'''simple docstring'''


def 					_lowerCamelCase    (      lowerCamelCase_					:							Dict	,     lowerCamelCase_					:							List[str]   ):



     """simple docstring"""





     if len(str(_a   )   ) == 1 or len(str(_a   )   ) == 1:
          return a * b

     UpperCAmelCase_							:   Optional[int]   =      max(len(str(_a   )   )	,     len(str(_a   )   )   )
     UpperCAmelCase_							:   int   =      ma // 2

     UpperCAmelCase_							:   Tuple   =      divmod(_a	,     10**ma   )
     UpperCAmelCase_							:   List[str]   =      divmod(_a	,     10**ma   )

     UpperCAmelCase_							:   Tuple   =      karatsuba(_a	,     _a   )
     UpperCAmelCase_							:   List[str]   =      karatsuba((aa + aa)	,     (ba + ba)   )
     UpperCAmelCase_							:   Tuple   =      karatsuba(_a	,     _a   )

     return (z * 10 ** (2 * ma)) + ((y - z - x) * 10 ** (ma)) + (x)


def 					_lowerCamelCase    (      ):



     """simple docstring"""





     print(karatsuba(15463	,     23489   )   )


if __name__ == "__main__":
 main()














from __future__ import annotations

from collections.abc import Generator

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

		yield n
		while n != 1:
				if n % 2 == 0:
						n //= 2
				else:
						snake_case_ :							List[str]         =				3 * n + 1
				yield n

def    lowerCAmelCase__		(			):
		snake_case_ :							Optional[int]         =				43
		snake_case_ :							Union[str, Any]         =				tuple(collatz_sequence(_a			)			)
		print(_a			)
		print(F'''Collatz sequence from {n} took {len(_a			)} steps.'''			)


if __name__ == "__main__":
							main()
