

'''simple docstring'''







import itertools
import math
def       UpperCAmelCase__    (      UpperCAmelCase__				)			->			bool:

       if 1 < number < 4:
              # 2 and 3 are primes
              return True
       elif number < 2 or number % 2 == 0 or number % 3 == 0:
              # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
              return False

       # All primes number are in format of 6k +/- 1
       for i in range(5,       int(math.sqrt(UpperCAmelCase__				) + 1				),       6				):
              if number % i == 0 or number % (i + 2) == 0:
                     return False
       return True
def       UpperCAmelCase__    (      )			->			Optional[Any]:
       A_						=      2
       while True:
              if is_prime(UpperCAmelCase__				):
                     yield num
              num += 1
def       UpperCAmelCase__    (      UpperCAmelCase__ = 1_00_01				)			->			int:
       return next(itertools.islice(prime_generator(),       nth - 1,       UpperCAmelCase__				)				)


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



'''simple docstring'''







def       UpperCAmelCase__    (      UpperCAmelCase__,       UpperCAmelCase__				)			->			float:
       _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       UpperCAmelCase__    (      UpperCAmelCase__				)			->			None:
       if point:
              if isinstance(UpperCAmelCase__,       UpperCAmelCase__				):
                     for item in point:
                            if not isinstance(UpperCAmelCase__,       (int, float)				):
                                   A_						=      (
                                       """Expected a list of numbers as input, found """
                                       F'''{type(UpperCAmelCase__				).__name__}'''
                                   )
                                   raise TypeError(UpperCAmelCase__				)
              else:
                     A_						=      F'''Expected a list of numbers as input, found {type(UpperCAmelCase__				).__name__}'''
                     raise TypeError(UpperCAmelCase__				)
       else:
              raise ValueError("""Missing an input"""				)
def       UpperCAmelCase__    (      UpperCAmelCase__,       UpperCAmelCase__				)			->			float:
       _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()
