





def A_	(		A__ = 10**12				)  ->		int:
       a__						:	Optional[Any] =				1
       a__						:	List[Any] =				0

       a__						:	Dict =				1
       a__						:	Union[str, Any] =				1

       while numerator <= 2 * min_total - 1:
              prev_numerator += 2 * numerator
              numerator += 2 * prev_numerator

              prev_denominator += 2 * denominator
              denominator += 2 * prev_denominator

       return (denominator + 1) // 2


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









from ...utils import is_torch_available, is_transformers_available


if is_transformers_available() and is_torch_available():
    from .pipeline_vq_diffusion import LearnedClassifierFreeSamplingEmbeddings, VQDiffusionPipeline


