
'''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					):







		"""simple docstring"""

		def __init__(      self				:			Dict  ,	UpperCamelCase__				:			float  ,	UpperCamelCase__				:			Callable  ,	UpperCamelCase__				:			int  ,	UpperCamelCase__				:			float = 1.0  ,	UpperCamelCase__				:			str = None  ,	)						->			Dict:






				"""simple docstring"""







				super().__init__()
				snake_case  :       Optional[Any]     			=						initial_learning_rate
				snake_case  :       Optional[Any]     			=						warmup_steps
				snake_case  :       List[str]     			=						power
				snake_case  :       Tuple     			=						decay_schedule_fn
				snake_case  :       str     			=						name



		def __call__(      self				:			List[str]  ,	UpperCamelCase__				:			Tuple      )						->			Optional[int]:






				"""simple docstring"""







				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`.
						snake_case  :       Optional[int]     			=						tf.cast(UpperCamelCase__  ,	tf.floataa      )
						snake_case  :       List[Any]     			=						tf.cast(self.warmup_steps  ,	tf.floataa      )
						snake_case  :       Optional[int]     			=						global_step_float / warmup_steps_float
						snake_case  :       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				:			Dict      )						->			List[Any]:






				"""simple docstring"""







				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    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__ = 0.0 ,       SCREAMING_SNAKE_CASE__ = 0.9 ,       SCREAMING_SNAKE_CASE__ = 0.999 ,       SCREAMING_SNAKE_CASE__ = 1E-8 ,       SCREAMING_SNAKE_CASE__ = None ,       SCREAMING_SNAKE_CASE__ = None ,       SCREAMING_SNAKE_CASE__ = 0.0 ,       SCREAMING_SNAKE_CASE__ = 1.0 ,       SCREAMING_SNAKE_CASE__ = None ,       )  ->							str:


		'''simple docstring'''


		snake_case  :       Optional[Any]     			=						tf.keras.optimizers.schedules.PolynomialDecay(
		    initial_learning_rate=SCREAMING_SNAKE_CASE__ ,       decay_steps=num_train_steps - num_warmup_steps ,       end_learning_rate=init_lr * min_lr_ratio ,       power=SCREAMING_SNAKE_CASE__ ,       )
		if num_warmup_steps:
				snake_case  :       Union[str, Any]     			=						WarmUp(
				    initial_learning_rate=SCREAMING_SNAKE_CASE__ ,       decay_schedule_fn=SCREAMING_SNAKE_CASE__ ,       warmup_steps=SCREAMING_SNAKE_CASE__ ,       )
		if weight_decay_rate > 0.0:
				snake_case  :       List[Any]     			=						AdamWeightDecay(
				    learning_rate=SCREAMING_SNAKE_CASE__ ,       weight_decay_rate=SCREAMING_SNAKE_CASE__ ,       beta_a=SCREAMING_SNAKE_CASE__ ,       beta_a=SCREAMING_SNAKE_CASE__ ,       epsilon=SCREAMING_SNAKE_CASE__ ,       clipnorm=SCREAMING_SNAKE_CASE__ ,       global_clipnorm=SCREAMING_SNAKE_CASE__ ,       exclude_from_weight_decay=['''LayerNorm''', '''layer_norm''', '''bias'''] ,       include_in_weight_decay=SCREAMING_SNAKE_CASE__ ,       )
		else:
				snake_case  :       Union[str, Any]     			=						tf.keras.optimizers.Adam(
				    learning_rate=SCREAMING_SNAKE_CASE__ ,       beta_a=SCREAMING_SNAKE_CASE__ ,       beta_a=SCREAMING_SNAKE_CASE__ ,       epsilon=SCREAMING_SNAKE_CASE__ ,       clipnorm=SCREAMING_SNAKE_CASE__ ,       global_clipnorm=SCREAMING_SNAKE_CASE__ ,       )
		# 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__       (      __SCREAMING_SNAKE_CASE					):







		"""simple docstring"""

		def __init__(      self				:			Union[str, Any]  ,	UpperCamelCase__				:			Union[float, tf.keras.optimizers.schedules.LearningRateSchedule] = 0.001  ,	UpperCamelCase__				:			float = 0.9  ,	UpperCamelCase__				:			float = 0.999  ,	UpperCamelCase__				:			float = 1e-7  ,	UpperCamelCase__				:			bool = False  ,	UpperCamelCase__				:			float = 0.0  ,	UpperCamelCase__				:			Optional[List[str]] = None  ,	UpperCamelCase__				:			Optional[List[str]] = None  ,	UpperCamelCase__				:			str = "AdamWeightDecay"  ,	**UpperCamelCase__				:			str  ,	)						->			int:






