


"""simple docstring"""





import re
from typing import Callable, List, Optional, Union

import tensorflow as tf


try:
	from tensorflow.keras.optimizers.legacy import Adam
except ImportError:
	from tensorflow.keras.optimizers import Adam



class 		snake_case_(       tf.keras.optimizers.schedules.LearningRateSchedule			):






					def __init__(	self  :					Tuple					,				UpperCamelCase_  :					Optional[Any]					,				UpperCamelCase_  :					Dict					,				UpperCamelCase_  :					int					,				UpperCamelCase_  :					Optional[int] = 1.0					,				UpperCamelCase_  :					int = None					,				):
											super().__init__()
											lowerCAmelCase					:	Tuple       =   initial_learning_rate
											lowerCAmelCase					:	List[str]       =   warmup_steps
											lowerCAmelCase					:	int       =   power
											lowerCAmelCase					:	Dict       =   decay_schedule_fn
											lowerCAmelCase					:	Any       =   name






					def __call__(	self  :					List[str]					,				UpperCamelCase_  :					Union[str, Any]				):





											with tf.name_scope(self.name or '''WarmUp'''				) as name:
																	# Implements polynomial warmup. i.e., if global_step < warmup_steps, the
																	# learning rate will be `global_step/num_warmup_steps * init_lr`.
																	lowerCAmelCase					:	Optional[int]       =   tf.cast(UpperCamelCase_					,				tf.floataa				)
																	lowerCAmelCase					:	int       =   tf.cast(self.warmup_steps					,				tf.floataa				)
																	lowerCAmelCase					:	Optional[int]       =   global_step_float / warmup_steps_float
																	lowerCAmelCase					:	Optional[Any]       =   self.initial_learning_rate * tf.math.pow(UpperCamelCase_					,				self.power				)
																	return tf.cond(
																	    global_step_float < warmup_steps_float					,				lambda: warmup_learning_rate					,				lambda: self.decay_schedule_fn(step - self.warmup_steps				)					,				name=UpperCamelCase_					,				)






					def      lowerCamelCase__     (	self  :					Tuple				):
											return {
											    "initial_learning_rate": self.initial_learning_rate,
											    "decay_schedule_fn": self.decay_schedule_fn,
											    "warmup_steps": self.warmup_steps,
											    "power": self.power,
											    "name": self.name,
											}



def      _snake_case						(						_snake_case				:			float ,   _snake_case				:			int ,   _snake_case				:			int ,   _snake_case				:			float = 0.0 ,   _snake_case				:			float = 0.9 ,   _snake_case				:			float = 0.999 ,   _snake_case				:			float = 1E-8 ,   _snake_case				:			Optional[float] = None ,   _snake_case				:			Optional[float] = None ,   _snake_case				:			float = 0.0 ,   _snake_case				:			float = 1.0 ,   _snake_case				:			Optional[List[str]] = None ,   ):
						lowerCAmelCase					:	List[str]       =   tf.keras.optimizers.schedules.PolynomialDecay(
						    initial_learning_rate=__lowercase ,   decay_steps=num_train_steps - num_warmup_steps ,   end_learning_rate=init_lr * min_lr_ratio ,   power=__lowercase ,   )
						if num_warmup_steps:
												lowerCAmelCase					:	Tuple       =   WarmUp(
												    initial_learning_rate=__lowercase ,   decay_schedule_fn=__lowercase ,   warmup_steps=__lowercase ,   )
						if weight_decay_rate > 0.0:
												lowerCAmelCase					:	Union[str, Any]       =   AdamWeightDecay(
												    learning_rate=__lowercase ,   weight_decay_rate=__lowercase ,   beta_a=__lowercase ,   beta_a=__lowercase ,   epsilon=__lowercase ,   clipnorm=__lowercase ,   global_clipnorm=__lowercase ,   exclude_from_weight_decay=['''LayerNorm''', '''layer_norm''', '''bias'''] ,   include_in_weight_decay=__lowercase ,   )
						else:
												lowerCAmelCase					:	Dict       =   tf.keras.optimizers.Adam(
												    learning_rate=__lowercase ,   beta_a=__lowercase ,   beta_a=__lowercase ,   epsilon=__lowercase ,   clipnorm=__lowercase ,   global_clipnorm=__lowercase ,   )
						# We return the optimizer and the LR scheduler in order to better track the
						# evolution of the LR independently of the optimizer.
						return optimizer, lr_schedule



class 		snake_case_(       __A			):






					def __init__(	self  :					List[str]					,				UpperCamelCase_  :					Any = 0.001					,				UpperCamelCase_  :					Optional[Any] = 0.9					,				UpperCamelCase_  :					str = 0.999					,				UpperCamelCase_  :					Union[str, Any] = 1E-7					,				UpperCamelCase_  :					str = False					,				UpperCamelCase_  :					Optional[Any] = 0.0					,				UpperCamelCase_  :					str = None					,				UpperCamelCase_  :					List[Any] = None					,				UpperCamelCase_  :					Any = "AdamWeightDecay"					,				**UpperCamelCase_  :					Optional[int]					,				):
											super().__init__(UpperCamelCase_					,				UpperCamelCase_					,				UpperCamelCase_					,				UpperCamelCase_					,				UpperCamelCase_					,				UpperCamelCase_					,				**UpperCamelCase_				)
											lowerCAmelCase					:	Dict       =   weight_decay_rate
											lowerCAmelCase					:	Union[str, Any]       =   include_in_weight_decay
											lowerCAmelCase					:	str       =   exclude_from_weight_decay






