

'''simple docstring'''



from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter







def   a__			(    a__ ,       a__ ,       a__ = 1 / sqrt(2		)		):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE      = tau * frequency / samplerate
     __SCREAMING_SNAKE_CASE      = sin(__snake_case		)
     __SCREAMING_SNAKE_CASE      = cos(__snake_case		)
     __SCREAMING_SNAKE_CASE      = _sin / (2 * q_factor)

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

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

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







def   a__			(    a__ ,       a__ ,       a__ = 1 / sqrt(2		)		):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE      = tau * frequency / samplerate
     __SCREAMING_SNAKE_CASE      = sin(__snake_case		)
     __SCREAMING_SNAKE_CASE      = cos(__snake_case		)
     __SCREAMING_SNAKE_CASE      = _sin / (2 * q_factor)

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

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

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







def   a__			(    a__ ,       a__ ,       a__ = 1 / sqrt(2		)		):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE      = tau * frequency / samplerate
     __SCREAMING_SNAKE_CASE      = sin(__snake_case		)
     __SCREAMING_SNAKE_CASE      = cos(__snake_case		)
     __SCREAMING_SNAKE_CASE      = _sin / (2 * q_factor)

     __SCREAMING_SNAKE_CASE      = _sin / 2
     __SCREAMING_SNAKE_CASE      = 0
     __SCREAMING_SNAKE_CASE      = -ba

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

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







def   a__			(    a__ ,       a__ ,       a__ = 1 / sqrt(2		)		):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE      = tau * frequency / samplerate
     __SCREAMING_SNAKE_CASE      = sin(__snake_case		)
     __SCREAMING_SNAKE_CASE      = cos(__snake_case		)
     __SCREAMING_SNAKE_CASE      = _sin / (2 * q_factor)

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

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







def   a__			(    a__ ,       a__ ,       a__ ,       a__ = 1 / sqrt(2		) ,       ):




     """simple docstring"""


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

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

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







def   a__			(    a__ ,       a__ ,       a__ ,       a__ = 1 / sqrt(2		) ,       ):




     """simple docstring"""


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

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

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







def   a__			(    a__ ,       a__ ,       a__ ,       a__ = 1 / sqrt(2		) ,       ):




     """simple docstring"""


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

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

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







def 					_snake_case	(  __snake_case = 100						):
					_UpperCamelCase			     =     (n * (n + 1) // 2) ** 2
					_UpperCamelCase			     =     n * (n + 1) * (2 * n + 1) // 6
					return sum_cubes - sum_squares


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