



'''simple docstring'''


import math







def 							__lowerCamelCase							(  A__       )			->      list:






   """simple docstring"""
   UpperCamelCase      							=    [True] * n
   UpperCamelCase      							=    False
   UpperCamelCase      							=    False
   UpperCamelCase      							=    True

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

   UpperCamelCase      							=    [2]

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

   return primes







def 							__lowerCamelCase							(  A__ = 999_966_663_333       )			->      int:






   """simple docstring"""
   UpperCamelCase      							=    math.floor(math.sqrt(A__       )       ) + 100
   UpperCamelCase      							=    prime_sieve(A__       )

   UpperCamelCase      							=    0
   UpperCamelCase      							=    0
   UpperCamelCase      							=    primes[prime_index]

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

      UpperCamelCase      							=    last_prime**2
      UpperCamelCase      							=    next_prime**2

      # Get numbers divisible by lps(current)
      UpperCamelCase      							=    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)
      UpperCamelCase      							=    upper_bound - next_prime
      while current > lower_bound:
         matches_sum += current
         current -= next_prime

      # Remove the numbers divisible by both ups and lps
      UpperCamelCase      							=    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
      UpperCamelCase      							=    next_prime
      prime_index += 1

   return matches_sum


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



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 							lowerCAmelCase__   ( unittest.TestCase						):

						@property
						def 			A_					(      self					)       ->   int:


								'''simple docstring'''

								torch.manual_seed(0					)
								_UpperCamelCase         =						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 			A_					(      self					)       ->   Any:


								'''simple docstring'''

								_UpperCamelCase         =						self.dummy_uncond_unet
								_UpperCamelCase         =						PNDMScheduler()

								_UpperCamelCase         =						PNDMPipeline(unet=a							,				scheduler=a					)
								pndm.to(a					)
								pndm.set_progress_bar_config(disable=a					)

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

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

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

								assert image.shape == (1, 32, 32, 3)
								_UpperCamelCase         =						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 							lowerCAmelCase__   ( unittest.TestCase						):

						def 			A_					(      self					)       ->   Optional[Any]:


								'''simple docstring'''

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

								_UpperCamelCase         =						UNetaDModel.from_pretrained(a					)
								_UpperCamelCase         =						PNDMScheduler()

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

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

								assert image.shape == (1, 32, 32, 3)
								_UpperCamelCase         =						np.array([0.1564, 0.1_4645, 0.1406, 0.1_4715, 0.1_2425, 0.1_4045, 0.1_3115, 0.1_2175, 0.125]					)

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



