






from __future__ import annotations




def    __A    (   _lowercase       ):

					'''simple docstring'''







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




def    __A    (   _lowercase       ):

					'''simple docstring'''







					_A									=       set()
					for number in unique_coefficients:
										_A									=       2
										_A									=       number
										while divisor**2 <= copy_number:
															_A									=       0
															while copy_number % divisor == 0:
																				copy_number //= divisor
																				multiplicity += 1
															if multiplicity >= 2:
																				non_squarefrees.add(_lowercase       )
																				break
															divisor += 1

					return unique_coefficients.difference(_lowercase       )




def    __A    (   _lowercase = 51       ):

					'''simple docstring'''







					_A									=       get_pascal_triangle_unique_coefficients(_lowercase       )
					_A									=       get_squarefrees(_lowercase       )
					return sum(_lowercase       )


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











from __future__ import annotations

from collections.abc import Generator




def    __A    (   _lowercase       ):

					'''simple docstring'''







					if not isinstance(_lowercase    ,	_lowercase       ) or n < 1:
										raise Exception('''Sequence only defined for positive integers'''       )

					yield n
					while n != 1:
										if n % 2 == 0:
															n //= 2
										else:
															_A									=       3 * n + 1
										yield n




def    __A    (   ):

					'''simple docstring'''







					_A									=       43
					_A									=       tuple(collatz_sequence(_lowercase       )       )
					print(_lowercase       )
					print(f"""Collatz sequence from {n} took {len(_lowercase       )} steps."""       )


if __name__ == "__main__":
				main()



