





"""simple docstring"""
import math

import flax.linen as nn
import jax.numpy as jnp






def 					A__				(			UpperCamelCase					,  UpperCamelCase					,  UpperCamelCase = 1					,  UpperCamelCase = 1					,  UpperCamelCase = 1.0E4					,  UpperCamelCase = False					,  UpperCamelCase = 1.0					,  ):
							assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
							assert embedding_dim % 2 == 0, F"Embedding dimension {embedding_dim} should be even"
							A		=  float(embedding_dim // 2       )
							A		=  math.log(max_timescale / min_timescale       ) / (num_timescales - freq_shift)
							A		=  min_timescale * jnp.exp(jnp.arange(UpperCamelCase					,  dtype=jnp.floataa       ) * -log_timescale_increment       )
							A		=  jnp.expand_dims(UpperCamelCase					,  1       ) * jnp.expand_dims(UpperCamelCase					,  0       )

							# scale embeddings
							A		=  scale * emb

							if flip_sin_to_cos:
														A		=  jnp.concatenate([jnp.cos(UpperCamelCase       ), jnp.sin(UpperCamelCase       )]					,  axis=1       )
							else:
														A		=  jnp.concatenate([jnp.sin(UpperCamelCase       ), jnp.cos(UpperCamelCase       )]					,  axis=1       )
							A		=  jnp.reshape(UpperCamelCase					,  [jnp.shape(UpperCamelCase       )[0], embedding_dim]       )
							return signal






class 					_UpperCAmelCase   (	nn.Module ):
					UpperCamelCase      =							3_2
					UpperCamelCase      =							jnp.floataa


					@nn.compact
					def __call__(					self			:Any     ,       __UpperCamelCase			:Any		):
												A		=  nn.Dense(self.time_embed_dim     ,       dtype=self.dtype     ,       name="linear_1"		)(__UpperCamelCase		)
												A		=  nn.silu(__UpperCamelCase		)
												A		=  nn.Dense(self.time_embed_dim     ,       dtype=self.dtype     ,       name="linear_2"		)(__UpperCamelCase		)
												return temb







class 					_UpperCAmelCase   (	nn.Module ):
					UpperCamelCase      =							3_2
					UpperCamelCase      =							False
					UpperCamelCase      =							1


					@nn.compact
					def __call__(					self			:List[Any]     ,       __UpperCamelCase			:Union[str, Any]		):
												return get_sinusoidal_embeddings(
												    __UpperCamelCase     ,       embedding_dim=self.dim     ,       flip_sin_to_cos=self.flip_sin_to_cos     ,       freq_shift=self.freq_shift		)









"""simple docstring"""
from math import isqrt, loga






def 					A__				(			UpperCamelCase       ):
							A		=  [True] * max_number
							for i in range(2					,  isqrt(max_number - 1       ) + 1       ):
														if is_prime[i]:
																					for j in range(i**2					,  UpperCamelCase					,  UpperCamelCase       ):
																												A		=  False

							return [i for i in range(2					,  UpperCamelCase       ) if is_prime[i]]






def 					A__				(			UpperCamelCase = 800_800					,  UpperCamelCase = 800_800       ):
							A		=  degree * loga(UpperCamelCase       )
							A		=  int(UpperCamelCase       )
							A		=  calculate_prime_numbers(UpperCamelCase       )

							A		=  0
							A		=  0
							A		=  len(UpperCamelCase       ) - 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() = }""")


