"""simple docstring"""






from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase = 1 / sqrt(2 ) )  ->  IIRFilter:
   lowercase__:   Dict					=      tau * frequency / samplerate
   lowercase__:   List[Any]					=      sin(__UpperCAmelCase )
   lowercase__:   List[str]					=      cos(__UpperCAmelCase )
   lowercase__:   List[Any]					=      _sin / (2 * q_factor)

   lowercase__:   Dict					=      (1 - _cos) / 2
   lowercase__:   Tuple					=      1 - _cos

   lowercase__:   Dict					=      1 + alpha
   lowercase__:   Optional[Any]					=      -2 * _cos
   lowercase__:   Any					=      1 - alpha

   lowercase__:   str					=      IIRFilter(2 )
   filt.set_coefficients([aa, aa, aa]       ,    [ba, ba, ba] )
   return filt



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase = 1 / sqrt(2 ) )  ->  IIRFilter:
   lowercase__:   Optional[Any]					=      tau * frequency / samplerate
   lowercase__:   Optional[int]					=      sin(__UpperCAmelCase )
   lowercase__:   Tuple					=      cos(__UpperCAmelCase )
   lowercase__:   Any					=      _sin / (2 * q_factor)

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

   lowercase__:   int					=      1 + alpha
   lowercase__:   Tuple					=      -2 * _cos
   lowercase__:   Any					=      1 - alpha

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



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase = 1 / sqrt(2 ) )  ->  IIRFilter:
   lowercase__:   str					=      tau * frequency / samplerate
   lowercase__:   Dict					=      sin(__UpperCAmelCase )
   lowercase__:   Optional[Any]					=      cos(__UpperCAmelCase )
   lowercase__:   str					=      _sin / (2 * q_factor)

   lowercase__:   Dict					=      _sin / 2
   lowercase__:   Tuple					=      0
   lowercase__:   str					=      -ba

   lowercase__:   Optional[Any]					=      1 + alpha
   lowercase__:   Any					=      -2 * _cos
   lowercase__:   Any					=      1 - alpha

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



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase = 1 / sqrt(2 ) )  ->  IIRFilter:
   lowercase__:   Tuple					=      tau * frequency / samplerate
   lowercase__:   Optional[int]					=      sin(__UpperCAmelCase )
   lowercase__:   Union[str, Any]					=      cos(__UpperCAmelCase )
   lowercase__:   Any					=      _sin / (2 * q_factor)

   lowercase__:   Tuple					=      1 - alpha
   lowercase__:   Dict					=      -2 * _cos
   lowercase__:   Optional[Any]					=      1 + alpha

   lowercase__:   str					=      IIRFilter(2 )
   filt.set_coefficients([ba, ba, ba]       ,    [ba, ba, ba] )
   return filt



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase = 1 / sqrt(2 )       ,    )  ->  IIRFilter:
   lowercase__:   int					=      tau * frequency / samplerate
   lowercase__:   int					=      sin(__UpperCAmelCase )
   lowercase__:   Optional[Any]					=      cos(__UpperCAmelCase )
   lowercase__:   Any					=      _sin / (2 * q_factor)
   lowercase__:   Tuple					=      1_0 ** (gain_db / 4_0)

   lowercase__:   Dict					=      1 + alpha * big_a
   lowercase__:   Union[str, Any]					=      -2 * _cos
   lowercase__:   str					=      1 - alpha * big_a
   lowercase__:   List[str]					=      1 + alpha / big_a
   lowercase__:   Any					=      -2 * _cos
   lowercase__:   Optional[Any]					=      1 - alpha / big_a

   lowercase__:   int					=      IIRFilter(2 )
   filt.set_coefficients([aa, aa, aa]       ,    [ba, ba, ba] )
   return filt



def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase = 1 / sqrt(2 )       ,    )  ->  IIRFilter:
   lowercase__:   Optional[int]					=      tau * frequency / samplerate
   lowercase__:   List[Any]					=      sin(__UpperCAmelCase )
   lowercase__:   List[str]					=      cos(__UpperCAmelCase )
   lowercase__:   List[str]					=      _sin / (2 * q_factor)
   lowercase__:   Any					=      1_0 ** (gain_db / 4_0)
   lowercase__:   Union[str, Any]					=      (big_a + 1) - (big_a - 1) * _cos
   lowercase__:   int					=      (big_a + 1) + (big_a - 1) * _cos
   lowercase__:   Any					=      (big_a - 1) - (big_a + 1) * _cos
   lowercase__:   Optional[Any]					=      (big_a - 1) + (big_a + 1) * _cos
   lowercase__:   List[str]					=      2 * sqrt(__UpperCAmelCase ) * alpha

   lowercase__:   Optional[Any]					=      big_a * (pmc + aaa)
   lowercase__:   int					=      2 * big_a * mpc
   lowercase__:   List[Any]					=      big_a * (pmc - aaa)
   lowercase__:   Optional[Any]					=      ppmc + aaa
   lowercase__:   List[Any]					=      -2 * pmpc
   lowercase__:   Tuple					=      ppmc - aaa

   lowercase__:   Any					=      IIRFilter(2 )
   filt.set_coefficients([aa, aa, aa]       ,    [ba, ba, ba] )
   return filt




def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase       ,    __UpperCAmelCase = 1 / sqrt(2 )       ,    )  ->  IIRFilter:
   lowercase__:   List[str]					=      tau * frequency / samplerate
   lowercase__:   Optional[Any]					=      sin(__UpperCAmelCase )
   lowercase__:   Any					=      cos(__UpperCAmelCase )
   lowercase__:   Tuple					=      _sin / (2 * q_factor)
   lowercase__:   str					=      1_0 ** (gain_db / 4_0)
   lowercase__:   Optional[Any]					=      (big_a + 1) - (big_a - 1) * _cos
   lowercase__:   Tuple					=      (big_a + 1) + (big_a - 1) * _cos
   lowercase__:   int					=      (big_a - 1) - (big_a + 1) * _cos
   lowercase__:   Union[str, Any]					=      (big_a - 1) + (big_a + 1) * _cos
   lowercase__:   Any					=      2 * sqrt(__UpperCAmelCase ) * alpha

   lowercase__:   Optional[int]					=      big_a * (ppmc + aaa)
   lowercase__:   Optional[Any]					=      -2 * big_a * pmpc
   lowercase__:   int					=      big_a * (ppmc - aaa)
   lowercase__:   str					=      pmc + aaa
   lowercase__:   Any					=      2 * mpc
   lowercase__:   Tuple					=      pmc - aaa

   lowercase__:   List[str]					=      IIRFilter(2 )
   filt.set_coefficients([aa, aa, aa]       ,    [ba, ba, ba] )
   return filt

"""simple docstring"""






def SCREAMING_SNAKE_CASE__			(   __UpperCAmelCase=2_8_1_2_3 )  ->  Any:
   lowercase__:   Optional[Any]					=      [1] * (limit + 1)

   for i in range(2       ,    int(limit**0.5 ) + 1 ):
      sum_divs[i * i] += i
      for k in range(i + 1       ,    limit // i + 1 ):
         sum_divs[k * i] += k + i

   lowercase__:   Union[str, Any]					=      set()
   lowercase__:   Optional[Any]					=      0

   for n in range(1       ,    limit + 1 ):
      if sum_divs[n] > n:
         abundants.add(__UpperCAmelCase )

      if not any((n - a in abundants) for a in abundants ):
         res += n

   return res


if __name__ == "__main__":
       print(solution())
