	return len(find_circular_primes()  )


if __name__ == "__main__":
					print(f'''{len(find_circular_primes()) = }''')






