





'''simple docstring'''


from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter
def 							UpperCAmelCase_  (						__lowerCamelCase					:					int	,__lowerCamelCase					:					int	,__lowerCamelCase					:					float = 1 / sqrt(2 ) ):
   lowercase_			:Tuple    			= tau * frequency / samplerate
   lowercase_			:Any    			= sin(__lowerCamelCase )
   lowercase_			:int    			= cos(__lowerCamelCase )
   lowercase_			:int    			= _sin / (2 * q_factor)

   lowercase_			:Dict    			= (1 - _cos) / 2
   lowercase_			:str    			= 1 - _cos

   lowercase_			:Dict    			= 1 + alpha
   lowercase_			:str    			= -2 * _cos
   lowercase_			:List[str]    			= 1 - alpha

   lowercase_			:Any    			= IIRFilter(2 )
   filt.set_coefficients([aa, aa, aa]	,[ba, ba, ba] )
   return filt
def 							UpperCAmelCase_  (						__lowerCamelCase					:					int	,__lowerCamelCase					:					int	,__lowerCamelCase					:					float = 1 / sqrt(2 ) ):
   lowercase_			:Dict    			= tau * frequency / samplerate
   lowercase_			:List[str]    			= sin(__lowerCamelCase )
   lowercase_			:List[str]    			= cos(__lowerCamelCase )
   lowercase_			:List[str]    			= _sin / (2 * q_factor)

   lowercase_			:Union[str, Any]    			= (1 + _cos) / 2
   lowercase_			:Tuple    			= -1 - _cos

   lowercase_			:str    			= 1 + alpha
   lowercase_			:Union[str, Any]    			= -2 * _cos
   lowercase_			:Dict    			= 1 - alpha

   lowercase_			:int    			= IIRFilter(2 )
   filt.set_coefficients([aa, aa, aa]	,[ba, ba, ba] )
   return filt
def 							UpperCAmelCase_  (						__lowerCamelCase					:					int	,__lowerCamelCase					:					int	,__lowerCamelCase					:					float = 1 / sqrt(2 ) ):
   lowercase_			:int    			= tau * frequency / samplerate
   lowercase_			:Any    			= sin(__lowerCamelCase )
   lowercase_			:str    			= cos(__lowerCamelCase )
   lowercase_			:Any    			= _sin / (2 * q_factor)

   lowercase_			:Optional[Any]    			= _sin / 2
   lowercase_			:Dict    			= 0
   lowercase_			:Optional[int]    			= -ba

   lowercase_			:Tuple    			= 1 + alpha
   lowercase_			:Dict    			= -2 * _cos
   lowercase_			:str    			= 1 - alpha

   lowercase_			:str    			= IIRFilter(2 )
   filt.set_coefficients([aa, aa, aa]	,[ba, ba, ba] )
   return filt
def 							UpperCAmelCase_  (						__lowerCamelCase					:					int	,__lowerCamelCase					:					int	,__lowerCamelCase					:					float = 1 / sqrt(2 ) ):
   lowercase_			:List[Any]    			= tau * frequency / samplerate
   lowercase_			:int    			= sin(__lowerCamelCase )
   lowercase_			:int    			= cos(__lowerCamelCase )
   lowercase_			:str    			= _sin / (2 * q_factor)

   lowercase_			:Union[str, Any]    			= 1 - alpha
   lowercase_			:Any    			= -2 * _cos
   lowercase_			:Optional[Any]    			= 1 + alpha

   lowercase_			:str    			= IIRFilter(2 )
   filt.set_coefficients([ba, ba, ba]	,[ba, ba, ba] )
   return filt
def 							UpperCAmelCase_  (						__lowerCamelCase					:					int	,__lowerCamelCase					:					int	,__lowerCamelCase					:					float	,__lowerCamelCase					:					float = 1 / sqrt(2 )	,):
   lowercase_			:Union[str, Any]    			= tau * frequency / samplerate
   lowercase_			:Any    			= sin(__lowerCamelCase )
   lowercase_			:Tuple    			= cos(__lowerCamelCase )
   lowercase_			:Tuple    			= _sin / (2 * q_factor)
   lowercase_			:Any    			= 10 ** (gain_db / 40)

   lowercase_			:Optional[int]    			= 1 + alpha * big_a
   lowercase_			:Optional[Any]    			= -2 * _cos
   lowercase_			:int    			= 1 - alpha * big_a
   lowercase_			:int    			= 1 + alpha / big_a
   lowercase_			:List[Any]    			= -2 * _cos
   lowercase_			:Optional[int]    			= 1 - alpha / big_a

