

'''simple docstring'''






from __future__ import annotations


def 					__lowerCamelCase			(      SCREAMING_SNAKE_CASE_     :	Any    )							->   Any:
      """simple docstring"""

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


def 					__lowerCamelCase			(      SCREAMING_SNAKE_CASE_     :	List[str]    )							->   str:
      """simple docstring"""

      SCREAMING_SNAKE_CASE_      :			Optional[Any]     =       set()
      for number in unique_coefficients:
            SCREAMING_SNAKE_CASE_      :			int     =       2
            SCREAMING_SNAKE_CASE_      :			Any     =       number
            while divisor**2 <= copy_number:
                  SCREAMING_SNAKE_CASE_      :			Optional[Any]     =       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 					__lowerCamelCase			(      SCREAMING_SNAKE_CASE_     :	Optional[int] = 5_1    )							->   List[str]:
      """simple docstring"""

      SCREAMING_SNAKE_CASE_      :			Tuple     =       get_pascal_triangle_unique_coefficients(_lowercase    )
      SCREAMING_SNAKE_CASE_      :			Any     =       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()



