


'''simple docstring'''
from ..utils import DummyObject, requires_backends
class    lowercase	(							metaclass=lowerCAmelCase_					):

		"""simple docstring"""

		_a     =				['torch', 'torchsde']




		def __init__(		self    ,   *UpperCamelCase_    ,   **UpperCamelCase_							):

							'''simple docstring'''


							requires_backends(self    ,   ['''torch''', '''torchsde''']							)




		@classmethod
		def     lowerCAmelCase__				(		cls    ,   *UpperCamelCase_    ,   **UpperCamelCase_							):

							'''simple docstring'''


							requires_backends(cls    ,   ['''torch''', '''torchsde''']							)




		@classmethod
		def     lowerCAmelCase__				(		cls    ,   *UpperCamelCase_    ,   **UpperCamelCase_							):

							'''simple docstring'''


							requires_backends(cls    ,   ['''torch''', '''torchsde''']							)
"""simple docstring"""


import math






def 			__UpperCAmelCase    (	lowercase						):







  """simple docstring"""
  _UpperCAmelCase         =					[]
  _UpperCAmelCase         =					2
  _UpperCAmelCase         =					int(math.sqrt(lowercase						)						)  # Size of every segment
  _UpperCAmelCase         =					[True] * (end + 1)
  _UpperCAmelCase         =					[]

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

  _UpperCAmelCase         =					end + 1
  _UpperCAmelCase         =					min(2 * end      ,lowercase						)

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

      for j in range(lowercase      ,high + 1      ,lowercase						):
        _UpperCAmelCase         =					False

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

    _UpperCAmelCase         =					high + 1
    _UpperCAmelCase         =					min(high + end      ,lowercase						)

  return prime

print(sieve(1_0**6))
