


'''simple docstring'''
from __future__ import annotations






class        lowerCAmelCase_  :






       def __init__( self			,     _UpperCamelCase   )->      None:
            _A				=							order

            # a_{0} ... a_{k}
            _A				=							[1.0] + [0.0] * order
            # b_{0} ... b_{k}
            _A				=							[1.0] + [0.0] * order

            # x[n-1] ... x[n-k]
            _A				=							[0.0] * self.order
            # y[n-1] ... y[n-k]
            _A				=							[0.0] * self.order






       def   UpperCamelCase						( self			,     _UpperCamelCase			,     _UpperCamelCase   )->      None:
            if len(_UpperCamelCase   ) < self.order:
                 _A				=							[1.0, *a_coeffs]

            if len(_UpperCamelCase   ) != self.order + 1:
                 _A				=							(
                     F'Expected a_coeffs to have {self.order + 1} elements '
                     F'for {self.order}-order filter, got {len(_UpperCamelCase   )}'
                 )
                 raise ValueError(_UpperCamelCase   )

            if len(_UpperCamelCase   ) != self.order + 1:
                 _A				=							(
                     F'Expected b_coeffs to have {self.order + 1} elements '
                     F'for {self.order}-order filter, got {len(_UpperCamelCase   )}'
                 )
                 raise ValueError(_UpperCamelCase   )

            _A				=							a_coeffs
            _A				=							b_coeffs






       def   UpperCamelCase						( self			,     _UpperCamelCase   )->      float:
            _A				=							0.0

            # Start at index 1 and do index 0 at the end.
            for i in range(1			,     self.order + 1   ):
                 result += (
                     self.b_coeffs[i] * self.input_history[i - 1]
                     - self.a_coeffs[i] * self.output_history[i - 1]
                 )

            _A				=							(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

            _A				=							self.input_history[:-1]
            _A				=							self.output_history[:-1]

            _A				=							sample
            _A				=							result

            return result









'''simple docstring'''
def 					lowerCamelCase_ ( __UpperCamelCase					:       int		)					->	bool:







     """simple docstring"""
     return str(__UpperCamelCase		) == str(__UpperCamelCase		)[::-1]

def 					lowerCamelCase_ ( __UpperCamelCase					:       int		)					->	int:







     """simple docstring"""
     return int(__UpperCamelCase		) + int(str(__UpperCamelCase		)[::-1]		)

def 					lowerCamelCase_ ( __UpperCamelCase					:       int = 1_0_0_0_0		)					->	int:







     """simple docstring"""
     _A				=							[]
     for num in range(1							,    __UpperCamelCase		):
          _A				=							0
          _A				=							num
          while iterations < 5_0:
               _A				=							sum_reverse(__UpperCamelCase		)
               iterations += 1
               if is_palindrome(__UpperCamelCase		):
                    break
          else:
               lychrel_nums.append(__UpperCamelCase		)
     return len(__UpperCamelCase		)


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





