





"""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       :      Optional[Any]						,				__lowercase       :      float						,				__lowercase       :      Callable						,				__lowercase       :      int						,				__lowercase       :      float = 1.0						,				__lowercase       :      str = None						,				):


								'''simple docstring'''




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

						def __call__(							self       :      str						,				__lowercase       :      str ):


								'''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`.
										__UpperCAmelCase    :						Union[str, Any]       =						tf.cast(__lowercase						,				tf.floataa )
										__UpperCAmelCase    :						str       =						tf.cast(self.warmup_steps						,				tf.floataa )
										__UpperCAmelCase    :						Dict       =						global_step_float / warmup_steps_float
										__UpperCAmelCase    :						Any       =						self.initial_learning_rate * tf.math.pow(__lowercase						,				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=__lowercase						,				)







						def       A_					(							self       :      Tuple ):


								'''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       lowerCamelCase_       (   UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_  ,			UpperCAmelCase_ = 0.0  ,			UpperCAmelCase_ = 0.9  ,			UpperCAmelCase_ = 0.999  ,			UpperCAmelCase_ = 1e-8  ,			UpperCAmelCase_ = None  ,			UpperCAmelCase_ = None  ,			UpperCAmelCase_ = 0.0  ,			UpperCAmelCase_ = 1.0  ,			UpperCAmelCase_ = None  ,			)						->List[Any]:





		"""simple docstring"""


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

						'''simple docstring'''



						def __init__(							self       :      Tuple						,				__lowercase       :      Union[float, tf.keras.optimizers.schedules.LearningRateSchedule] = 0.0_0_1						,				__lowercase       :      float = 0.9						,				__lowercase       :      float = 0.9_9_9						,				__lowercase       :      float = 1e-7						,				__lowercase       :      bool = False						,				__lowercase       :      float = 0.0						,				__lowercase       :      Optional[List[str]] = None						,				__lowercase       :      Optional[List[str]] = None						,				__lowercase       :      str = "AdamWeightDecay"						,				**__lowercase       :      Any						,				):


								'''simple docstring'''




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

						@classmethod
						def       A_					(							cls       :      int						,				__lowercase       :      List[str] ):


								'''simple docstring'''




								__UpperCAmelCase    :						Dict       =						{'''WarmUp''': WarmUp}
								return super(__lowercase						,				cls ).from_config(__lowercase						,				custom_objects=__lowercase )

						def       A_					(							self       :      List[Any]						,				__lowercase       :      Optional[int]						,				__lowercase       :      Optional[Any]						,				__lowercase       :      Optional[int] ):


								'''simple docstring'''




								super(__lowercase						,				self )._prepare_local(__lowercase						,				__lowercase						,				__lowercase )
								__UpperCAmelCase    :						Tuple       =						tf.constant(
								    self.weight_decay_rate						,				name='''adam_weight_decay_rate''' )

						def       A_					(							self       :      List[str]						,				__lowercase       :      Dict						,				__lowercase       :      Any						,				__lowercase       :      str ):


								'''simple docstring'''




								__UpperCAmelCase    :						Tuple       =						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       A_					(							self       :      List[Any]						,				__lowercase       :      Any						,				__lowercase       :      Any=None						,				**__lowercase       :      Union[str, Any] ):


								'''simple docstring'''




								__UpperCAmelCase    :						Tuple       =						list(zip(*__lowercase ) )
								return super(__lowercase						,				self ).apply_gradients(zip(__lowercase						,				__lowercase )						,				name=__lowercase						,				**__lowercase )

						def       A_					(							self       :      Tuple						,				__lowercase       :      Union[str, Any]						,				__lowercase       :      Any						,				__lowercase       :      List[str] ):


								'''simple docstring'''




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

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

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

						def       A_					(							self       :      List[Any]						,				__lowercase       :      Any						,				__lowercase       :      List[str]						,				__lowercase       :      Dict=None ):


								'''simple docstring'''




								__UpperCAmelCase    :						Optional[Any]       =						self._get_lr(var.device						,				var.dtype.base_dtype						,				__lowercase )
								__UpperCAmelCase    :						List[Any]       =						self._decay_weights_op(__lowercase						,				__lowercase						,				__lowercase )
								with tf.control_dependencies([decay] ):
										return super(__lowercase						,				self )._resource_apply_dense(__lowercase						,				__lowercase						,				**__lowercase )

						def       A_					(							self       :      Dict						,				__lowercase       :      List[Any]						,				__lowercase       :      str						,				__lowercase       :      Tuple						,				__lowercase       :      Union[str, Any]=None ):


								'''simple docstring'''




								__UpperCAmelCase    :						str       =						self._get_lr(var.device						,				var.dtype.base_dtype						,				__lowercase )
								__UpperCAmelCase    :						List[Any]       =						self._decay_weights_op(__lowercase						,				__lowercase						,				__lowercase )
								with tf.control_dependencies([decay] ):
										return super(__lowercase						,				self )._resource_apply_sparse(__lowercase						,				__lowercase						,				__lowercase						,				**__lowercase )

						def       A_					(							self       :      Optional[Any] ):


