
from math import sqrt
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     Optional[Any]				)			->						int:

       if 1 < number < 4:
              # 2 and 3 are primes
              return True
       elif number < 2 or number % 2 == 0 or number % 3 == 0:
              # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
              return False

       # All primes number are in format of 6k +/- 1
       for i in range(5			,							int(sqrt(A__				) + 1				)			,							6				):
              if number % i == 0 or number % (i + 2) == 0:
                     return False
       return True
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     str = 1_0_0_0_1				)			->						str:
       SCREAMING_SNAKE_CASE_							:				str		=0
       SCREAMING_SNAKE_CASE_							:				Any		=1
       while count != nth and number < 3:
              number += 1
              if is_prime(A__				):
                     count += 1
       while count != nth:
              number += 2
              if is_prime(A__				):
                     count += 1
       return number


if __name__ == "__main__":
 print(F"{solution() = }")





import random
import unittest

import torch

from diffusers import IFImgaImgSuperResolutionPipeline
from diffusers.utils import floats_tensor
from diffusers.utils.import_utils import is_xformers_available
from diffusers.utils.testing_utils import skip_mps, torch_device

from ..pipeline_params import TEXT_GUIDED_IMAGE_VARIATION_BATCH_PARAMS, TEXT_GUIDED_IMAGE_VARIATION_PARAMS
from ..test_pipelines_common import PipelineTesterMixin
from . import IFPipelineTesterMixin



@skip_mps
class    UpperCAmelCase__(				lowerCamelCase  ,				lowerCamelCase  ,				unittest.TestCase						):

   '''simple docstring'''




   A     :	str												=     IFImgaImgSuperResolutionPipeline
   A     :	Dict												=     TEXT_GUIDED_IMAGE_VARIATION_PARAMS - {"width", "height"}
   A     :	Any												=     TEXT_GUIDED_IMAGE_VARIATION_BATCH_PARAMS.union({"original_image"}						)
   A     :	str												=     PipelineTesterMixin.required_optional_params - {"latents"}


   def       UpperCAmelCase		(    self	:      Dict)						->					Dict:




         """simple docstring"""

         return self._get_superresolution_dummy_components()


   def       UpperCAmelCase		(    self	:      Optional[Any]      ,					lowerCAmelCase	:      Tuple      ,					lowerCAmelCase	:      Union[str, Any]=0)						->					str:




         """simple docstring"""

         if str(lowerCAmelCase).startswith('mps'):
               lowercase__  =	torch.manual_seed(lowerCAmelCase)
         else:
               lowercase__  =	torch.Generator(device=lowerCAmelCase).manual_seed(lowerCAmelCase)

         lowercase__  =	floats_tensor((1, 3, 32, 32)      ,					rng=random.Random(lowerCAmelCase)).to(lowerCAmelCase)
         lowercase__  =	floats_tensor((1, 3, 16, 16)      ,					rng=random.Random(lowerCAmelCase)).to(lowerCAmelCase)

         lowercase__  =	{
             'prompt': 'A painting of a squirrel eating a burger',
             'image': image,
             'original_image': original_image,
             'generator': generator,
             'num_inference_steps': 2,
             'output_type': 'numpy',
         }

         return inputs


   @unittest.skipIf(
       torch_device != 'cuda' or not is_xformers_available()      ,					reason='XFormers attention is only available with CUDA and `xformers` installed'      ,					)
   def       UpperCAmelCase		(    self	:      str)						->					Dict:




         """simple docstring"""

         self._test_xformers_attention_forwardGenerator_pass(expected_max_diff=1E-3)


   def       UpperCAmelCase		(    self	:      List[Any])						->					Dict:




         """simple docstring"""

         self._test_save_load_optional_components()


   @unittest.skipIf(torch_device != 'cuda'      ,					reason='float16 requires CUDA')
   def       UpperCAmelCase		(    self	:      Optional[Any])						->					List[Any]:




         """simple docstring"""

         super().test_save_load_floataa(expected_max_diff=1E-1)


   def       UpperCAmelCase		(    self	:      str)						->					Union[str, Any]:




         """simple docstring"""

         self._test_attention_slicing_forward_pass(expected_max_diff=1E-2)


   def       UpperCAmelCase		(    self	:      Tuple)						->					Tuple:




         """simple docstring"""

         self._test_save_load_local()



   def       UpperCAmelCase		(    self	:      List[str])						->					Tuple:




         """simple docstring"""

         self._test_inference_batch_single_identical(
             expected_max_diff=1E-2      ,					)
