

"""simple docstring"""



import math





def  _snake_case     (    UpperCAmelCase_  :					int			):
     A__										=  [True] * n
     A__										=  False
     A__										=  False
     A__										=  True

     for i in range(3					,   int(n**0.5 + 1			)					,   2			):
          A__										=  i * 2
          while index < n:
               A__										=  False
               A__										=  index + i

     A__										=  [2]

     for i in range(3					,   UpperCAmelCase_					,   2			):
          if is_prime[i]:
               primes.append(UpperCAmelCase_			)

     return primes





def  _snake_case     (    UpperCAmelCase_  :					int = 9999_6666_3333			):
     A__										=  math.floor(math.sqrt(UpperCAmelCase_			)			) + 100
     A__										=  prime_sieve(UpperCAmelCase_			)

     A__										=  0
     A__										=  0
     A__										=  primes[prime_index]

     while (last_prime**2) <= limit:
          A__										=  primes[prime_index + 1]

          A__										=  last_prime**2
          A__										=  next_prime**2

          # Get numbers divisible by lps(current)
          A__										=  lower_bound + last_prime
          while upper_bound > current <= limit:
               matches_sum += current
               current += last_prime

          # Reset the upper_bound
          while (upper_bound - next_prime) > limit:
               upper_bound -= next_prime

          # Add the numbers divisible by ups(current)
          A__										=  upper_bound - next_prime
          while current > lower_bound:
               matches_sum += current
               current -= next_prime

          # Remove the numbers divisible by both ups and lps
          A__										=  0
          while upper_bound > current <= limit:
               if current <= lower_bound:
                    # Increment the current number
                    current += last_prime * next_prime
                    continue

               if current > limit:
                    break

               # Remove twice since it was added by both ups and lps
               matches_sum -= current * 2

               # Increment the current number
               current += last_prime * next_prime

          # Setup for next pair
          A__										=  next_prime
          prime_index += 1

     return matches_sum


if __name__ == "__main__":
 print(solution())









"""simple docstring"""



import unittest

import numpy as np
import torch

from diffusers import PNDMPipeline, PNDMScheduler, UNetaDModel
from diffusers.utils.testing_utils import enable_full_determinism, require_torch, slow, torch_device


enable_full_determinism()



class 					a						(       unittest.TestCase				):



    """simple docstring"""



    @property
    def 				UpperCamelCase	(     self: Any       ):






         """simple docstring"""


         torch.manual_seed(0       )
         A__										=  UNetaDModel(
             block_out_channels=(32, 64)    ,						layers_per_block=2    ,						sample_size=32    ,						in_channels=3    ,						out_channels=3    ,						down_block_types=("""DownBlock2D""", """AttnDownBlock2D""")    ,						up_block_types=("""AttnUpBlock2D""", """UpBlock2D""")    ,						)
         return model





    def 				UpperCamelCase	(     self: str       ):






         """simple docstring"""


         A__										=  self.dummy_uncond_unet
         A__										=  PNDMScheduler()

         A__										=  PNDMPipeline(unet=UpperCamelCase    ,						scheduler=UpperCamelCase       )
         pndm.to(UpperCamelCase       )
         pndm.set_progress_bar_config(disable=UpperCamelCase       )

         A__										=  torch.manual_seed(0       )
         A__										=  pndm(generator=UpperCamelCase    ,						num_inference_steps=20    ,						output_type="""numpy"""       ).images

         A__										=  torch.manual_seed(0       )
         A__										=  pndm(generator=UpperCamelCase    ,						num_inference_steps=20    ,						output_type="""numpy"""    ,						return_dict=UpperCamelCase       )[0]

         A__										=  image[0, -3:, -3:, -1]
         A__										=  image_from_tuple[0, -3:, -3:, -1]

         assert image.shape == (1, 32, 32, 3)
         A__										=  np.array([1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0]       )

         assert np.abs(image_slice.flatten() - expected_slice       ).max() < 1e-2
         assert np.abs(image_from_tuple_slice.flatten() - expected_slice       ).max() < 1e-2



@slow
@require_torch
class 					a						(       unittest.TestCase				):



    """simple docstring"""



    def 				UpperCamelCase	(     self: Dict       ):






         """simple docstring"""


         A__										=  """google/ddpm-cifar10-32"""

         A__										=  UNetaDModel.from_pretrained(UpperCamelCase       )
         A__										=  PNDMScheduler()

         A__										=  PNDMPipeline(unet=UpperCamelCase    ,						scheduler=UpperCamelCase       )
         pndm.to(UpperCamelCase       )
         pndm.set_progress_bar_config(disable=UpperCamelCase       )
         A__										=  torch.manual_seed(0       )
         A__										=  pndm(generator=UpperCamelCase    ,						output_type="""numpy"""       ).images

         A__										=  image[0, -3:, -3:, -1]

         assert image.shape == (1, 32, 32, 3)
         A__										=  np.array([0.1_564, 0.14_645, 0.1_406, 0.14_715, 0.12_425, 0.14_045, 0.13_115, 0.12_175, 0.125]       )

         assert np.abs(image_slice.flatten() - expected_slice       ).max() < 1e-2






