



'''simple docstring'''

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 			__magic_name__		(					_UpperCamelCase     ):
							lowerCAmelCase :					Union[List[PIL.Image.Image], np.ndarray]


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









'''simple docstring'''

import math



def   __lowerCamelCase  (   lowerCAmelCase_						)    ->   list:
		if n <= 0:
				raise ValueError('Only positive integers have prime factors'						)
		_a  :   Tuple				 =							[]
		while n % 2 == 0:
				pf.append(2						)
				_a  :   str				 =							int(n / 2						)
		for i in range(3		,    int(math.sqrt(lowerCAmelCase_						)						) + 1		,    2						):
				while n % i == 0:
						pf.append(lowerCAmelCase_						)
						_a  :   List[Any]				 =							int(n / i						)
		if n > 2:
				pf.append(lowerCAmelCase_						)
		return pf



def   __lowerCamelCase  (   lowerCAmelCase_						)    ->   int:
		if n <= 0:
				raise ValueError('Only positive numbers are accepted'						)
		_a  :   int				 =							1
		_a  :   Union[str, Any]				 =							1
		while n % 2 == 0:
				temp += 1
				_a  :   str				 =							int(n / 2						)
		div *= temp
		for i in range(3		,    int(math.sqrt(lowerCAmelCase_						)						) + 1		,    2						):
				_a  :   List[str]				 =							1
				while n % i == 0:
						temp += 1
						_a  :   List[str]				 =							int(n / i						)
				div *= temp
		if n > 1:
				div *= 2
		return div



def   __lowerCamelCase  (   lowerCAmelCase_						)    ->   int:
		if n <= 0:
				raise ValueError('Only positive numbers are accepted'						)
		_a  :   List[str]				 =							1
		_a  :   Union[str, Any]				 =							1
		while n % 2 == 0:
				temp += 1
				_a  :   Tuple				 =							int(n / 2						)
		if temp > 1:
				s *= (2**temp - 1) / (2 - 1)
		for i in range(3		,    int(math.sqrt(lowerCAmelCase_						)						) + 1		,    2						):
				_a  :   str				 =							1
				while n % i == 0:
						temp += 1
						_a  :   Any				 =							int(n / i						)
				if temp > 1:
						s *= (i**temp - 1) / (i - 1)
		return int(lowerCAmelCase_						)



def   __lowerCamelCase  (   lowerCAmelCase_						)    ->   int:
		_a  :   Dict				 =							n
		for x in set(prime_factors(lowerCAmelCase_						)						):
				s *= (x - 1) / x
		return int(lowerCAmelCase_						)


if __name__ == "__main__":
							import doctest

							doctest.testmod()