				"""simple docstring"""







				super().__init__(UpperCamelCase__  ,	UpperCamelCase__  ,	UpperCamelCase__  ,	UpperCamelCase__  ,	UpperCamelCase__  ,	UpperCamelCase__  ,	**UpperCamelCase__      )
				snake_case  :       Dict     			=						weight_decay_rate
				snake_case  :       Any     			=						include_in_weight_decay
				snake_case  :       Optional[Any]     			=						exclude_from_weight_decay



		@classmethod
		def       lowerCAmelCase				(      cls				:			Optional[Any]  ,	UpperCamelCase__				:			int      )						->			List[str]:






				"""simple docstring"""







				snake_case  :       List[str]     			=						{'''WarmUp''': WarmUp}
				return super(UpperCamelCase__  ,	cls      ).from_config(UpperCamelCase__  ,	custom_objects=UpperCamelCase__      )



		def       lowerCAmelCase				(      self				:			str  ,	UpperCamelCase__				:			str  ,	UpperCamelCase__				:			List[Any]  ,	UpperCamelCase__				:			int      )						->			Union[str, Any]:






				"""simple docstring"""







				super(UpperCamelCase__  ,	self      )._prepare_local(UpperCamelCase__  ,	UpperCamelCase__  ,	UpperCamelCase__      )
				snake_case  :       str     			=						tf.constant(
				    self.weight_decay_rate  ,	name='''adam_weight_decay_rate'''      )



		def       lowerCAmelCase				(      self				:			Dict  ,	UpperCamelCase__				:			Dict  ,	UpperCamelCase__				:			Dict  ,	UpperCamelCase__				:			Dict      )						->			Any:






				"""simple docstring"""







				snake_case  :       str     			=						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				:			Dict  ,	UpperCamelCase__				:			int  ,	UpperCamelCase__				:			List[str]=None  ,	**UpperCamelCase__				:			Optional[Any]      )						->			List[Any]:






				"""simple docstring"""







				snake_case			,snake_case  :       str     			=						list(zip(*UpperCamelCase__      )      )
				return super(UpperCamelCase__  ,	self      ).apply_gradients(zip(UpperCamelCase__  ,	UpperCamelCase__      )  ,	name=UpperCamelCase__  ,	**UpperCamelCase__      )



		def       lowerCAmelCase				(      self				:			List[Any]  ,	UpperCamelCase__				:			List[Any]  ,	UpperCamelCase__				:			Optional[Any]  ,	UpperCamelCase__				:			Union[str, Any]      )						->			List[str]:






				"""simple docstring"""







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

				snake_case  :       Dict     			=						apply_state or {}
				snake_case  :       Union[str, Any]     			=						apply_state.get((var_device, var_dtype)      )
				if coefficients is None:
						snake_case  :       Tuple     			=						self._fallback_apply_state(UpperCamelCase__  ,	UpperCamelCase__      )
						snake_case  :       List[str]     			=						coefficients

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



		def       lowerCAmelCase				(      self				:			int  ,	UpperCamelCase__				:			Dict  ,	UpperCamelCase__				:			Any  ,	UpperCamelCase__				:			Dict=None      )						->			Dict:






				"""simple docstring"""







				snake_case			,snake_case  :       Union[str, Any]     			=						self._get_lr(var.device  ,	var.dtype.base_dtype  ,	UpperCamelCase__      )
				snake_case  :       int     			=						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				:			Dict  ,	UpperCamelCase__				:			List[str]  ,	UpperCamelCase__				:			int  ,	UpperCamelCase__				:			str  ,	UpperCamelCase__				:			List[Any]=None      )						->			Dict:






				"""simple docstring"""







				snake_case			,snake_case  :       Union[str, Any]     			=						self._get_lr(var.device  ,	var.dtype.base_dtype  ,	UpperCamelCase__      )
				snake_case  :       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				:			Any      )						->			Union[str, Any]:






				"""simple docstring"""







				snake_case  :       List[str]     			=						super().get_config()
				config.update({'''weight_decay_rate''': self.weight_decay_rate}      )
				return config



		def       lowerCAmelCase				(      self				:			Any  ,	UpperCamelCase__				:			Optional[int]      )						->			List[str]:






				"""simple docstring"""







				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__       (      __SCREAMING_SNAKE_CASE					):







		"""simple docstring"""

		def __init__(      self				:			Any      )						->			List[Any]:






				"""simple docstring"""







				snake_case  :       List[Any]     			=						[]
				snake_case  :       Optional[Any]     			=						None



		@property
		def       lowerCAmelCase				(      self				:			Optional[int]      )						->			Union[str, Any]:






