




'''simple docstring'''



from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter




def   lowercase__(			__UpperCamelCase:					int      ,__UpperCamelCase:					int      ,__UpperCamelCase:					float = 1 / sqrt(2    )    ):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      int    					=						tau * frequency / samplerate
      SCREAMING_SNAKE_CASE   :      Tuple    					=						sin(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						cos(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Tuple    					=						_sin / (2 * q_factor)

      SCREAMING_SNAKE_CASE   :      int    					=						(1 - _cos) / 2
      SCREAMING_SNAKE_CASE   :      List[str]    					=						1 - _cos

      SCREAMING_SNAKE_CASE   :      List[Any]    					=						1 + alpha
      SCREAMING_SNAKE_CASE   :      Union[str, Any]    					=						-2 * _cos
      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						1 - alpha

      SCREAMING_SNAKE_CASE   :      Any    					=						IIRFilter(2    )
      filt.set_coefficients([aa, aa, aa]      ,[ba, ba, ba]    )
      return filt




def   lowercase__(			__UpperCamelCase:					int      ,__UpperCamelCase:					int      ,__UpperCamelCase:					float = 1 / sqrt(2    )    ):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      Any    					=						tau * frequency / samplerate
      SCREAMING_SNAKE_CASE   :      Any    					=						sin(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      List[Any]    					=						cos(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Dict    					=						_sin / (2 * q_factor)

      SCREAMING_SNAKE_CASE   :      str    					=						(1 + _cos) / 2
      SCREAMING_SNAKE_CASE   :      int    					=						-1 - _cos

      SCREAMING_SNAKE_CASE   :      Tuple    					=						1 + alpha
      SCREAMING_SNAKE_CASE   :      Union[str, Any]    					=						-2 * _cos
      SCREAMING_SNAKE_CASE   :      Tuple    					=						1 - alpha

      SCREAMING_SNAKE_CASE   :      Any    					=						IIRFilter(2    )
      filt.set_coefficients([aa, aa, aa]      ,[ba, ba, ba]    )
      return filt




def   lowercase__(			__UpperCamelCase:					int      ,__UpperCamelCase:					int      ,__UpperCamelCase:					float = 1 / sqrt(2    )    ):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      str    					=						tau * frequency / samplerate
      SCREAMING_SNAKE_CASE   :      Tuple    					=						sin(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Dict    					=						cos(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Dict    					=						_sin / (2 * q_factor)

      SCREAMING_SNAKE_CASE   :      List[str]    					=						_sin / 2
      SCREAMING_SNAKE_CASE   :      List[str]    					=						0
      SCREAMING_SNAKE_CASE   :      int    					=						-ba

      SCREAMING_SNAKE_CASE   :      List[str]    					=						1 + alpha
      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						-2 * _cos
      SCREAMING_SNAKE_CASE   :      Dict    					=						1 - alpha

      SCREAMING_SNAKE_CASE   :      str    					=						IIRFilter(2    )
      filt.set_coefficients([aa, aa, aa]      ,[ba, ba, ba]    )
      return filt




def   lowercase__(			__UpperCamelCase:					int      ,__UpperCamelCase:					int      ,__UpperCamelCase:					float = 1 / sqrt(2    )    ):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      Tuple    					=						tau * frequency / samplerate
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						sin(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						cos(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Dict    					=						_sin / (2 * q_factor)

      SCREAMING_SNAKE_CASE   :      Dict    					=						1 - alpha
      SCREAMING_SNAKE_CASE   :      int    					=						-2 * _cos
      SCREAMING_SNAKE_CASE   :      Tuple    					=						1 + alpha

      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						IIRFilter(2    )
      filt.set_coefficients([ba, ba, ba]      ,[ba, ba, ba]    )
      return filt




def   lowercase__(			__UpperCamelCase:					int      ,__UpperCamelCase:					int      ,__UpperCamelCase:					float      ,__UpperCamelCase:					float = 1 / sqrt(2    )      ,):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						tau * frequency / samplerate
      SCREAMING_SNAKE_CASE   :      Tuple    					=						sin(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						cos(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						_sin / (2 * q_factor)
      SCREAMING_SNAKE_CASE   :      List[str]    					=						10 ** (gain_db / 40)

      SCREAMING_SNAKE_CASE   :      Union[str, Any]    					=						1 + alpha * big_a
      SCREAMING_SNAKE_CASE   :      str    					=						-2 * _cos
      SCREAMING_SNAKE_CASE   :      List[Any]    					=						1 - alpha * big_a
      SCREAMING_SNAKE_CASE   :      List[str]    					=						1 + alpha / big_a
      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						-2 * _cos
      SCREAMING_SNAKE_CASE   :      Any    					=						1 - alpha / big_a

