

def 				snake_case_(_UpperCamelCase = 1_000_000					)							->     int:



  """simple docstring"""






  _snake_case						=							set(range(3			,	_UpperCamelCase			,	2					)					)
  primes.add(2					)
  for p in range(3			,	_UpperCamelCase			,	2					):
    if p not in primes:
      continue
    primes.difference_update(set(range(p * p			,	_UpperCamelCase			,	_UpperCamelCase					)					)					)

  _snake_case						=							[float(_UpperCamelCase					) for n in range(limit + 1					)]

  for p in primes:
    for n in range(_UpperCamelCase			,	limit + 1			,	_UpperCamelCase					):
      phi[n] *= 1 - 1 / p

  return int(sum(phi[2:]					)					)


if __name__ == "__main__":
 print(f'''{solution() = }''')




from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)					)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)

  _snake_case						=							(1 - _cos) / 2
  _snake_case						=							1 - _cos

  _snake_case						=							1 + alpha
  _snake_case						=							-2 * _cos
  _snake_case						=							1 - alpha

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([aa, aa, aa]			,	[ba, ba, ba]					)
  return filt



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)					)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)

  _snake_case						=							(1 + _cos) / 2
  _snake_case						=							-1 - _cos

  _snake_case						=							1 + alpha
  _snake_case						=							-2 * _cos
  _snake_case						=							1 - alpha

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([aa, aa, aa]			,	[ba, ba, ba]					)
  return filt



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)					)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)

  _snake_case						=							_sin / 2
  _snake_case						=							0
  _snake_case						=							-ba

  _snake_case						=							1 + alpha
  _snake_case						=							-2 * _cos
  _snake_case						=							1 - alpha

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([aa, aa, aa]			,	[ba, ba, ba]					)
  return filt



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)					)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)

  _snake_case						=							1 - alpha
  _snake_case						=							-2 * _cos
  _snake_case						=							1 + alpha

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([ba, ba, ba]			,	[ba, ba, ba]					)
  return filt



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)			,	)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)
  _snake_case						=							10 ** (gain_db / 40)

  _snake_case						=							1 + alpha * big_a
  _snake_case						=							-2 * _cos
  _snake_case						=							1 - alpha * big_a
  _snake_case						=							1 + alpha / big_a
  _snake_case						=							-2 * _cos
  _snake_case						=							1 - alpha / big_a

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([aa, aa, aa]			,	[ba, ba, ba]					)
  return filt



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)			,	)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)
  _snake_case						=							10 ** (gain_db / 40)
  _snake_case						=							(big_a + 1) - (big_a - 1) * _cos
  _snake_case						=							(big_a + 1) + (big_a - 1) * _cos
  _snake_case						=							(big_a - 1) - (big_a + 1) * _cos
  _snake_case						=							(big_a - 1) + (big_a + 1) * _cos
  _snake_case						=							2 * sqrt(_UpperCamelCase					) * alpha

  _snake_case						=							big_a * (pmc + aaa)
  _snake_case						=							2 * big_a * mpc
  _snake_case						=							big_a * (pmc - aaa)
  _snake_case						=							ppmc + aaa
  _snake_case						=							-2 * pmpc
  _snake_case						=							ppmc - aaa

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([aa, aa, aa]			,	[ba, ba, ba]					)
  return filt



def 				snake_case_(_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase			,	_UpperCamelCase = 1 / sqrt(2					)			,	)							->     IIRFilter:



  """simple docstring"""






  _snake_case						=							tau * frequency / samplerate
  _snake_case						=							sin(_UpperCamelCase					)
  _snake_case						=							cos(_UpperCamelCase					)
  _snake_case						=							_sin / (2 * q_factor)
  _snake_case						=							10 ** (gain_db / 40)
  _snake_case						=							(big_a + 1) - (big_a - 1) * _cos
  _snake_case						=							(big_a + 1) + (big_a - 1) * _cos
  _snake_case						=							(big_a - 1) - (big_a + 1) * _cos
  _snake_case						=							(big_a - 1) + (big_a + 1) * _cos
  _snake_case						=							2 * sqrt(_UpperCamelCase					) * alpha

  _snake_case						=							big_a * (ppmc + aaa)
  _snake_case						=							-2 * big_a * pmpc
  _snake_case						=							big_a * (ppmc - aaa)
  _snake_case						=							pmc + aaa
  _snake_case						=							2 * mpc
  _snake_case						=							pmc - aaa

  _snake_case						=							IIRFilter(2					)
  filt.set_coefficients([aa, aa, aa]			,	[ba, ba, ba]					)
  return filt

