
"""simple docstring"""



from math import factorial





class 				a			:



      def __init__(   self     ,	UpperCamelCase_     ,	UpperCamelCase_      ):
          UpperCAmelCase__	:      Optional[Any]     							=					real
          if isinstance(UpperCamelCase_     ,	UpperCamelCase_      ):
              UpperCAmelCase__	:      Dict     							=					[1] * rank
          else:
              UpperCAmelCase__	:      int     							=					rank



      def __repr__(   self      ):
          return (
              F'''{self.real}+'''
              F'''{'+'.join(str(UpperCamelCase_      )+'E'+str(n+1      )for n,dual in enumerate(self.duals      )      )}'''
          )



      def  __snake_case							(   self      ):
          UpperCAmelCase__	:      Any     							=					self.duals.copy()
          while cur[-1] == 0:
              cur.pop(-1      )
          return Dual(self.real     ,	UpperCamelCase_      )



      def __add__(   self     ,	UpperCamelCase_      ):
          if not isinstance(UpperCamelCase_     ,	UpperCamelCase_      ):
              return Dual(self.real + other     ,	self.duals      )
          UpperCAmelCase__	:      str     							=					self.duals.copy()
          UpperCAmelCase__	:      Optional[int]     							=					other.duals.copy()
          if len(UpperCamelCase_      ) > len(UpperCamelCase_      ):
              o_dual.extend([1] * (len(UpperCamelCase_      ) - len(UpperCamelCase_      ))      )
          elif len(UpperCamelCase_      ) < len(UpperCamelCase_      ):
              s_dual.extend([1] * (len(UpperCamelCase_      ) - len(UpperCamelCase_      ))      )
          UpperCAmelCase__	:      Optional[Any]     							=					[]
          for i in range(len(UpperCamelCase_      )      ):
              new_duals.append(s_dual[i] + o_dual[i]      )
          return Dual(self.real + other.real     ,	UpperCamelCase_      )

      UpperCamelCase							:   Dict           =     __add__



      def __sub__(   self     ,	UpperCamelCase_      ):
          return self + other * -1



      def __mul__(   self     ,	UpperCamelCase_      ):
          if not isinstance(UpperCamelCase_     ,	UpperCamelCase_      ):
              UpperCAmelCase__	:      Dict     							=					[]
              for i in self.duals:
                  new_duals.append(i * other      )
              return Dual(self.real * other     ,	UpperCamelCase_      )
          UpperCAmelCase__	:      Optional[int]     							=					[0] * (len(self.duals      ) + len(other.duals      ) + 1)
          for i, item in enumerate(self.duals      ):
              for j, jtem in enumerate(other.duals      ):
                  new_duals[i + j + 1] += item * jtem
          for k in range(len(self.duals      )      ):
              new_duals[k] += self.duals[k] * other.real
          for index in range(len(other.duals      )      ):
              new_duals[index] += other.duals[index] * self.real
          return Dual(self.real * other.real     ,	UpperCamelCase_      )

      UpperCamelCase							:   Union[str, Any]           =     __mul__



      def __truediv__(   self     ,	UpperCamelCase_      ):
          if not isinstance(UpperCamelCase_     ,	UpperCamelCase_      ):
              UpperCAmelCase__	:      Optional[int]     							=					[]
              for i in self.duals:
                  new_duals.append(i / other      )
              return Dual(self.real / other     ,	UpperCamelCase_      )
          raise ValueError



      def __floordiv__(   self     ,	UpperCamelCase_      ):
          if not isinstance(UpperCamelCase_     ,	UpperCamelCase_      ):
              UpperCAmelCase__	:      Optional[int]     							=					[]
              for i in self.duals:
                  new_duals.append(i // other      )
              return Dual(self.real // other     ,	UpperCamelCase_      )
          raise ValueError



      def __pow__(   self     ,	UpperCamelCase_      ):
          if n < 0 or isinstance(UpperCamelCase_     ,	UpperCamelCase_      ):
              raise ValueError('power must be a positive integer'      )
          if n == 0:
              return 1
          if n == 1:
              return self
          UpperCAmelCase__	:      Tuple     							=					self
          for _ in range(n - 1      ):
              x *= self
          return x




def 					lowerCamelCase   (     _snake_case    ,_snake_case    ,_snake_case ):
    if not callable(_snake_case ):
        raise ValueError('differentiate() requires a function as input for func' )
    if not isinstance(_snake_case    ,(float, int) ):
        raise ValueError('differentiate() requires a float as input for position' )
    if not isinstance(_snake_case    ,_snake_case ):
        raise ValueError('differentiate() requires an int as input for order' )
    UpperCAmelCase__	:      Dict     							=					Dual(_snake_case    ,1 )
    UpperCAmelCase__	:      int     							=					func(_snake_case )
    if order == 0:
        return result.real
    return result.duals[order - 1] * factorial(_snake_case )


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    def 					lowerCamelCase   (     _snake_case ):
        return y**2 * y**4

    print(differentiate(f, 9, 2))



"""simple docstring"""



import torch

from diffusers import StableDiffusionPipeline


UpperCamelCase__          =	'path-to-your-trained-model'
UpperCamelCase__          =	StableDiffusionPipeline.from_pretrained(model_id, torch_dtype=torch.floataa).to('cuda')

UpperCamelCase__          =	'A photo of sks dog in a bucket'
UpperCamelCase__          =	pipe(prompt, num_inference_steps=50, guidance_scale=7.5).images[0]

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