   lowercase_			:Dict    			= IIRFilter(2 )
   filt.set_coefficients([aa, aa, aa]	,[ba, ba, ba] )
   return filt
def 							UpperCAmelCase_  (						__lowerCamelCase					:					int	,__lowerCamelCase					:					int	,__lowerCamelCase					:					float	,__lowerCamelCase					:					float = 1 / sqrt(2 )	,):
   lowercase_			:Optional[int]    			= tau * frequency / samplerate
   lowercase_			:Optional[int]    			= sin(__lowerCamelCase )
   lowercase_			:int    			= cos(__lowerCamelCase )
   lowercase_			:int    			= _sin / (2 * q_factor)
   lowercase_			:Optional[Any]    			= 10 ** (gain_db / 40)
   lowercase_			:str    			= (big_a + 1) - (big_a - 1) * _cos
   lowercase_			:Dict    			= (big_a + 1) + (big_a - 1) * _cos
   lowercase_			:Union[str, Any]    			= (big_a - 1) - (big_a + 1) * _cos
   lowercase_			:List[str]    			= (big_a - 1) + (big_a + 1) * _cos
   lowercase_			:Tuple    			= 2 * sqrt(__lowerCamelCase ) * alpha

   lowercase_			:Optional[int]    			= big_a * (pmc + aaa)
   lowercase_			:int    			= 2 * big_a * mpc
   lowercase_			:List[Any]    			= big_a * (pmc - aaa)
   lowercase_			:Optional[int]    			= ppmc + aaa
   lowercase_			:Any    			= -2 * pmpc
   lowercase_			:Union[str, Any]    			= ppmc - aaa

   lowercase_			:Tuple    			= IIRFilter(2 )
   filt.set_coefficients([aa, aa, aa]	,[ba, ba, ba] )
   return filt


def 							UpperCAmelCase_  (						__lowerCamelCase					:					int	,__lowerCamelCase					:					int	,__lowerCamelCase					:					float	,__lowerCamelCase					:					float = 1 / sqrt(2 )	,):
   lowercase_			:str    			= tau * frequency / samplerate
   lowercase_			:Dict    			= sin(__lowerCamelCase )
   lowercase_			:List[str]    			= cos(__lowerCamelCase )
   lowercase_			:Optional[Any]    			= _sin / (2 * q_factor)
   lowercase_			:List[str]    			= 10 ** (gain_db / 40)
   lowercase_			:Optional[int]    			= (big_a + 1) - (big_a - 1) * _cos
   lowercase_			:Tuple    			= (big_a + 1) + (big_a - 1) * _cos
   lowercase_			:List[str]    			= (big_a - 1) - (big_a + 1) * _cos
   lowercase_			:Dict    			= (big_a - 1) + (big_a + 1) * _cos
   lowercase_			:int    			= 2 * sqrt(__lowerCamelCase ) * alpha

   lowercase_			:int    			= big_a * (ppmc + aaa)
   lowercase_			:Any    			= -2 * big_a * pmpc
   lowercase_			:Dict    			= big_a * (ppmc - aaa)
   lowercase_			:Any    			= pmc + aaa
   lowercase_			:List[str]    			= 2 * mpc
   lowercase_			:List[str]    			= pmc - aaa

   lowercase_			:Dict    			= IIRFilter(2 )
   filt.set_coefficients([aa, aa, aa]	,[ba, ba, ba] )
   return filt









'''simple docstring'''


import math
def 							UpperCAmelCase_  (						__lowerCamelCase					:					int ):
   lowercase_			:Dict    			= []
   lowercase_			:List[Any]    			= 2
   lowercase_			:Optional[Any]    			= int(math.sqrt(__lowerCamelCase ) )  # Size of every segment
   lowercase_			:Optional[Any]    			= [True] * (end + 1)
   lowercase_			:Dict    			= []

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

   lowercase_			:Dict    			= end + 1
   lowercase_			:Dict    			= min(2 * end	,__lowerCamelCase )

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

         for j in range(__lowerCamelCase	,high + 1	,__lowerCamelCase ):
            lowercase_			:str    			= False

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

      lowercase_			:Dict    			= high + 1
      lowercase_			:Dict    			= min(high + end	,__lowerCamelCase )

   return prime


print(sieve(10**6))


