






import functools






def 							lowerCamelCase__ (       __lowerCamelCase     :	list[int]    ,						__lowerCamelCase     :	list[int]						):

  # Validation
  if not isinstance(__lowerCamelCase    ,						__lowerCamelCase						) or not all(isinstance(__lowerCamelCase    ,						__lowerCamelCase						) for day in days						):
    raise ValueError("""The parameter days should be a list of integers"""						)

  if len(__lowerCamelCase						) != 3 or not all(isinstance(__lowerCamelCase    ,						__lowerCamelCase						) for cost in costs						):
    raise ValueError("""The parameter costs should be a list of three integers"""						)

  if len(__lowerCamelCase						) == 0:
    return 0

  if min(__lowerCamelCase						) <= 0:
    raise ValueError("""All days elements should be greater than 0"""						)

  if max(__lowerCamelCase						) >= 366:
    raise ValueError("""All days elements should be less than 366"""						)

  __UpperCAmelCase				:      List[str]	 =    set(__lowerCamelCase						)

  @functools.cache
  def dynamic_programming(__lowerCamelCase     :	int						) -> int:
    if index > 365:
      return 0

    if index not in days_set:
      return dynamic_programming(index + 1						)

    return min(
        costs[0] + dynamic_programming(index + 1						)    ,						costs[1] + dynamic_programming(index + 7						)    ,						costs[2] + dynamic_programming(index + 30						)    ,						)

  return dynamic_programming(1						)


if __name__ == "__main__":
       import doctest

       doctest.testmod()





from math import isqrt, loga







def 						lowerCamelCase__      ( __A    :int		):


       """simple docstring"""




       __snake_case       	=							[True] * max_number
       for i in range(2	,isqrt(max_number - 1		) + 1		):
              if is_prime[i]:
                     for j in range(i**2	,__A	,__A		):
                            __snake_case       	=							False

       return [i for i in range(2	,__A		) if is_prime[i]]







def 						lowerCamelCase__      ( __A    :int = 8_0_0_8_0_0	,__A    :int = 8_0_0_8_0_0		):


       """simple docstring"""




       __snake_case       	=							degree * loga(__A		)
       __snake_case       	=							int(__A		)
       __snake_case       	=							calculate_prime_numbers(__A		)

       __snake_case       	=							0
       __snake_case       	=							0
       __snake_case       	=							len(__A		) - 1
       while left < right:
              while (
                  prime_numbers[right] * loga(prime_numbers[left]		)
                  + prime_numbers[left] * loga(prime_numbers[right]		)
                  > upper_bound
              ):
                     right -= 1
              hybrid_integers_count += right - left
              left += 1

       return hybrid_integers_count


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

