

'''simple docstring'''




import doctest
from collections import deque

import numpy as np






class   _SCREAMING_SNAKE_CASE   :



 def __init__(   self		:   str      ):
      __magic_name__						       =    [2, 1, 2, -1]
      __magic_name__						       =    [1, 2, 3, 4]



 def 			snake_case__  (   self		:   Optional[int]      ):
      __magic_name__						       =    len(self.first_signal      )
      __magic_name__						       =    len(self.second_signal      )

      __magic_name__						       =    max(a__			,				a__      )

      # create a zero matrix of max_length x max_length
      __magic_name__						       =    [[0] * max_length for i in range(a__      )]

      # fills the smaller signal with zeros to make both signals of same length
      if length_first_signal < length_second_signal:
           self.first_signal += [0] * (max_length - length_first_signal)
      elif length_first_signal > length_second_signal:
           self.second_signal += [0] * (max_length - length_second_signal)
      for i in range(a__      ):
           __magic_name__						       =    deque(self.second_signal      )
           rotated_signal.rotate(a__      )
           for j, item in enumerate(a__      ):
                matrix[i][j] += item

        # multiply the matrix with the first signal
      __magic_name__						       =    np.matmul(np.transpose(a__      )			,				np.transpose(self.first_signal      )      )

      # rounding-off to two decimal places
      return [round(a__			,				2      ) for i in final_signal]


if __name__ == "__main__":
      doctest.testmod()









'''simple docstring'''




from __future__ import annotations

from fractions import Fraction




def 						UpperCamelCase	(			a		,						a			)				->     bool:






     '''simple docstring'''
     return (
         num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
     )




def 						UpperCamelCase	(			a			)				->     list[str]:






     '''simple docstring'''
     __magic_name__						       =    []
     __magic_name__						       =    11
     __magic_name__						       =    int('''1''' + '''0''' * digit_len			)
     for num in range(a		,						a			):
          while den <= 99:
               if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
                    if is_digit_cancelling(a		,						a			):
                         solutions.append(F'''{num}/{den}'''			)
               den += 1
          num += 1
          __magic_name__						       =    10
     return solutions




def 						UpperCamelCase	(			a = 2			)				->     int:






     '''simple docstring'''
     __magic_name__						       =    1.0
     for fraction in fraction_list(a			):
          __magic_name__						       =    Fraction(a			)
          result *= frac.denominator / frac.numerator
     return int(a			)


if __name__ == "__main__":
      print(solution())






