"""simple docstring"""






import math

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




def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase  ,					__UpperCAmelCase  ,					__UpperCAmelCase = 1  ,					__UpperCAmelCase = 1  ,					__UpperCAmelCase = 1.0e4  ,					__UpperCAmelCase = False  ,					__UpperCAmelCase = 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"""
				SCREAMING_SNAKE_CASE__		  =				float(embedding_dim // 2       )
				SCREAMING_SNAKE_CASE__		  =				math.log(max_timescale / min_timescale       ) / (num_timescales - freq_shift)
				SCREAMING_SNAKE_CASE__		  =				min_timescale * jnp.exp(jnp.arange(__UpperCAmelCase  ,					dtype=jnp.floataa       ) * -log_timescale_increment       )
				SCREAMING_SNAKE_CASE__		  =				jnp.expand_dims(__UpperCAmelCase  ,					1       ) * jnp.expand_dims(__UpperCAmelCase  ,					0       )

				# scale embeddings
				SCREAMING_SNAKE_CASE__		  =				scale * emb

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

class lowerCamelCase		(nn.Module      ):






					'''simple docstring'''


					a   	=		3_2
					a   	=		jnp.floataa



					@nn.compact
					def __call__(						self			:				Optional[int]   , _snake_case			:				str		)							->       Optional[int]:
									SCREAMING_SNAKE_CASE__		  =				nn.Dense(self.time_embed_dim   , dtype=self.dtype   , name="linear_1"		)(_snake_case		)
									SCREAMING_SNAKE_CASE__		  =				nn.silu(_snake_case		)
									SCREAMING_SNAKE_CASE__		  =				nn.Dense(self.time_embed_dim   , dtype=self.dtype   , name="linear_2"		)(_snake_case		)
									return temb



class lowerCamelCase		(nn.Module      ):






					'''simple docstring'''


					a   	=		3_2
					a   	=		False
					a   	=		1



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





"""simple docstring"""






def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase       )							->   List[str]:
				if not head:
								return True
				# split the list to two parts
				SCREAMING_SNAKE_CASE__  ,       SCREAMING_SNAKE_CASE__		  =				head.next, head
				while fast and fast.next:
								SCREAMING_SNAKE_CASE__		  =				fast.next.next
								SCREAMING_SNAKE_CASE__		  =				slow.next
				SCREAMING_SNAKE_CASE__		  =				slow.next
				SCREAMING_SNAKE_CASE__		  =				None  # Don't forget here! But forget still works!
				# reverse the second part
				SCREAMING_SNAKE_CASE__		  =				None
				while second:
								SCREAMING_SNAKE_CASE__		  =				second.next
								SCREAMING_SNAKE_CASE__		  =				node
								SCREAMING_SNAKE_CASE__		  =				second
								SCREAMING_SNAKE_CASE__		  =				nxt
				# compare two parts
				# second part has the same or one less node
				while node:
								if node.val != head.val:
												return False
								SCREAMING_SNAKE_CASE__		  =				node.next
								SCREAMING_SNAKE_CASE__		  =				head.next
				return True




def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase       )							->   str:
				if not head or not head.next:
								return True

				# 1. Get the midpoint (slow)
				SCREAMING_SNAKE_CASE__		  =				SCREAMING_SNAKE_CASE__		  =				SCREAMING_SNAKE_CASE__		  =				head
				while fast and fast.next:
								SCREAMING_SNAKE_CASE__  ,       SCREAMING_SNAKE_CASE__		  =				fast.next.next, slow.next

				# 2. Push the second half into the stack
				SCREAMING_SNAKE_CASE__		  =				[slow.val]
				while slow.next:
								SCREAMING_SNAKE_CASE__		  =				slow.next
								stack.append(slow.val       )

				# 3. Comparison
				while stack:
								if stack.pop() != cur.val:
												return False
								SCREAMING_SNAKE_CASE__		  =				cur.next

				return True




def 						SCREAMING_SNAKE_CASE					(  __UpperCAmelCase       )							->   str:
				if not head or not head.next:
								return True
				SCREAMING_SNAKE_CASE__		  =				{}
				SCREAMING_SNAKE_CASE__		  =				0
				while head:
								if head.val in d:
												d[head.val].append(__UpperCAmelCase       )
								else:
												SCREAMING_SNAKE_CASE__		  =				[pos]
								SCREAMING_SNAKE_CASE__		  =				head.next
								pos += 1
				SCREAMING_SNAKE_CASE__		  =				pos - 1
				SCREAMING_SNAKE_CASE__		  =				0
				for v in d.values():
								if len(__UpperCAmelCase       ) % 2 != 0:
												middle += 1
								else:
												SCREAMING_SNAKE_CASE__		  =				0
												for i in range(0  ,					len(__UpperCAmelCase       )       ):
																if v[i] + v[len(__UpperCAmelCase       ) - 1 - step] != checksum:
																				return False
																step += 1
								if middle > 1:
												return False
				return True




