'''simple docstring'''






from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter





def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			int   ,		__snake_case							:			int   ,		__snake_case							:			float = 1 / sqrt(2				)				):
     _A    		=  tau * frequency / samplerate
     _A    		=  sin(__snake_case				)
     _A    		=  cos(__snake_case				)
     _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  _SCREAMING_SNAKE_CASE		(      __snake_case							:			int   ,		__snake_case							:			int   ,		__snake_case							:			float = 1 / sqrt(2				)				):
     _A    		=  tau * frequency / samplerate
     _A    		=  sin(__snake_case				)
     _A    		=  cos(__snake_case				)
     _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  _SCREAMING_SNAKE_CASE		(      __snake_case							:			int   ,		__snake_case							:			int   ,		__snake_case							:			float = 1 / sqrt(2				)				):
     _A    		=  tau * frequency / samplerate
     _A    		=  sin(__snake_case				)
     _A    		=  cos(__snake_case				)
     _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  _SCREAMING_SNAKE_CASE		(      __snake_case							:			int   ,		__snake_case							:			int   ,		__snake_case							:			float = 1 / sqrt(2				)				):
     _A    		=  tau * frequency / samplerate
     _A    		=  sin(__snake_case				)
     _A    		=  cos(__snake_case				)
     _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  _SCREAMING_SNAKE_CASE		(      __snake_case							:			int   ,		__snake_case							:			int   ,		__snake_case							:			float   ,		__snake_case							:			float = 1 / sqrt(2				)   ,		):
     _A    		=  tau * frequency / samplerate
     _A    		=  sin(__snake_case				)
     _A    		=  cos(__snake_case				)
     _A    		=  _sin / (2 * q_factor)
     _A    		=  1_0 ** (gain_db / 4_0)

     _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  _SCREAMING_SNAKE_CASE		(      __snake_case							:			int   ,		__snake_case							:			int   ,		__snake_case							:			float   ,		__snake_case							:			float = 1 / sqrt(2				)   ,		):
     _A    		=  tau * frequency / samplerate
     _A    		=  sin(__snake_case				)
     _A    		=  cos(__snake_case				)
     _A    		=  _sin / (2 * q_factor)
     _A    		=  1_0 ** (gain_db / 4_0)
     _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(__snake_case				) * 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  _SCREAMING_SNAKE_CASE		(      __snake_case							:			int   ,		__snake_case							:			int   ,		__snake_case							:			float   ,		__snake_case							:			float = 1 / sqrt(2				)   ,		):
     _A    		=  tau * frequency / samplerate
     _A    		=  sin(__snake_case				)
     _A    		=  cos(__snake_case				)
     _A    		=  _sin / (2 * q_factor)
     _A    		=  1_0 ** (gain_db / 4_0)
     _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(__snake_case				) * 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








"""simple docstring"""







from math import ceil, sqrt

def     UpperCAmelCase_					(				__a   :			int = 1_00_00_00						):




			'''simple docstring'''



			_lowerCamelCase					:					Tuple	       =    0

			for outer_width in range(3      ,							(limit // 4) + 2						):
						if outer_width**2 > limit:
									_lowerCamelCase					:					Optional[int]	       =    max(ceil(sqrt(outer_width**2 - limit						)						)      ,							1						)
						else:
									_lowerCamelCase					:					Any	       =    1
						if (outer_width - hole_width_lower_bound) % 2:
									hole_width_lower_bound += 1

						answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

			return answer


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





