
"""simple docstring"""





import math

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



def  lowerCamelCase__						(     __snake_case,	__snake_case,	__snake_case = 1,	__snake_case = 1,	__snake_case = 1.0e4,	__snake_case = False,	__snake_case = 1.0,	)				->						jnp.ndarray:


					"""simple docstring"""





					assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
					assert embedding_dim % 2 == 0, F'''Embedding dimension {embedding_dim} should be even'''
					_UpperCamelCase									=    float(embedding_dim // 2      )
					_UpperCamelCase									=    math.log(max_timescale / min_timescale      ) / (num_timescales - freq_shift)
					_UpperCamelCase									=    min_timescale * jnp.exp(jnp.arange(__snake_case,	dtype=jnp.floataa      ) * -log_timescale_increment      )
					_UpperCamelCase									=    jnp.expand_dims(__snake_case,	1      ) * jnp.expand_dims(__snake_case,	0      )

					# scale embeddings
					_UpperCamelCase									=    scale * emb

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






class        _UpperCAmelCase(       nn.Module      ):
		lowercase__         = 32
		lowercase__         = jnp.floataa



		@nn.compact
		def __call__(   self							,						__a)			->			Any:






							'''simple docstring'''
							_UpperCamelCase									=    nn.Dense(self.time_embed_dim							,						dtype=self.dtype							,						name='''linear_1''')(__a)
							_UpperCamelCase									=    nn.silu(__a)
							_UpperCamelCase									=    nn.Dense(self.time_embed_dim							,						dtype=self.dtype							,						name='''linear_2''')(__a)
							return temb






class        _UpperCAmelCase(       nn.Module      ):
		lowercase__         = 32
		lowercase__         = False
		lowercase__         = 1



		@nn.compact
		def __call__(   self							,						__a)			->			Optional[Any]:






							'''simple docstring'''
							return get_sinusoidal_embeddings(
							    __a							,						embedding_dim=self.dim							,						flip_sin_to_cos=self.flip_sin_to_cos							,						freq_shift=self.freq_shift)








"""simple docstring"""





from __future__ import annotations

from functools import lru_cache
from math import ceil

_a								=						100

_a								=						set(range(3, NUM_PRIMES, 2))
primes.add(2)
_a								=						42

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
				if prime not in primes:
								continue
				primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))



@lru_cache(maxsize=1_00      )
def  lowerCamelCase__						(     __snake_case      )				->						set[int]:


					"""simple docstring"""





					if number_to_partition < 0:
										return set()
					elif number_to_partition == 0:
										return {1}

					_UpperCamelCase									=    set()
					_UpperCamelCase									=    42
					_UpperCamelCase									=    42

					for prime in primes:
										if prime > number_to_partition:
															continue
										for sub in partition(number_to_partition - prime      ):
															ret.add(sub * prime      )

					return ret



def  lowerCamelCase__						(     __snake_case = 50_00      )				->						int | None:


					"""simple docstring"""





					for number_to_partition in range(1,	__snake_case      ):
										if len(partition(__snake_case      )      ) > number_unique_partitions:
															return number_to_partition
					return None


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






