

'''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    A__ ( tf.keras.optimizers.schedules.LearningRateSchedule     ):



    def __init__(   self						,			UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__ = 1.0						,			UpperCamelCase__ = None						,			)  -> Optional[int]:





           '''simple docstring'''
           super().__init__()
           A_		   = initial_learning_rate
           A_		   = warmup_steps
           A_		   = power
           A_		   = decay_schedule_fn
           A_		   = name



    def __call__(   self						,			UpperCamelCase__    )  -> Tuple:





           '''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`.
                  A_		   = tf.cast(UpperCamelCase__						,			tf.floataa    )
                  A_		   = tf.cast(self.warmup_steps						,			tf.floataa    )
                  A_		   = global_step_float / warmup_steps_float
                  A_		   = 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    snake_case_     (   self    )  -> Union[str, 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__      ( 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,    )     ->     Any:
       A_		   = 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:
              A_		   = WarmUp(
                  initial_learning_rate=UpperCAmelCase__,    decay_schedule_fn=UpperCAmelCase__,    warmup_steps=UpperCAmelCase__,    )
       if weight_decay_rate > 0.0:
              A_		   = 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:
              A_		   = 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    A__ ( _snake_case     ):



    def __init__(   self						,			UpperCamelCase__ = 0.001						,			UpperCamelCase__ = 0.9						,			UpperCamelCase__ = 0.999						,			UpperCamelCase__ = 1e-7						,			UpperCamelCase__ = False						,			UpperCamelCase__ = 0.0						,			UpperCamelCase__ = None						,			UpperCamelCase__ = None						,			UpperCamelCase__ = "AdamWeightDecay"						,			**UpperCamelCase__						,			)  -> Optional[Any]:





           '''simple docstring'''
           super().__init__(UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__						,			**UpperCamelCase__    )
           A_		   = weight_decay_rate
           A_		   = include_in_weight_decay
           A_		   = exclude_from_weight_decay



    @classmethod
    def    snake_case_     (   cls						,			UpperCamelCase__    )  -> Optional[Any]:





           '''simple docstring'''
           A_		   = {"""WarmUp""": WarmUp}
           return super(UpperCamelCase__						,			cls    ).from_config(UpperCamelCase__						,			custom_objects=UpperCamelCase__    )



    def    snake_case_     (   self						,			UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__    )  -> Tuple:





           '''simple docstring'''
           super(UpperCamelCase__						,			self    )._prepare_local(UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__    )
           A_		   = tf.constant(
               self.weight_decay_rate						,			name="""adam_weight_decay_rate"""    )



    def    snake_case_     (   self						,			UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__    )  -> Union[str, Any]:





           '''simple docstring'''
           A_		   = 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    snake_case_     (   self						,			UpperCamelCase__						,			UpperCamelCase__=None						,			**UpperCamelCase__    )  -> Optional[int]:





           '''simple docstring'''
           A_   ,     A_		   = list(zip(*UpperCamelCase__    )    )
           return super(UpperCamelCase__						,			self    ).apply_gradients(zip(UpperCamelCase__						,			UpperCamelCase__    )						,			name=UpperCamelCase__						,			**UpperCamelCase__    )



    def    snake_case_     (   self						,			UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__    )  -> int:





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

           A_		   = apply_state or {}
           A_		   = apply_state.get((var_device, var_dtype)    )
           if coefficients is None:
                  A_		   = self._fallback_apply_state(UpperCamelCase__						,			UpperCamelCase__    )
                  A_		   = coefficients

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



    def    snake_case_     (   self						,			UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__=None    )  -> List[Any]:





           '''simple docstring'''
           A_   ,     A_		   = self._get_lr(var.device						,			var.dtype.base_dtype						,			UpperCamelCase__    )
           A_		   = self._decay_weights_op(UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__    )
           with tf.control_dependencies([decay]    ):
                  return super(UpperCamelCase__						,			self    )._resource_apply_dense(UpperCamelCase__						,			UpperCamelCase__						,			**UpperCamelCase__    )



    def    snake_case_     (   self						,			UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__=None    )  -> Any:





           '''simple docstring'''
           A_   ,     A_		   = self._get_lr(var.device						,			var.dtype.base_dtype						,			UpperCamelCase__    )
           A_		   = self._decay_weights_op(UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__    )
           with tf.control_dependencies([decay]    ):
                  return super(UpperCamelCase__						,			self    )._resource_apply_sparse(UpperCamelCase__						,			UpperCamelCase__						,			UpperCamelCase__						,			**UpperCamelCase__    )



    def    snake_case_     (   self    )  -> List[str]:





           '''simple docstring'''
           A_		   = super().get_config()
           config.update({"""weight_decay_rate""": self.weight_decay_rate}    )
           return config







    def    snake_case_     (   self						,			UpperCamelCase__    )  -> Any:





           '''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    A__ ( _snake_case     ):



    def __init__(   self    )  -> int:





           '''simple docstring'''
           A_		   = []
           A_		   = None



    @property
    def    snake_case_     (   self    )  -> Optional[Any]:





           '''simple docstring'''
           if self._accum_steps is None:
                  A_		   = 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    snake_case_     (   self    )  -> Any:





           '''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						,			UpperCamelCase__    )  -> Dict:





           '''simple docstring'''
           if not self._gradients:
                  A_		   = 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    snake_case_     (   self    )  -> List[str]:





           '''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'''







def  UpperCAmelCase__      ( UpperCAmelCase__ = 1_00			)     ->     int:
       A_		   = n * (n + 1) * (2 * n + 1) / 6
       A_		   = (n * (n + 1) / 2) ** 2
       return int(square_of_sum - sum_of_squares			)


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