					@classmethod
					def      lowerCamelCase__     (	cls  :					Union[str, Any]					,				UpperCamelCase_  :					Union[str, Any]				):
											lowerCAmelCase					:	Tuple       =   {'WarmUp': WarmUp}
											return super(UpperCamelCase_					,				cls				).from_config(UpperCamelCase_					,				custom_objects=UpperCamelCase_				)






					def      lowerCamelCase__     (	self  :					Any					,				UpperCamelCase_  :					str					,				UpperCamelCase_  :					List[Any]					,				UpperCamelCase_  :					str				):
											super(UpperCamelCase_					,				self				)._prepare_local(UpperCamelCase_					,				UpperCamelCase_					,				UpperCamelCase_				)
											lowerCAmelCase					:	Optional[Any]       =   tf.constant(
											    self.weight_decay_rate					,				name='''adam_weight_decay_rate'''				)






					def      lowerCamelCase__     (	self  :					Optional[int]					,				UpperCamelCase_  :					Any					,				UpperCamelCase_  :					List[Any]					,				UpperCamelCase_  :					Tuple				):
											lowerCAmelCase					:	Dict       =   self._do_use_weight_decay(var.name				)
											if do_decay:
																	return var.assign_sub(
																	    learning_rate * var * apply_state[(var.device, var.dtype.base_dtype)]['''weight_decay_rate''']					,				use_locking=self._use_locking					,				)
											return tf.no_op()






					def      lowerCamelCase__     (	self  :					List[str]					,				UpperCamelCase_  :					Optional[int]					,				UpperCamelCase_  :					str=None					,				**UpperCamelCase_  :					Optional[int]				):
											lowerCAmelCase					:	Optional[int]       =   list(zip(*UpperCamelCase_				)				)
											return super(UpperCamelCase_					,				self				).apply_gradients(zip(UpperCamelCase_					,				UpperCamelCase_				)					,				name=UpperCamelCase_					,				**UpperCamelCase_				)






					def      lowerCamelCase__     (	self  :					Optional[Any]					,				UpperCamelCase_  :					str					,				UpperCamelCase_  :					Union[str, Any]					,				UpperCamelCase_  :					int				):





											if apply_state is None:
																	return self._decayed_lr_t[var_dtype], {}

											lowerCAmelCase					:	List[str]       =   apply_state or {}
											lowerCAmelCase					:	Dict       =   apply_state.get((var_device, var_dtype)				)
											if coefficients is None:
																	lowerCAmelCase					:	Dict       =   self._fallback_apply_state(UpperCamelCase_					,				UpperCamelCase_				)
																	lowerCAmelCase					:	int       =   coefficients

											return coefficients["lr_t"], {"apply_state": apply_state}






					def      lowerCamelCase__     (	self  :					Optional[int]					,				UpperCamelCase_  :					Optional[Any]					,				UpperCamelCase_  :					Dict					,				UpperCamelCase_  :					Optional[int]=None				):
											lowerCAmelCase					:	Optional[Any]       =   self._get_lr(var.device					,				var.dtype.base_dtype					,				UpperCamelCase_				)
											lowerCAmelCase					:	Union[str, Any]       =   self._decay_weights_op(UpperCamelCase_					,				UpperCamelCase_					,				UpperCamelCase_				)
											with tf.control_dependencies([decay]				):
																	return super(UpperCamelCase_					,				self				)._resource_apply_dense(UpperCamelCase_					,				UpperCamelCase_					,				**UpperCamelCase_				)






					def      lowerCamelCase__     (	self  :					str					,				UpperCamelCase_  :					Any					,				UpperCamelCase_  :					List[str]					,				UpperCamelCase_  :					List[str]					,				UpperCamelCase_  :					Union[str, Any]=None				):
											lowerCAmelCase					:	Optional[Any]       =   self._get_lr(var.device					,				var.dtype.base_dtype					,				UpperCamelCase_				)
											lowerCAmelCase					:	Optional[Any]       =   self._decay_weights_op(UpperCamelCase_					,				UpperCamelCase_					,				UpperCamelCase_				)
											with tf.control_dependencies([decay]				):
																	return super(UpperCamelCase_					,				self				)._resource_apply_sparse(UpperCamelCase_					,				UpperCamelCase_					,				UpperCamelCase_					,				**UpperCamelCase_				)






