'''simple docstring'''




from __future__ import annotations

import math
import random

def _UpperCamelCase (							SCREAMING_SNAKE_CASE_	,							SCREAMING_SNAKE_CASE_	,							SCREAMING_SNAKE_CASE_				):
     lowercase_       :							str  					=       d * e - 1
     lowercase_       :							Optional[Any]  					=       0
     lowercase_       :							List[Any]  					=       0
     while p == 0:
          lowercase_       :							int  					=       random.randint(2	,							n - 1				)
          lowercase_       :							Optional[int]  					=       k
          while True:
               if t % 2 == 0:
                    lowercase_       :							Optional[Any]  					=       t // 2
                    lowercase_       :							int  					=       (g**t) % n
                    lowercase_       :							Union[str, Any]  					=       math.gcd(x - 1	,							SCREAMING_SNAKE_CASE_				)
                    if x > 1 and y > 1:
                         lowercase_       :							List[Any]  					=       y
                         lowercase_       :							Dict  					=       n // y
                         break  # find the correct factors
               else:
                    break  # t is not divisible by 2, break and choose another g
     return sorted([p, q]				)


if __name__ == "__main__":
 import doctest

 doctest.testmod()





'''simple docstring'''




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

import numpy as np
import PIL
from PIL import Image

from ...utils import BaseOutput, is_torch_available, is_transformers_available


@dataclass
# Copied from diffusers.pipelines.stable_diffusion.__init__.StableDiffusionPipelineOutput with Stable->Alt
class    UpperCAmelCase__	(							_snake_case      ):






   """simple docstring"""
   A				:							Union[List[PIL.Image.Image], np.ndarray]
   A				:							Optional[List[bool]]


if is_transformers_available() and is_torch_available():
 from .modeling_roberta_series import RobertaSeriesModelWithTransformation
 from .pipeline_alt_diffusion import AltDiffusionPipeline
 from .pipeline_alt_diffusion_imgaimg import AltDiffusionImgaImgPipeline




