





import math





def    _lowercase    (  _UpperCAmelCase )  ->     list:
				if n <= 0:
								raise ValueError("""Only positive integers have prime factors""" )
				lowerCamelCase		       =[]
				while n % 2 == 0:
								pf.append(2 )
								lowerCamelCase		       =int(n / 2 )
				for i in range(3	,					int(math.sqrt(_UpperCAmelCase ) ) + 1	,					2 ):
								while n % i == 0:
												pf.append(_UpperCAmelCase )
												lowerCamelCase		       =int(n / i )
				if n > 2:
								pf.append(_UpperCAmelCase )
				return pf





def    _lowercase    (  _UpperCAmelCase )  ->     int:
				if n <= 0:
								raise ValueError("""Only positive numbers are accepted""" )
				lowerCamelCase		       =1
				lowerCamelCase		       =1
				while n % 2 == 0:
								temp += 1
								lowerCamelCase		       =int(n / 2 )
				div *= temp
				for i in range(3	,					int(math.sqrt(_UpperCAmelCase ) ) + 1	,					2 ):
								lowerCamelCase		       =1
								while n % i == 0:
												temp += 1
												lowerCamelCase		       =int(n / i )
								div *= temp
				if n > 1:
								div *= 2
				return div





def    _lowercase    (  _UpperCAmelCase )  ->     int:
				if n <= 0:
								raise ValueError("""Only positive numbers are accepted""" )
				lowerCamelCase		       =1
				lowerCamelCase		       =1
				while n % 2 == 0:
								temp += 1
								lowerCamelCase		       =int(n / 2 )
				if temp > 1:
								s *= (2**temp - 1) / (2 - 1)
				for i in range(3	,					int(math.sqrt(_UpperCAmelCase ) ) + 1	,					2 ):
								lowerCamelCase		       =1
								while n % i == 0:
												temp += 1
												lowerCamelCase		       =int(n / i )
								if temp > 1:
												s *= (i**temp - 1) / (i - 1)
				return int(_UpperCAmelCase )





def    _lowercase    (  _UpperCAmelCase )  ->     int:
				lowerCamelCase		       =n
				for x in set(prime_factors(_UpperCAmelCase ) ):
								s *= (x - 1) / x
				return int(_UpperCAmelCase )


if __name__ == "__main__":
							import doctest

							doctest.testmod()












from dataclasses import dataclass
from typing import List, Optional, Union

import numpy as np
import PIL

from ...utils import BaseOutput, is_invisible_watermark_available, is_torch_available, is_transformers_available

@dataclass
class 					__A   (  a			):
				__A            = 42


if is_transformers_available() and is_torch_available() and is_invisible_watermark_available():
							from .pipeline_stable_diffusion_xl import StableDiffusionXLPipeline
							from .pipeline_stable_diffusion_xl_imgaimg import StableDiffusionXLImgaImgPipeline





