






import math






def      _snake_case     (__lowercase):
   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))












"""simple docstring"""


import math

def      UpperCamelCase							(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ):
						return math.pow(SCREAMING_SNAKE_CASE							,     2     ) - a

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						return 2 * x

def      UpperCamelCase							(SCREAMING_SNAKE_CASE     ):
						UpperCamelCase				:		Union[str, Any]				   =			2.0

						while start <= a:
												UpperCamelCase				:		Optional[Any]				   =			math.pow(SCREAMING_SNAKE_CASE							,     2     )

						return start

def      UpperCamelCase							(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE = 9999							,     SCREAMING_SNAKE_CASE = 0.00_00_00_00_00_00_01     ):

						if a < 0:
												raise ValueError("""math domain error"""     )

						UpperCamelCase				:		Optional[Any]				   =			get_initial_point(SCREAMING_SNAKE_CASE     )

						for _ in range(SCREAMING_SNAKE_CASE     ):
												UpperCamelCase				:		List[str]				   =			value
												UpperCamelCase				:		Tuple				   =			value - fx(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE     ) / fx_derivative(SCREAMING_SNAKE_CASE     )
												if abs(prev_value - value     ) < tolerance:
																		return value

						return value


if __name__ == "__main__":
		from doctest import testmod

		testmod()



