


'''simple docstring'''






import math

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


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

							# scale embeddings
							lowerCAmelCase__			  =      scale * emb

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




class 						a__							(				nn.Module    ):





							'''simple docstring'''






							lowercase__     :  int      		= 3_2
							lowercase__     :  jnp.dtype      		= jnp.floataa







							@nn.compact
							def __call__(						self   ,       lowerCamelCase_  )			->				Tuple:
														lowerCAmelCase__			  =      nn.Dense(self.time_embed_dim   ,       dtype=self.dtype   ,       name='''linear_1'''  )(lowerCamelCase_  )
														lowerCAmelCase__			  =      nn.silu(lowerCamelCase_  )
														lowerCAmelCase__			  =      nn.Dense(self.time_embed_dim   ,       dtype=self.dtype   ,       name='''linear_2'''  )(lowerCamelCase_  )
														return temb




class 						a__							(				nn.Module    ):





							'''simple docstring'''






							lowercase__     :  int      		= 3_2
							lowercase__     :  bool      		= False
							lowercase__     :  float      		= 1







							@nn.compact
							def __call__(						self   ,       lowerCamelCase_  )			->				Optional[Any]:
														return get_sinusoidal_embeddings(
														    lowerCamelCase_   ,       embedding_dim=self.dim   ,       flip_sin_to_cos=self.flip_sin_to_cos   ,       freq_shift=self.freq_shift  )



'''simple docstring'''






def    _snake_case  (	A					,       A			)		->       int:
							return x if y == 0 else greatest_common_divisor(A					,       x % y			)


def    _snake_case  (	A					,       A			)		->       int:
							return (x * y) // greatest_common_divisor(A					,       A			)


def    _snake_case  (	A = 20			)		->       int:
							lowerCAmelCase__			  =      1
							for i in range(1					,       n + 1			):
														lowerCAmelCase__			  =      lcm(A					,       A			)
							return g


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