



'''simple docstring'''





import math




def lowerCAmelCase    (__A):



     """simple docstring"""



     _a           =    [True] * n
     _a           =    False
     _a           =    False
     _a           =    True

     for i in range(3    ,      int(n**0.5 + 1)    ,      2):
          _a           =    i * 2
          while index < n:
               _a           =    False
               _a           =    index + i

     _a           =    [2]

     for i in range(3    ,      __A    ,      2):
          if is_prime[i]:
               primes.append(__A)

     return primes




def lowerCAmelCase    (__A = 999_966_663_333):



     """simple docstring"""



     _a           =    math.floor(math.sqrt(__A)) + 100
     _a           =    prime_sieve(__A)

     _a           =    0
     _a           =    0
     _a           =    primes[prime_index]

     while (last_prime**2) <= limit:
          _a           =    primes[prime_index + 1]

          _a           =    last_prime**2
          _a           =    next_prime**2

          # Get numbers divisible by lps(current)
          _a           =    lower_bound + last_prime
          while upper_bound > current <= limit:
               matches_sum += current
               current += last_prime

          # Reset the upper_bound
          while (upper_bound - next_prime) > limit:
               upper_bound -= next_prime

          # Add the numbers divisible by ups(current)
          _a           =    upper_bound - next_prime
          while current > lower_bound:
               matches_sum += current
               current -= next_prime

          # Remove the numbers divisible by both ups and lps
          _a           =    0
          while upper_bound > current <= limit:
               if current <= lower_bound:
                    # Increment the current number
                    current += last_prime * next_prime
                    continue

               if current > limit:
                    break

               # Remove twice since it was added by both ups and lps
               matches_sum -= current * 2

               # Increment the current number
               current += last_prime * next_prime

          # Setup for next pair
          _a           =    next_prime
          prime_index += 1

     return matches_sum


if __name__ == "__main__":
  print(solution())









from __future__ import annotations

from dataclasses import dataclass
@dataclass
class 						UpperCAmelCase  :







						'''simple docstring'''





						lowerCAmelCase_							=  42
						lowerCAmelCase_							=  None
						lowerCAmelCase_							=  None







def 		lowerCamelCase__       (						_A				):







	'''simple docstring'''





	def is_valid_tree(_A				) -> bool:
		if node is None:
			return True

		if not isinstance(_A	,      _A				):
			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(_A				):
		raise ValueError(
		    "Each node should be type of TreeNode and data should be float."				)

	def is_binary_search_tree_recursive_check(
	    _A	,      _A	,      _A				) -> bool:

		if node is None:
			return True

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

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


if __name__ == "__main__":
		import doctest

		doctest.testmod()