								'''simple docstring'''




								__UpperCAmelCase    :						str       =						super().get_config()
								config.update({'''weight_decay_rate''': self.weight_decay_rate} )
								return config







						def       A_					(							self       :      Optional[Any]						,				__lowercase       :      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(__lowercase						,				__lowercase ) is not None:
														return True

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




class 							snake_case							(			__UpperCAmelCase ):

						'''simple docstring'''



						def __init__(							self       :      str ):


								'''simple docstring'''




								__UpperCAmelCase    :						List[Any]       =						[]
								__UpperCAmelCase    :						List[str]       =						None

						@property
						def       A_					(							self       :      int ):


								'''simple docstring'''




								if self._accum_steps is None:
										__UpperCAmelCase    :						List[str]       =						tf.Variable(
										    tf.constant(0						,				dtype=tf.intaa )						,				trainable=__lowercase						,				synchronization=tf.VariableSynchronization.ON_READ						,				aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA						,				)

								return self._accum_steps.value()

						@property
						def       A_					(							self       :      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       :      List[str]						,				__lowercase       :      Optional[int] ):


								'''simple docstring'''




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

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

								self._accum_steps.assign_add(1 )







						def       A_					(							self       :      Dict ):


								'''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(__lowercase ) )






"""simple docstring"""





from __future__ import annotations

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

lowercase__				:int				   =       TypeVar('T')




class 							snake_case							(			Generic[T] ):

      '''simple docstring'''



      def __init__(							self       :      Optional[Any]						,				__lowercase       :      list[T]						,				__lowercase       :      Callable[[T, T], T] ):


        '''simple docstring'''




        __UpperCAmelCase    :						Any | T       =						None

        __UpperCAmelCase    :						int       =						len(__lowercase )
        __UpperCAmelCase    :						list[T]       =						[any_type for _ in range(self.N )] + arr
        __UpperCAmelCase    :						List[Any]       =						fnc
        self.build()

      def       A_					(							self       :      str ):


        '''simple docstring'''




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

      def       A_					(							self       :      Union[str, Any]						,				__lowercase       :      int						,				__lowercase       :      T ):


        '''simple docstring'''




        p += self.N
        __UpperCAmelCase    :						Tuple       =						v
        while p > 1:
          __UpperCAmelCase    :						Union[str, Any]       =						p // 2
          __UpperCAmelCase    :						Any       =						self.fn(self.st[p * 2]						,				self.st[p * 2 + 1] )







      def       A_					(							self       :      str						,				__lowercase       :      int						,				__lowercase       :      int ):  # noqa: E741


        '''simple docstring'''




        __UpperCAmelCase       ,     __UpperCAmelCase    :						int       =						l + self.N, r + self.N

        __UpperCAmelCase    :						T | None       =						None
        while l <= r:
          if l % 2 == 1:
            __UpperCAmelCase    :						Any       =						self.st[l] if res is None else self.fn(__lowercase						,				self.st[l] )
          if r % 2 == 0:
            __UpperCAmelCase    :						Any       =						self.st[r] if res is None else self.fn(__lowercase						,				self.st[r] )
          __UpperCAmelCase       ,     __UpperCAmelCase    :						Any       =						(l + 1) // 2, (r - 1) // 2
        return res


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

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

  lowercase__				:List[Any]				   =       {
      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__				:List[str]				   =       SegmentTree(test_array, min)
  lowercase__				:List[str]				   =       SegmentTree(test_array, max)
  lowercase__				:Tuple				   =       SegmentTree(test_array, lambda a, b: a + b)


  def       lowerCamelCase_       (   )						->None:





    """simple docstring"""


    for i in range(len(UpperCAmelCase_  )  ):
      for j in range(UpperCAmelCase_  ,			len(UpperCAmelCase_  )  ):
        __UpperCAmelCase    :						Optional[Any]       =						reduce(UpperCAmelCase_  ,			test_array[i : j + 1]  )
        __UpperCAmelCase    :						Optional[int]       =						reduce(UpperCAmelCase_  ,			test_array[i : j + 1]  )
        __UpperCAmelCase    :						Union[str, Any]       =						reduce(lambda UpperCAmelCase_  ,			UpperCAmelCase_  : a + b  ,			test_array[i : j + 1]  )
        assert min_range == min_segment_tree.query(UpperCAmelCase_  ,			UpperCAmelCase_  )
        assert max_range == max_segment_tree.query(UpperCAmelCase_  ,			UpperCAmelCase_  )
        assert sum_range == sum_segment_tree.query(UpperCAmelCase_  ,			UpperCAmelCase_  )

  test_all_segments()

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