import math





def 		__lowerCamelCase							(UpperCAmelCase__       :							int					):
					SCREAMING_SNAKE_CASE           =    []
					SCREAMING_SNAKE_CASE           =    2
					SCREAMING_SNAKE_CASE           =    int(math.sqrt(UpperCAmelCase__					)					)  # Size of every segment
					SCREAMING_SNAKE_CASE           =    [True] * (end + 1)
					SCREAMING_SNAKE_CASE           =    []

					while start <= end:
										if temp[start] is True:
															in_prime.append(UpperCAmelCase__					)
															for i in range(start * start ,	end + 1 ,	UpperCAmelCase__					):
																				SCREAMING_SNAKE_CASE           =    False
										start += 1
					prime += in_prime

					SCREAMING_SNAKE_CASE           =    end + 1
					SCREAMING_SNAKE_CASE           =    min(2 * end ,	UpperCAmelCase__					)

					while low <= n:
										SCREAMING_SNAKE_CASE           =    [True] * (high - low + 1)
										for each in in_prime:
															SCREAMING_SNAKE_CASE           =    math.floor(low / each					) * each
															if t < low:
																				t += each

															for j in range(UpperCAmelCase__ ,	high + 1 ,	UpperCAmelCase__					):
																				SCREAMING_SNAKE_CASE           =    False

										for j in range(len(UpperCAmelCase__					)					):
															if temp[j] is True:
																				prime.append(j + low					)

										SCREAMING_SNAKE_CASE           =    high + 1
										SCREAMING_SNAKE_CASE           =    min(high + end ,	UpperCAmelCase__					)

					return prime
print(sieve(10**6))





from __future__ import annotations

from collections.abc import Iterator


class   lowercase      :




							def __init__(  self				:   str		,							_UpperCamelCase				:   int )   ->			None:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE           =    value
												SCREAMING_SNAKE_CASE           =    None
												SCREAMING_SNAKE_CASE           =    None



class   lowercase      :




							def __init__(  self				:   str		,							_UpperCamelCase				:   Node )   ->			None:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE           =    tree




							def 		__snake_case(  self				:   int		,							_UpperCamelCase				:   Node | None )   ->			int:



												'''simple docstring'''

												if node is None:
																	return 0
												return node.value + (
												    self.depth_first_search(node.left ) + self.depth_first_search(node.right )
												)





							def __iter__(  self				:   List[Any] )   ->			Iterator[int]:



												'''simple docstring'''

												yield self.depth_first_search(self.tree )


if __name__ == "__main__":
							import doctest

							doctest.testmod()




