
from __future__ import annotations

from collections.abc import Generator






def        lowerCamelCase__    (    __lowerCAmelCase  :  int    ):




			"""simple docstring"""


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

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






def        lowerCamelCase__    (    ):




			"""simple docstring"""


			lowerCAmelCase_      =     43
			lowerCAmelCase_      =     tuple(collatz_sequence(__lowerCAmelCase    )    )
			print(__lowerCAmelCase    )
			print(F"""Collatz sequence from {n} took {len(__lowerCAmelCase    )} steps."""    )


if __name__ == "__main__":
			main()





import math






def        lowerCamelCase__    (    __lowerCAmelCase  :  int    ):




			"""simple docstring"""


			if 1 < number < 4:
						# 2 and 3 are primes
						return True
			elif number < 2 or number % 2 == 0 or number % 3 == 0:
						# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
						return False

			# All primes number are in format of 6k +/- 1
			for i in range(5   ,							int(math.sqrt(__lowerCAmelCase    ) + 1    )   ,							6    ):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True






def        lowerCamelCase__    (    __lowerCAmelCase  :  int = 600851475143    ):




			"""simple docstring"""


			try:
						lowerCAmelCase_      =     int(__lowerCAmelCase    )
			except (TypeError, ValueError):
						raise TypeError("Parameter n must be int or castable to int."    )
			if n <= 0:
						raise ValueError("Parameter n must be greater than or equal to one."    )
			lowerCAmelCase_      =     0
			if is_prime(__lowerCAmelCase    ):
						return n
			while n % 2 == 0:
						n //= 2
			if is_prime(__lowerCAmelCase    ):
						return n
			for i in range(3   ,							int(math.sqrt(__lowerCAmelCase    )    ) + 1   ,							2    ):
						if n % i == 0:
									if is_prime(n // i    ):
												lowerCAmelCase_      =     n // i
												break
									elif is_prime(__lowerCAmelCase    ):
												lowerCAmelCase_      =     i
			return max_number


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



