


import math
import sys


def 			UpperCAmelCase_				(      UpperCAmelCase__  ):
					if number != int(UpperCAmelCase__  ):
										raise ValueError("""the value of input must be a natural number"""  )
					if number < 0:
										raise ValueError("""the value of input must not be a negative number"""  )
					if number == 0:
										return 1
					lowercase_  							=			[-1] * (number + 1)
					lowercase_  							=			0
					for i in range(1						,							number + 1  ):
										lowercase_  							=			sys.maxsize
										lowercase_  							=			int(math.sqrt(UpperCAmelCase__  )  )
										for j in range(1						,							root + 1  ):
															lowercase_  							=			1 + answers[i - (j**2)]
															lowercase_  							=			min(UpperCAmelCase__						,							UpperCAmelCase__  )
										lowercase_  							=			answer
					return answers[number]


if __name__ == "__main__":
							import doctest

							doctest.testmod()






from ...utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_torch_available,
    is_transformers_available,
)


try:
							if not (is_transformers_available() and is_torch_available()):
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							from ...utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
							from .multicontrolnet import MultiControlNetModel
							from .pipeline_controlnet import StableDiffusionControlNetPipeline
							from .pipeline_controlnet_imgaimg import StableDiffusionControlNetImgaImgPipeline
							from .pipeline_controlnet_inpaint import StableDiffusionControlNetInpaintPipeline


if is_transformers_available() and is_flax_available():
							from .pipeline_flax_controlnet import FlaxStableDiffusionControlNetPipeline


