'''simple docstring'''

def 			__UpperCamelCase       (   UpperCAmelCase     ):
 lowercase__				:    List[str]  =					0
 while num > 0:
  digit_sum += num % 10
  num //= 10
 return digit_sum
def 			__UpperCamelCase       (   UpperCAmelCase = 100     ):
 lowercase__				:    Dict  =					1
 lowercase__				:    Optional[int]  =					2

 for i in range(2		,     max_n + 1     ):
  lowercase__				:    List[str]  =					pre_numerator
  lowercase__				:    Optional[Any]  =					2 * i // 3 if i % 3 == 0 else 1
  lowercase__				:    Union[str, Any]  =					cur_numerator
  lowercase__				:    int  =					e_cont * pre_numerator + temp

 return sum_digits(UpperCAmelCase     )


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


'''simple docstring'''

import doctest
from collections import deque

import numpy as np



class 			UpperCAmelCase  :





       '''simple docstring'''



       def __init__(						self )  ->  None:
        lowercase__				:    str  =					[2, 1, 2, -1]
        lowercase__				:    str  =					[1, 2, 3, 4]


       def _lowerCAmelCase(						self )  ->  list[float]:
        lowercase__				:    Optional[Any]  =					len(self.first_signal )
        lowercase__				:    Union[str, Any]  =					len(self.second_signal )

        lowercase__				:    int  =					max(__lowerCAmelCase	,   __lowerCAmelCase )

        # create a zero matrix of max_length x max_length
        lowercase__				:    List[str]  =					[[0] * max_length for i in range(__lowerCAmelCase )]

        # 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(__lowerCAmelCase ):
         lowercase__				:    int  =					deque(self.second_signal )
         rotated_signal.rotate(__lowerCAmelCase )
         for j, item in enumerate(__lowerCAmelCase ):
          matrix[i][j] += item

        # multiply the matrix with the first signal
        lowercase__				:    Optional[int]  =					np.matmul(np.transpose(__lowerCAmelCase )	,   np.transpose(self.first_signal ) )

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


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

