
"""simple docstring"""





def 						_lowerCAmelCase				(				UpperCamelCase_  ,				UpperCamelCase_				):
		_validate_point(UpperCamelCase_				)
		_validate_point(UpperCamelCase_				)
		if len(UpperCamelCase_				) != len(UpperCamelCase_				):
				raise ValueError("""Both points must be in the same n-dimensional space"""				)

		return float(sum(abs(a - b				) for a, b in zip(UpperCamelCase_  ,				UpperCamelCase_				)				)				)



def 						_lowerCAmelCase				(				UpperCamelCase_				):
		if point:
				if isinstance(UpperCamelCase_  ,				UpperCamelCase_				):
						for item in point:
								if not isinstance(UpperCamelCase_  ,				(int, float)				):
										__SCREAMING_SNAKE_CASE            = (
										    """Expected a list of numbers as input, found """
										    f"{type(UpperCamelCase_				).__name__}"
										)
										raise TypeError(UpperCamelCase_				)
				else:
						__SCREAMING_SNAKE_CASE            = f"Expected a list of numbers as input, found {type(UpperCamelCase_				).__name__}"
						raise TypeError(UpperCamelCase_				)
		else:
				raise ValueError("""Missing an input"""				)



def 						_lowerCAmelCase				(				UpperCamelCase_  ,				UpperCamelCase_				):
		_validate_point(UpperCamelCase_				)
		_validate_point(UpperCamelCase_				)
		if len(UpperCamelCase_				) != len(UpperCamelCase_				):
				raise ValueError("""Both points must be in the same n-dimensional space"""				)

		return float(sum(abs(x - y				) for x, y in zip(UpperCamelCase_  ,				UpperCamelCase_				)				)				)


if __name__ == "__main__":
							import doctest

							doctest.testmod()






def    __UpperCamelCase     (				lowerCAmelCase__							:				int = 5_0_0_0_0_0_0_0  ):
 __a :  int						=  set()
 __a :  str						=  int((limit - 2_4) ** (1 / 2)  )

 __a :  int						=  set(range(3  ,   prime_square_limit + 1  ,   2  )  )
 primes.add(2  )
 for p in range(3  ,   prime_square_limit + 1  ,   2  ):
  if p not in primes:
   continue
  primes.difference_update(set(range(p * p  ,   prime_square_limit + 1  ,   lowerCAmelCase__  )  )  )

 for primea in primes:
  __a :  Union[str, Any]						=  primea * primea
  for primea in primes:
   __a :  Union[str, Any]						=  primea * primea * primea
   if square + cube >= limit - 1_6:
    break
   for primea in primes:
    __a :  int						=  primea * primea * primea * primea
    __a :  Union[str, Any]						=  square + cube + tetr
    if total >= limit:
     break
    ret.add(lowerCAmelCase__  )

 return len(lowerCAmelCase__  )


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