




'''simple docstring'''






from __future__ import annotations




def 		a_(			lowerCamelCase   )					->set[int]:






       '''simple docstring'''




       lowercase	:		Dict    =   {1}
       lowercase	:		Union[str, Any]    =   [1]
       for _ in range(2 ,					depth + 1   ):
              lowercase	:		Tuple    =   [*previous_coefficients, 0]
              lowercase	:		List[str]    =   [0, *previous_coefficients]
              lowercase	:		Optional[int]    =   []
              for x, y in zip(lowerCamelCase ,					lowerCamelCase   ):
                     coefficients.add(x + y   )
                     previous_coefficients.append(x + y   )
       return coefficients




def 		a_(			lowerCamelCase   )					->set[int]:






       '''simple docstring'''




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

       return unique_coefficients.difference(lowerCamelCase   )




def 		a_(			lowerCamelCase = 51   )					->int:






       '''simple docstring'''




       lowercase	:		Union[str, Any]    =   get_pascal_triangle_unique_coefficients(lowerCamelCase   )
       lowercase	:		str    =   get_squarefrees(lowerCamelCase   )
       return sum(lowerCamelCase   )


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







'''simple docstring'''

def      __magic_name__							(			A				)      ->		tuple[int, int]:
	# base case
	if len(A				) == 1:
		return a[0], a[0]
	else:
		# split A into half.
		snake_case							=					a[: len(A				) // 2]
		snake_case							=					a[len(A				) // 2 :]

		# 2 sub problems, 1/2 of original size.
		snake_case			,			snake_case							=					max_difference(A				)
		snake_case			,			snake_case							=					max_difference(A				)

		# get min of first and max of second
		# linear time
		snake_case							=					min(A				)
		snake_case							=					max(A				)

		# 3 cases, either (small1, big1),
		# (min_first, max_second), (small2, big2)
		# constant comparisons
		if biga - smalla > max_second - min_first and biga - smalla > biga - smalla:
			return smalla, biga
		elif biga - smalla > max_second - min_first:
			return smalla, biga
		else:
			return min_first, max_second


if __name__ == "__main__":
						import doctest

						doctest.testmod()





