

from typing import Any


class      lowerCamelCase_ :




 def __init__(			self							):
   __UpperCAmelCase	:  int		=     []
   __UpperCAmelCase	:  List[str]		=     0




 def __str__(			self							):
   __UpperCAmelCase	:  Union[str, Any]		=     '<' + str(self.stack							)[1:-1] + '>'
   return printed




 def     a       (			self  ,  _UpperCAmelCase							):
   self.stack.append(_UpperCAmelCase							)
   __UpperCAmelCase	:  int		=     self.length + 1




 def     a       (			self							):
   self.rotate(1							)
   __UpperCAmelCase	:  Optional[int]		=     self.stack[self.length - 1]
   __UpperCAmelCase	:  Optional[int]		=     self.stack[:-1]
   self.rotate(self.length - 1							)
   __UpperCAmelCase	:  Any		=     self.length - 1
   return dequeued




 def     a       (			self  ,  _UpperCAmelCase							):
   for _ in range(_UpperCAmelCase							):
     __UpperCAmelCase	:  Dict		=     self.stack[0]
     __UpperCAmelCase	:  Optional[int]		=     self.stack[1:]
     self.put(_UpperCAmelCase							)
     __UpperCAmelCase	:  List[Any]		=     self.length - 1




 def     a       (			self							):
   __UpperCAmelCase	:  List[str]		=     self.get()
   self.put(_UpperCAmelCase							)
   self.rotate(self.length - 1							)
   return front




 def     a       (			self							):
   return self.length






"""simple docstring"""
import math
from collections.abc import Generator





def  lowerCAmelCase__     (      _UpperCamelCase							:					int       )       ->					Generator[int, None, None]:





						"""simple docstring"""






						snake_case             =      (i for i in range(1			,      (max_n + 1)       ))
						for i in (n for n in numbers if n > 1):
												for j in range(2			,      _UpperCamelCase       ):
																		if (i % j) == 0:
																								break
												else:
																		yield i





def  lowerCAmelCase__     (      _UpperCamelCase							:					int       )       ->					Generator[int, None, None]:





						"""simple docstring"""






						snake_case             =      (i for i in range(1			,      (max_n + 1)       ))
						for i in (n for n in numbers if n > 1):
												# only need to check for factors up to sqrt(i)
												snake_case             =      int(math.sqrt(_UpperCamelCase       )       ) + 1
												for j in range(2			,      _UpperCamelCase       ):
																		if (i % j) == 0:
																								break
												else:
																		yield i





def  lowerCAmelCase__     (      _UpperCamelCase							:					int       )       ->					Generator[int, None, None]:





						"""simple docstring"""






						snake_case             =      (i for i in range(1			,      (max_n + 1)			,      2       ))
						# It's useless to test even numbers as they will not be prime
						if max_n > 2:
												yield 2  # Because 2 will not be tested, it's necessary to yield it now
						for i in (n for n in numbers if n > 1):
												snake_case             =      int(math.sqrt(_UpperCamelCase       )       ) + 1
												for j in range(3			,      _UpperCamelCase			,      2       ):
																		# As we removed the even numbers, we don't need them now
																		if (i % j) == 0:
																								break
												else:
																		yield i





def  lowerCAmelCase__     (      )       ->					List[str]:





						"""simple docstring"""






						from timeit import timeit

						snake_case             =      'from __main__ import slow_primes, primes, fast_primes'
						print(timeit('slow_primes(1_000_000_000_000)'			,      setup=_UpperCamelCase			,      number=1_0_0_0_0_0_0       )       )
						print(timeit('primes(1_000_000_000_000)'			,      setup=_UpperCamelCase			,      number=1_0_0_0_0_0_0       )       )
						print(timeit('fast_primes(1_000_000_000_000)'			,      setup=_UpperCamelCase			,      number=1_0_0_0_0_0_0       )       )


if __name__ == "__main__":
					SCREAMING_SNAKE_CASE__       =	int(input("Calculate primes up to:\n>> ").strip())
					for ret in primes(number):
										print(ret)
					benchmark()


