






from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter






def   a			(						lowerCamelCase_		,   lowerCamelCase_		,   lowerCamelCase_ = 1 / sqrt(2				)				):






				'''simple docstring'''
				lowercase__    =			tau * frequency / samplerate
				lowercase__    =			sin(__lowerCAmelCase				)
				lowercase__    =			cos(__lowerCAmelCase				)
				lowercase__    =			_sin / (2 * q_factor)

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

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

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






def   a			(						lowerCamelCase_		,   lowerCamelCase_		,   lowerCamelCase_ = 1 / sqrt(2				)				):






				'''simple docstring'''
				lowercase__    =			tau * frequency / samplerate
				lowercase__    =			sin(__lowerCAmelCase				)
				lowercase__    =			cos(__lowerCAmelCase				)
				lowercase__    =			_sin / (2 * q_factor)

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

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

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






def   a			(						lowerCamelCase_		,   lowerCamelCase_		,   lowerCamelCase_ = 1 / sqrt(2				)				):






				'''simple docstring'''
				lowercase__    =			tau * frequency / samplerate
				lowercase__    =			sin(__lowerCAmelCase				)
				lowercase__    =			cos(__lowerCAmelCase				)
				lowercase__    =			_sin / (2 * q_factor)

				lowercase__    =			_sin / 2
				lowercase__    =			0
				lowercase__    =			-ba

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

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






def   a			(						lowerCamelCase_		,   lowerCamelCase_		,   lowerCamelCase_ = 1 / sqrt(2				)				):






				'''simple docstring'''
				lowercase__    =			tau * frequency / samplerate
				lowercase__    =			sin(__lowerCAmelCase				)
				lowercase__    =			cos(__lowerCAmelCase				)
				lowercase__    =			_sin / (2 * q_factor)

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

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






def   a			(						lowerCamelCase_		,   lowerCamelCase_		,   lowerCamelCase_		,   lowerCamelCase_ = 1 / sqrt(2				)		,   ):






				'''simple docstring'''
				lowercase__    =			tau * frequency / samplerate
				lowercase__    =			sin(__lowerCAmelCase				)
				lowercase__    =			cos(__lowerCAmelCase				)
				lowercase__    =			_sin / (2 * q_factor)
				lowercase__    =			10 ** (gain_db / 40)

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

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






def   a			(						lowerCamelCase_		,   lowerCamelCase_		,   lowerCamelCase_		,   lowerCamelCase_ = 1 / sqrt(2				)		,   ):






				'''simple docstring'''
				lowercase__    =			tau * frequency / samplerate
				lowercase__    =			sin(__lowerCAmelCase				)
				lowercase__    =			cos(__lowerCAmelCase				)
				lowercase__    =			_sin / (2 * q_factor)
				lowercase__    =			10 ** (gain_db / 40)
				lowercase__    =			(big_a + 1) - (big_a - 1) * _cos
				lowercase__    =			(big_a + 1) + (big_a - 1) * _cos
				lowercase__    =			(big_a - 1) - (big_a + 1) * _cos
				lowercase__    =			(big_a - 1) + (big_a + 1) * _cos
				lowercase__    =			2 * sqrt(__lowerCAmelCase				) * alpha

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

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






def   a			(						lowerCamelCase_		,   lowerCamelCase_		,   lowerCamelCase_		,   lowerCamelCase_ = 1 / sqrt(2				)		,   ):






				'''simple docstring'''
				lowercase__    =			tau * frequency / samplerate
				lowercase__    =			sin(__lowerCAmelCase				)
				lowercase__    =			cos(__lowerCAmelCase				)
				lowercase__    =			_sin / (2 * q_factor)
				lowercase__    =			10 ** (gain_db / 40)
				lowercase__    =			(big_a + 1) - (big_a - 1) * _cos
				lowercase__    =			(big_a + 1) + (big_a - 1) * _cos
				lowercase__    =			(big_a - 1) - (big_a + 1) * _cos
				lowercase__    =			(big_a - 1) + (big_a + 1) * _cos
				lowercase__    =			2 * sqrt(__lowerCAmelCase				) * alpha

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

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












from __future__ import annotations

import sys
from collections import deque
from typing import Generic, TypeVar

lowerCamelCase	:							int				=TypeVar('''T''')





class 			__a  (    Generic[T]       ):
 _lowerCAmelCase       :       deque[T]  # Cache store of keys
 _lowerCAmelCase       :       set[T]  # References of the keys in cache
 _lowerCAmelCase       :       int        = 1_0  # Maximum capacity of cache







 def __init__(		self					:   List[str]							,   SCREAMING_SNAKE_CASE					:   int						):


      '''simple docstring'''






      UpperCamelCase__			:   Tuple       				=  deque()
      UpperCamelCase__			:   Optional[int]       				=  set()
      if not n:
           UpperCamelCase__			:   Tuple       				=  sys.maxsize
      elif n < 0:
           raise ValueError("n should be an integer greater than 0."						)
      else:
           UpperCamelCase__			:   Dict       				=  n







 def 					__lowercase					(		self					:   List[Any]							,   SCREAMING_SNAKE_CASE					:   T						):


      '''simple docstring'''






      if x not in self.key_reference:
           if len(self.dq_store						) == LRUCache._MAX_CAPACITY:
                UpperCamelCase__			:   int       				=  self.dq_store.pop()
                self.key_reference.remove(SCREAMING_SNAKE_CASE						)
      else:
           self.dq_store.remove(SCREAMING_SNAKE_CASE						)

      self.dq_store.appendleft(SCREAMING_SNAKE_CASE						)
      self.key_reference.add(SCREAMING_SNAKE_CASE						)







 def 					__lowercase					(		self					:   Dict						):


      '''simple docstring'''






      for k in self.dq_store:
           print(SCREAMING_SNAKE_CASE						)







 def __repr__(		self					:   Union[str, Any]						):


      '''simple docstring'''






      return F'LRUCache({self._MAX_CAPACITY}) => {list(self.dq_store						)}'


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 lowerCamelCase	:							LRUCache[str | int]				=LRUCache(4)
 lru_cache.refer('''A''')
 lru_cache.refer(2)
 lru_cache.refer(3)
 lru_cache.refer('''A''')
 lru_cache.refer(4)
 lru_cache.refer(5)
 lru_cache.display()

 print(lru_cache)
 assert str(lru_cache) == "LRUCache(4) => [5, 4, 'A', 3]"