      SCREAMING_SNAKE_CASE   :      List[str]    					=						IIRFilter(2    )
      filt.set_coefficients([aa, aa, aa]      ,[ba, ba, ba]    )
      return filt




def   lowercase__(			__UpperCamelCase:					int      ,__UpperCamelCase:					int      ,__UpperCamelCase:					float      ,__UpperCamelCase:					float = 1 / sqrt(2    )      ,):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      int    					=						tau * frequency / samplerate
      SCREAMING_SNAKE_CASE   :      List[Any]    					=						sin(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Union[str, Any]    					=						cos(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						_sin / (2 * q_factor)
      SCREAMING_SNAKE_CASE   :      Tuple    					=						10 ** (gain_db / 40)
      SCREAMING_SNAKE_CASE   :      str    					=						(big_a + 1) - (big_a - 1) * _cos
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						(big_a + 1) + (big_a - 1) * _cos
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						(big_a - 1) - (big_a + 1) * _cos
      SCREAMING_SNAKE_CASE   :      str    					=						(big_a - 1) + (big_a + 1) * _cos
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						2 * sqrt(__UpperCamelCase    ) * alpha

      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						big_a * (pmc + aaa)
      SCREAMING_SNAKE_CASE   :      str    					=						2 * big_a * mpc
      SCREAMING_SNAKE_CASE   :      Dict    					=						big_a * (pmc - aaa)
      SCREAMING_SNAKE_CASE   :      str    					=						ppmc + aaa
      SCREAMING_SNAKE_CASE   :      Union[str, Any]    					=						-2 * pmpc
      SCREAMING_SNAKE_CASE   :      List[Any]    					=						ppmc - aaa

      SCREAMING_SNAKE_CASE   :      List[Any]    					=						IIRFilter(2    )
      filt.set_coefficients([aa, aa, aa]      ,[ba, ba, ba]    )
      return filt





def   lowercase__(			__UpperCamelCase:					int      ,__UpperCamelCase:					int      ,__UpperCamelCase:					float      ,__UpperCamelCase:					float = 1 / sqrt(2    )      ,):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						tau * frequency / samplerate
      SCREAMING_SNAKE_CASE   :      Any    					=						sin(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      List[str]    					=						cos(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						_sin / (2 * q_factor)
      SCREAMING_SNAKE_CASE   :      List[Any]    					=						10 ** (gain_db / 40)
      SCREAMING_SNAKE_CASE   :      Dict    					=						(big_a + 1) - (big_a - 1) * _cos
      SCREAMING_SNAKE_CASE   :      str    					=						(big_a + 1) + (big_a - 1) * _cos
      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						(big_a - 1) - (big_a + 1) * _cos
      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						(big_a - 1) + (big_a + 1) * _cos
      SCREAMING_SNAKE_CASE   :      Dict    					=						2 * sqrt(__UpperCamelCase    ) * alpha

      SCREAMING_SNAKE_CASE   :      List[str]    					=						big_a * (ppmc + aaa)
      SCREAMING_SNAKE_CASE   :      Tuple    					=						-2 * big_a * pmpc
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						big_a * (ppmc - aaa)
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						pmc + aaa
      SCREAMING_SNAKE_CASE   :      Dict    					=						2 * mpc
      SCREAMING_SNAKE_CASE   :      int    					=						pmc - aaa

      SCREAMING_SNAKE_CASE   :      Tuple    					=						IIRFilter(2    )
      filt.set_coefficients([aa, aa, aa]      ,[ba, ba, ba]    )
      return filt








'''simple docstring'''



class 							_a				:





       '''simple docstring'''






       def __init__(      self,							A  ):







             '''simple docstring'''







             SCREAMING_SNAKE_CASE   :      Tuple    					=						val
             SCREAMING_SNAKE_CASE   :      Any    					=						None
             SCREAMING_SNAKE_CASE   :      Union[str, Any]    					=						None







       def        UpperCamelCase_							(      self,							A  ):







             '''simple docstring'''







             if self.val:
                   if val < self.val:
                         if self.left is None:
                               SCREAMING_SNAKE_CASE   :      Optional[int]    					=						Node(A  )
                         else:
                               self.left.insert(A  )
                   elif val > self.val:
                         if self.right is None:
                               SCREAMING_SNAKE_CASE   :      int    					=						Node(A  )
                         else:
                               self.right.insert(A  )
             else:
                   SCREAMING_SNAKE_CASE   :      int    					=						val




def   lowercase__(			__UpperCamelCase:					Optional[int]      ,__UpperCamelCase:					List[str]    ):

      """simple docstring"""






      if root:
            inorder(root.left      ,__UpperCamelCase    )
            res.append(root.val    )
            inorder(root.right      ,__UpperCamelCase    )




def   lowercase__(			__UpperCamelCase:					List[Any]    ):

      """simple docstring"""






      if len(__UpperCamelCase    ) == 0:
            return arr
      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						Node(arr[0]    )
      for i in range(1      ,len(__UpperCamelCase    )    ):
            root.insert(arr[i]    )
      # Traverse BST in order.
      SCREAMING_SNAKE_CASE   :      Dict    					=						[]
      inorder(__UpperCamelCase      ,__UpperCamelCase    )
      return res


if __name__ == "__main__":
      print(tree_sort([1_0, 1, 3, 2, 9, 1_4, 1_3]))


