import math






def     lowerCAmelCase_			(   _SCREAMING_SNAKE_CASE     :				int			):
						UpperCamelCase_		:							str  =		math.loga(math.sqrt(4 * positive_integer + 1			) / 2 + 1 / 2			)

						return exponent == int(lowerCAmelCase__			)






def     lowerCAmelCase_			(   _SCREAMING_SNAKE_CASE     :				float = 1 / 1_2345			):
						UpperCamelCase_		:							Union[str, Any]  =		0
						UpperCamelCase_		:							Any  =		0

						UpperCamelCase_		:							Optional[int]  =		3
						while True:
												UpperCamelCase_		:							Optional[int]  =		(integer**2 - 1) / 4
												# if candidate is an integer, then there is a partition for k
												if partition_candidate == int(lowerCAmelCase__			):
																		UpperCamelCase_		:							Union[str, Any]  =		int(lowerCAmelCase__			)
																		total_partitions += 1
																		if check_partition_perfect(lowerCAmelCase__			):
																								perfect_partitions += 1
												if perfect_partitions > 0:
																		if perfect_partitions / total_partitions < max_proportion:
																								return int(lowerCAmelCase__			)
												integer += 1


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







"""simple docstring"""






import torch

from diffusers import StableDiffusionPipeline


__lowerCAmelCase       :			str   	="""path-to-your-trained-model"""
__lowerCAmelCase       :			int   	=StableDiffusionPipeline.from_pretrained(model_id, torch_dtype=torch.floataa).to("""cuda""")

__lowerCAmelCase       :			Optional[int]   	="""A photo of sks dog in a bucket"""
__lowerCAmelCase       :			int   	=pipe(prompt, num_inference_steps=5_0, guidance_scale=7.5).images[0]

image.save("""dog-bucket.png""")



