


'''simple docstring'''
import doctest
from collections import deque

import numpy as np

class     _lowerCamelCase       :




 '''simple docstring'''


 def __init__(   self    ):

  """simple docstring"""







  __A	:		str	  =      [2, 1, 2, -1]
  __A	:		Any	  =      [1, 2, 3, 4]







 def 			snake_case__ (   self    ):

  """simple docstring"""







  __A	:		int	  =      len(self.first_signal    )
  __A	:		Optional[Any]	  =      len(self.second_signal    )

  __A	:		List[Any]	  =      max(__lowercase   ,   __lowercase    )

  # create a zero matrix of max_length x max_length
  __A	:		Tuple	  =      [[0] * max_length for i in range(__lowercase    )]

  # 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(__lowercase    ):
   __A	:		Union[str, Any]	  =      deque(self.second_signal    )
   rotated_signal.rotate(__lowercase    )
   for j, item in enumerate(__lowercase    ):
    matrix[i][j] += item

        # multiply the matrix with the first signal
  __A	:		Dict	  =      np.matmul(np.transpose(__lowercase    )   ,   np.transpose(self.first_signal    )    )

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


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










'''simple docstring'''
from math import factorial

UpperCAmelCase_			:  List[str]										=   {str(d): factorial(d) for d in range(1_0)}


def       _lowercase							(					UpperCamelCase__							:       int      ):
 return sum(DIGIT_FACTORIAL[d] for d in str(UpperCamelCase__      )      )


def       _lowercase							(					):
 __A	:		Union[str, Any]	  =      7 * factorial(9      ) + 1
 return sum(i for i in range(3,					UpperCamelCase__      ) if sum_of_digit_factorial(UpperCamelCase__      ) == i      )


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






