

'''simple docstring'''

from __future__ import annotations

def      __magic_name__							(			A				)      ->		set[int]:
	snake_case							=					{1}
	snake_case							=					[1]
	for _ in range(2       , depth + 1				):
		snake_case							=					[*previous_coefficients, 0]
		snake_case							=					[0, *previous_coefficients]
		snake_case							=					[]
		for x, y in zip(A       , A				):
			coefficients.add(x + y				)
			previous_coefficients.append(x + y				)
	return coefficients

def      __magic_name__							(			A				)      ->		set[int]:
	snake_case							=					set()
	for number in unique_coefficients:
		snake_case							=					2
		snake_case							=					number
		while divisor**2 <= copy_number:
			snake_case							=					0
			while copy_number % divisor == 0:
				copy_number //= divisor
				multiplicity += 1
			if multiplicity >= 2:
				non_squarefrees.add(A				)
				break
			divisor += 1

	return unique_coefficients.difference(A				)

def      __magic_name__							(			A = 5_1				)      ->		int:
	snake_case							=					get_pascal_triangle_unique_coefficients(A				)
	snake_case							=					get_squarefrees(A				)
	return sum(A				)


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










from ..utils import DummyObject, requires_backends
class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[str]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Dict									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Union[str, Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Any									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Dict									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Dict									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     str									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Any									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Any									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Dict									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[str]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Union[str, Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     str									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[str]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[str]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Union[str, Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Union[str, Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Optional[int]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Union[str, Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Dict									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[str]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Union[str, Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     int									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     str									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Dict									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     str									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Optional[Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Optional[int]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Optional[int]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Tuple									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Dict									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     int									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Dict									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Any									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Optional[int]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[str]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Any									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Optional[Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Optional[int]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Dict									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Optional[Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Any									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Optional[int]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     int									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[str]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Union[str, Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Tuple									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Union[str, Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     str									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[str]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Any									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     int									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Optional[Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Optional[int]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Union[str, Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[str]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Tuple									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Tuple									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Tuple									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[Any]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     List[str]									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Tuple									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     str									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     int									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Any									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     int									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     str									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Any									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )


class lowerCAmelCase_       (   metaclass=A_			):







	'''simple docstring'''




	A_       :     Dict									=		['vision']

	def __init__(	self   ,       *lowerCamelCase   ,       **lowerCamelCase       ):



				'''simple docstring'''


				requires_backends(self   ,       ["""vision"""]       )