				"""simple docstring"""







				if self._accum_steps is None:
						snake_case  :       Optional[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				:			Tuple      )						->			Tuple:






				"""simple docstring"""







				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				:			Any  ,	UpperCamelCase__				:			List[str]      )						->			str:






				"""simple docstring"""







				if not self._gradients:
						snake_case  :       Optional[int]     			=						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				:			List[Any]      )						->			int:






				"""simple docstring"""







				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'''
from __future__ import annotations

from collections.abc import Callable
from typing import Any, Generic, TypeVar

lowercase__						       =      TypeVar("T")






class 	snake_case__       (      Generic[T]					):







		"""simple docstring"""

		def __init__(      self				:			str  ,	UpperCamelCase__				:			list[T]  ,	UpperCamelCase__				:			Callable[[T, T], T]      )						->			None:






				"""simple docstring"""







				snake_case  :       Any | T     			=						None

				snake_case  :       int     			=						len(UpperCamelCase__      )
				snake_case  :       list[T]     			=						[any_type for _ in range(self.N      )] + arr
				snake_case  :       Optional[int]     			=						fnc
				self.build()



		def       lowerCAmelCase				(      self				:			Optional[Any]      )						->			None:






				"""simple docstring"""







				for p in range(self.N - 1  ,	0  ,	-1      ):
						snake_case  :       List[Any]     			=						self.fn(self.st[p * 2]  ,	self.st[p * 2 + 1]      )



		def       lowerCAmelCase				(      self				:			List[Any]  ,	UpperCamelCase__				:			int  ,	UpperCamelCase__				:			T      )						->			None:






				"""simple docstring"""







				p += self.N
				snake_case  :       int     			=						v
				while p > 1:
						snake_case  :       List[Any]     			=						p // 2
						snake_case  :       List[Any]     			=						self.fn(self.st[p * 2]  ,	self.st[p * 2 + 1]      )



		def       lowerCAmelCase				(      self				:			Union[str, Any]  ,	UpperCamelCase__				:			int  ,	UpperCamelCase__				:			int      )						->			T | None:  # noqa: E741






				"""simple docstring"""







				snake_case			,snake_case  :       Union[str, Any]     			=						l + self.N, r + self.N

				snake_case  :       T | None     			=						None
				while l <= r:
						if l % 2 == 1:
								snake_case  :       str     			=						self.st[l] if res is None else self.fn(UpperCamelCase__  ,	self.st[l]      )
						if r % 2 == 0:
								snake_case  :       Tuple     			=						self.st[r] if res is None else self.fn(UpperCamelCase__  ,	self.st[r]      )
						snake_case			,snake_case  :       Dict     			=						(l + 1) // 2, (r - 1) // 2
				return res


if __name__ == "__main__":
						from functools import reduce

						lowercase__						       =      [1, 1_0, -2, 9, -3, 8, 4, -7, 5, 6, 1_1, -1_2]

						lowercase__						       =      {
						    0: 7,
						    1: 2,
						    2: 6,
						    3: -1_4,
						    4: 5,
						    5: 4,
						    6: 7,
						    7: -1_0,
						    8: 9,
						    9: 1_0,
						    1_0: 1_2,
						    1_1: 1,
						}

						lowercase__						       =      SegmentTree(test_array, min)
						lowercase__						       =      SegmentTree(test_array, max)
						lowercase__						       =      SegmentTree(test_array, lambda a, b: a + b)




						def    _UpperCamelCase						(       )  ->							None:


								'''simple docstring'''


								for i in range(len(SCREAMING_SNAKE_CASE__			)			):
										for j in range(SCREAMING_SNAKE_CASE__ ,       len(SCREAMING_SNAKE_CASE__			)			):
												snake_case  :       int     			=						reduce(SCREAMING_SNAKE_CASE__ ,       test_array[i : j + 1]			)
												snake_case  :       List[str]     			=						reduce(SCREAMING_SNAKE_CASE__ ,       test_array[i : j + 1]			)
												snake_case  :       Tuple     			=						reduce(lambda SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			: a + b ,       test_array[i : j + 1]			)
												assert min_range == min_segment_tree.query(SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			)
												assert max_range == max_segment_tree.query(SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			)
												assert sum_range == sum_segment_tree.query(SCREAMING_SNAKE_CASE__ ,       SCREAMING_SNAKE_CASE__			)

						test_all_segments()

						for index, value in test_updates.items():
												lowercase__						       =      value
												min_segment_tree.update(index, value)
												max_segment_tree.update(index, value)
												sum_segment_tree.update(index, value)
												test_all_segments()


