

import numpy as np





def    A_  (							a					,   a					,   a					,   a					,   a  ):

      """simple docstring"""



      SCREAMING_SNAKE_CASE_				:  str           =     int(np.ceil((x_end - xa) / h  )  )
      SCREAMING_SNAKE_CASE_				:  Dict           =     np.zeros((n + 1,)  )
      SCREAMING_SNAKE_CASE_				:  int           =     ya
      SCREAMING_SNAKE_CASE_				:  Optional[int]           =     xa

      for k in range(_SCREAMING_SNAKE_CASE  ):
            SCREAMING_SNAKE_CASE_				:  List[str]           =     f(_SCREAMING_SNAKE_CASE					,   y[k]  )
            SCREAMING_SNAKE_CASE_				:  List[str]           =     f(x + 0.5 * h					,   y[k] + 0.5 * h * ka  )
            SCREAMING_SNAKE_CASE_				:  Union[str, Any]           =     f(x + 0.5 * h					,   y[k] + 0.5 * h * ka  )
            SCREAMING_SNAKE_CASE_				:  str           =     f(x + h					,   y[k] + h * ka  )
            SCREAMING_SNAKE_CASE_				:  Optional[Any]           =     y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
            x += h

      return y


if __name__ == "__main__":
    import doctest

    doctest.testmod()









def    A_  (							a  ):

      """simple docstring"""



      SCREAMING_SNAKE_CASE_				:  List[Any]           =     0
      while num > 0:
            digit_sum += num % 1_0
            num //= 1_0
      return digit_sum

def    A_  (							a = 1_0_0  ):

      """simple docstring"""



      SCREAMING_SNAKE_CASE_				:  List[str]           =     1
      SCREAMING_SNAKE_CASE_				:  Union[str, Any]           =     2

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

      return sum_digits(a  )


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






