"""simple docstring"""


import math





def       lowerCamelCase_			( __lowerCAmelCase    )							-> float:




						'''simple docstring'''



						lowerCamelCase__ =math.log(2       ,   10    ) * number
						lowerCamelCase__ =round((log_number - int(__lowerCAmelCase    ))       ,   15    )

						return difference





def       lowerCamelCase_			( __lowerCAmelCase = 67_8910    )							-> int:




						'''simple docstring'''



						lowerCamelCase__ =90
						lowerCamelCase__ =0

						lowerCamelCase__ =math.log(1.23       ,   10    )
						lowerCamelCase__ =math.log(1.24       ,   10    )
						lowerCamelCase__ =0

						while position < number:
												lowerCamelCase__ =log_difference(__lowerCAmelCase    )

												if difference >= upper_limit:
																		power_iterator += 93

												elif difference < lower_limit:
																		power_iterator += 196

												else:
																		lowerCamelCase__ =power_iterator
																		power_iterator += 196
																		position += 1

						return previous_power


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	print(F'''{solution() = }''')



"""simple docstring"""


from __future__ import annotations

from collections.abc import Generator





def       lowerCamelCase_			( __lowerCAmelCase    )							-> Generator[int, None, None]:




						'''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_			( )							-> List[str]:




						'''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()


