
def 				a						(							snake_case__:					int = 100					):


				'''simple docstring'''
				lowercase_       =					(n * (n + 1) // 2) ** 2
				lowercase_       =					n * (n + 1) * (2 * n + 1) // 6
				return sum_cubes - sum_squares


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






from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter


def     __lowerCAmelCase			(			a__						,    a__						,    a__ = 1 / sqrt(2  )  )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)

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

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

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


def     __lowerCAmelCase			(			a__						,    a__						,    a__ = 1 / sqrt(2  )  )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)

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

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

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


def     __lowerCAmelCase			(			a__						,    a__						,    a__ = 1 / sqrt(2  )  )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)

				__a										=    _sin / 2
				__a										=    0
				__a										=    -ba

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

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


def     __lowerCAmelCase			(			a__						,    a__						,    a__ = 1 / sqrt(2  )  )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)

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

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


def     __lowerCAmelCase			(			a__						,    a__						,    a__						,    a__ = 1 / sqrt(2  )						,    )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)
				__a										=    10 ** (gain_db / 40)

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

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


def     __lowerCAmelCase			(			a__						,    a__						,    a__						,    a__ = 1 / sqrt(2  )						,    )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)
				__a										=    10 ** (gain_db / 40)
				__a										=    (big_a + 1) - (big_a - 1) * _cos
				__a										=    (big_a + 1) + (big_a - 1) * _cos
				__a										=    (big_a - 1) - (big_a + 1) * _cos
				__a										=    (big_a - 1) + (big_a + 1) * _cos
				__a										=    2 * sqrt(a__  ) * alpha

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

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






def     __lowerCAmelCase			(			a__						,    a__						,    a__						,    a__ = 1 / sqrt(2  )						,    )       ->  IIRFilter:
				__a										=    tau * frequency / samplerate
				__a										=    sin(a__  )
				__a										=    cos(a__  )
				__a										=    _sin / (2 * q_factor)
				__a										=    10 ** (gain_db / 40)
				__a										=    (big_a + 1) - (big_a - 1) * _cos
				__a										=    (big_a + 1) + (big_a - 1) * _cos
				__a										=    (big_a - 1) - (big_a + 1) * _cos
				__a										=    (big_a - 1) + (big_a + 1) * _cos
				__a										=    2 * sqrt(a__  ) * alpha

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

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