					def      lowerCamelCase__     (	self  :					Optional[Any]				):
											lowerCAmelCase					:	Optional[int]       =   super().get_config()
											config.update({'''weight_decay_rate''': self.weight_decay_rate}				)
											return config






					def      lowerCamelCase__     (	self  :					int					,				UpperCamelCase_  :					str				):





											if self.weight_decay_rate == 0:
																	return False

											if self._include_in_weight_decay:
																	for r in self._include_in_weight_decay:
																							if re.search(UpperCamelCase_					,				UpperCamelCase_				) is not None:
																													return True

											if self._exclude_from_weight_decay:
																	for r in self._exclude_from_weight_decay:
																							if re.search(UpperCamelCase_					,				UpperCamelCase_				) is not None:
																													return False
											return True



class 		snake_case_(       __A			):






					def __init__(	self  :					List[str]				):
											lowerCAmelCase					:	int       =   []
											lowerCAmelCase					:	Optional[int]       =   None






					@property
					def      lowerCamelCase__     (	self  :					Union[str, Any]				):





											if self._accum_steps is None:
																	lowerCAmelCase					:	int       =   tf.Variable(
																	    tf.constant(0					,				dtype=tf.intaa				)					,				trainable=UpperCamelCase_					,				synchronization=tf.VariableSynchronization.ON_READ					,				aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA					,				)

											return self._accum_steps.value()






					@property
					def      lowerCamelCase__     (	self  :					Any				):





											if not self._gradients:
																	raise ValueError('''The accumulator should be called first to initialize the gradients'''				)
											return [gradient.value() if gradient is not None else gradient for gradient in self._gradients]






					def __call__(	self  :					Union[str, Any]					,				UpperCamelCase_  :					Tuple				):





											if not self._gradients:
																	lowerCAmelCase					:	Optional[Any]       =   self.step  # Create the step variable.
																	self._gradients.extend(
																	    [
																	        tf.Variable(
																	            tf.zeros_like(UpperCamelCase_				)					,				trainable=UpperCamelCase_					,				synchronization=tf.VariableSynchronization.ON_READ					,				aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA					,				)
																	        if gradient is not None
																	        else gradient
																	        for gradient in gradients
																	    ]				)
											if len(UpperCamelCase_				) != len(self._gradients				):
																	raise ValueError(F'''Expected {len(self._gradients				)} gradients, but got {len(UpperCamelCase_				)}'''				)

											for accum_gradient, gradient in zip(self._gradients					,				UpperCamelCase_				):
																	if accum_gradient is not None and gradient is not None:
																							accum_gradient.assign_add(UpperCamelCase_				)

											self._accum_steps.assign_add(1				)






					def      lowerCamelCase__     (	self  :					Optional[Any]				):





											if not self._gradients:
																	return
											self._accum_steps.assign(0				)
											for gradient in self._gradients:
																	if gradient is not None:
																							gradient.assign(tf.zeros_like(UpperCamelCase_				)				)






"""simple docstring"""





class 		snake_case_:






     def __init__(	self  :					Union[str, Any]					,				UpperCamelCase_  :					str				):
           lowerCAmelCase					:	Dict       =   val
           lowerCAmelCase					:	str       =   None
           lowerCAmelCase					:	Dict       =   None






     def      lowerCamelCase__     (	self  :					Union[str, Any]					,				UpperCamelCase_  :					Dict				):
           if self.val:
                 if val < self.val:
                       if self.left is None:
                             lowerCAmelCase					:	int       =   Node(UpperCamelCase_				)
                       else:
                             self.left.insert(UpperCamelCase_				)
                 elif val > self.val:
                       if self.right is None:
                             lowerCAmelCase					:	Any       =   Node(UpperCamelCase_				)
                       else:
                             self.right.insert(UpperCamelCase_				)
           else:
                 lowerCAmelCase					:	Optional[Any]       =   val



def      _snake_case						(						_snake_case				:			Tuple ,   _snake_case				:			str			):
      # Recursive traversal
      if root:
            inorder(root.left ,   _snake_case			)
            res.append(root.val			)
            inorder(root.right ,   _snake_case			)


def      _snake_case						(						_snake_case				:			Optional[Any]			):
      # Build BST
      if len(_snake_case			) == 0:
            return arr
      lowerCAmelCase					:	Optional[Any]       =   Node(arr[0]			)
      for i in range(1 ,   len(_snake_case			)			):
            root.insert(arr[i]			)
      # Traverse BST in order.
      lowerCAmelCase					:	Optional[int]       =   []
      inorder(_snake_case ,   _snake_case			)
      return res


if __name__ == "__main__":
 print(tree_sort([10, 1, 3, 2, 9, 14, 13]))


