

'''simple docstring'''
import math
class  _snake_case						:






			def __init__(   self       ,_snake_case       ,_snake_case       ,_snake_case			):
				UpperCAmelCase_			:	int      =   x
				UpperCAmelCase_			:	str      =   y
				UpperCAmelCase_			:	List[str]      =   z






			def __repr__(   self			):
				return f'''Point({self.x}, {self.y}, {self.z})'''




def       a__    (  _SCREAMING_SNAKE_CASE					:    Point     ,							_SCREAMING_SNAKE_CASE					:    Point							)			-> float:


	"""simple docstring"""





	return math.sqrt(abs((b.x - a.x) ** 2 + (b.y - a.y) ** 2 + (b.z - a.z) ** 2							)							)


if __name__ == "__main__":
					import doctest

					doctest.testmod()







'''simple docstring'''
from __future__ import annotations


def       a__    (  _SCREAMING_SNAKE_CASE					:    int							)			-> set[int]:


	"""simple docstring"""





	UpperCAmelCase_			:	Dict      =   {1}
	UpperCAmelCase_			:	int      =   [1]
	for _ in range(2     ,							depth + 1							):
		UpperCAmelCase_			:	Dict      =   [*previous_coefficients, 0]
		UpperCAmelCase_			:	Tuple      =   [0, *previous_coefficients]
		UpperCAmelCase_			:	Dict      =   []
		for x, y in zip(_SCREAMING_SNAKE_CASE     ,							_SCREAMING_SNAKE_CASE							):
			coefficients.add(x + y							)
			previous_coefficients.append(x + y							)
	return coefficients


def       a__    (  _SCREAMING_SNAKE_CASE					:    set[int]							)			-> set[int]:


	"""simple docstring"""





	UpperCAmelCase_			:	List[Any]      =   set()
	for number in unique_coefficients:
		UpperCAmelCase_			:	Tuple      =   2
		UpperCAmelCase_			:	Tuple      =   number
		while divisor**2 <= copy_number:
			UpperCAmelCase_			:	List[Any]      =   0
			while copy_number % divisor == 0:
				copy_number //= divisor
				multiplicity += 1
			if multiplicity >= 2:
				non_squarefrees.add(_SCREAMING_SNAKE_CASE							)
				break
			divisor += 1

	return unique_coefficients.difference(_SCREAMING_SNAKE_CASE							)


def       a__    (  _SCREAMING_SNAKE_CASE					:    int = 51							)			-> int:


	"""simple docstring"""





	UpperCAmelCase_			:	Optional[Any]      =   get_pascal_triangle_unique_coefficients(_SCREAMING_SNAKE_CASE							)
	UpperCAmelCase_			:	Union[str, Any]      =   get_squarefrees(_SCREAMING_SNAKE_CASE							)
	return sum(_SCREAMING_SNAKE_CASE							)


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




