





'''simple docstring'''




from __future__ import annotations




def 						snake_case__    ( lowerCamelCase__				:   Dict			)   ->   set[int]:
					A_ :     List[str] =							{1}
					A_ :     int =							[1]
					for _ in range(2			,		depth + 1			):
										A_ :     str =							[*previous_coefficients, 0]
										A_ :     Optional[int] =							[0, *previous_coefficients]
										A_ :     Tuple =							[]
										for x, y in zip(_UpperCAmelCase			,		_UpperCAmelCase			):
															coefficients.add(x + y			)
															previous_coefficients.append(x + y			)
					return coefficients




def 						snake_case__    ( lowerCamelCase__				:   Dict			)   ->   set[int]:
					A_ :     str =							set()
					for number in unique_coefficients:
										A_ :     Dict =							2
										A_ :     Tuple =							number
										while divisor**2 <= copy_number:
															A_ :     List[str] =							0
															while copy_number % divisor == 0:
																				copy_number //= divisor
																				multiplicity += 1
															if multiplicity >= 2:
																				non_squarefrees.add(_UpperCAmelCase			)
																				break
															divisor += 1

					return unique_coefficients.difference(_UpperCAmelCase			)




def 						snake_case__    ( lowerCamelCase__				:   List[Any] = 5_1			)   ->   int:
					A_ :     int =							get_pascal_triangle_unique_coefficients(_UpperCAmelCase			)
					A_ :     Optional[int] =							get_squarefrees(_UpperCAmelCase			)
					return sum(_UpperCAmelCase			)


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









'''simple docstring'''




def 						snake_case__    ( lowerCamelCase__				:   int			)   ->   bool:
					if not isinstance(lowerCamelCase__			,		lowerCamelCase__			):
										A_ :     int =							f'Input value of [number={number}] must be an integer'
										raise TypeError(lowerCamelCase__			)
					if number < 0 or number % 2 == 1:
										return False
					A_ :     Dict =							int(number**0.5			)
					return number == number_sqrt * (number_sqrt + 1)


if __name__ == "__main__":
							import doctest

							doctest.testmod()



