


from math import isqrt, loga
def        UpperCamelCase_(				_A   :int  )->		list[int]:

			'''simple docstring'''





			UpperCamelCase__					=       [True] * max_number
			for i in range(2				,     isqrt(max_number - 1  ) + 1  ):
						if is_prime[i]:
									for j in range(i**2				,     _A				,     _A  ):
												UpperCamelCase__					=       False

			return [i for i in range(2				,     _A  ) if is_prime[i]]
def        UpperCamelCase_(				_A   :int = 80_08_00				,     _A   :int = 80_08_00  )->		int:

			'''simple docstring'''





			UpperCamelCase__					=       degree * loga(_A  )
			UpperCamelCase__					=       int(_A  )
			UpperCamelCase__					=       calculate_prime_numbers(_A  )

			UpperCamelCase__					=       0
			UpperCamelCase__					=       0
			UpperCamelCase__					=       len(_A  ) - 1
			while left < right:
						while (
						    prime_numbers[right] * loga(prime_numbers[left]  )
						    + prime_numbers[left] * loga(prime_numbers[right]  )
						    > upper_bound
						):
									right -= 1
						hybrid_integers_count += right - left
						left += 1

			return hybrid_integers_count


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






import unittest

from diffusers import FlaxAutoencoderKL
from diffusers.utils import is_flax_available
from diffusers.utils.testing_utils import require_flax

from .test_modeling_common_flax import FlaxModelTesterMixin


if is_flax_available():
						import jax







@require_flax
class        lowerCamelCase__	(							UpperCAmelCase					,	unittest.TestCase      ):






			"""simple docstring"""






			_UpperCamelCase		:					List[str]    =		FlaxAutoencoderKL




			@property
			def 				snake_case__				(							self     ):

						'''simple docstring'''


						UpperCamelCase__					=       4
						UpperCamelCase__					=       3
						UpperCamelCase__					=       (32, 32)

						UpperCamelCase__					=       jax.random.PRNGKey(0     )
						UpperCamelCase__					=       jax.random.uniform(snake_case      ,						((batch_size, num_channels) + sizes)     )

						return {"sample": image, "prng_key": prng_key}







			def 				snake_case__				(							self     ):

						'''simple docstring'''


						UpperCamelCase__					=       {
						    "block_out_channels": [32, 64],
						    "in_channels": 3,
						    "out_channels": 3,
						    "down_block_types": ["DownEncoderBlock2D", "DownEncoderBlock2D"],
						    "up_block_types": ["UpDecoderBlock2D", "UpDecoderBlock2D"],
						    "latent_channels": 4,
						}
						UpperCamelCase__					=       self.dummy_input
						return init_dict, inputs_dict


