






"""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			,):
			assert timesteps.ndim == 1, "Timesteps should be a 1d-array"
			assert embedding_dim % 2 == 0, F"""Embedding dimension {embedding_dim} should be even"""
			UpperCAmelCase_  :				Any      =      float(embedding_dim // 2		)
			UpperCAmelCase_  :				Optional[int]      =      math.log(max_timescale / min_timescale		) / (num_timescales - freq_shift)
			UpperCAmelCase_  :				Any      =      min_timescale * jnp.exp(jnp.arange(A__			,dtype=jnp.floataa		) * -log_timescale_increment		)
			UpperCAmelCase_  :				Dict      =      jnp.expand_dims(A__			,1		) * jnp.expand_dims(A__			,0		)

			# scale embeddings
			UpperCAmelCase_  :				str      =      scale * emb

			if flip_sin_to_cos:
						UpperCAmelCase_  :				str      =      jnp.concatenate([jnp.cos(A__		), jnp.sin(A__		)]			,axis=1		)
			else:
						UpperCAmelCase_  :				Union[str, Any]      =      jnp.concatenate([jnp.sin(A__		), jnp.cos(A__		)]			,axis=1		)
			UpperCAmelCase_  :				Union[str, Any]      =      jnp.reshape(A__			,[jnp.shape(A__		)[0], embedding_dim]		)
			return signal







class     UpperCamelCase_ (nn.Module  ):
	__magic_name__			   =       32
	__magic_name__			   =       jnp.floataa





	@nn.compact
	def __call__(   self      :				int			,			lowerCAmelCase_      :				str		)		->    Any:
				UpperCAmelCase_  :				Dict      =      nn.Dense(self.time_embed_dim			,			dtype=self.dtype			,			name="linear_1"		)(lowerCAmelCase_		)
				UpperCAmelCase_  :				List[Any]      =      nn.silu(lowerCAmelCase_		)
				UpperCAmelCase_  :				List[Any]      =      nn.Dense(self.time_embed_dim			,			dtype=self.dtype			,			name="linear_2"		)(lowerCAmelCase_		)
				return temb







class     UpperCamelCase_ (nn.Module  ):
	__magic_name__			   =       32
	__magic_name__			   =       False
	__magic_name__			   =       1





	@nn.compact
	def __call__(   self      :				Optional[Any]			,			lowerCAmelCase_      :				Dict		)		->    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"""
from itertools import count

def        snake_case   (     A__ = 50		):
			UpperCAmelCase_  :				Any      =      [1] * min_block_length

			for n in count(A__		):
						fill_count_functions.append(1		)

						for block_length in range(A__			,n + 1		):
									for block_start in range(n - block_length		):
												fill_count_functions[n] += fill_count_functions[
												    n - block_start - block_length - 1
												]

									fill_count_functions[n] += 1

						if fill_count_functions[n] > 1_00_00_00:
									break

			return n


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



