
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 					_lowerCamelCase			(   tf.keras.optimizers.schedules.LearningRateSchedule			):





     """simple docstring"""







     def __init__(				self    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE = 1.0    ,    __SCREAMING_SNAKE_CASE = None    ,    )	-> Tuple:




           """simple docstring"""







           super().__init__()
           UpperCamelCase__     : Any											=					initial_learning_rate
           UpperCamelCase__     : Optional[int]											=					warmup_steps
           UpperCamelCase__     : Optional[Any]											=					power
           UpperCamelCase__     : Dict											=					decay_schedule_fn
           UpperCamelCase__     : Dict											=					name






     def __call__(				self    ,    __SCREAMING_SNAKE_CASE	)	-> Union[str, Any]:




           """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__     : int											=					tf.cast(__SCREAMING_SNAKE_CASE    ,    tf.floataa	)
                 UpperCamelCase__     : Dict											=					tf.cast(self.warmup_steps    ,    tf.floataa	)
                 UpperCamelCase__     : Optional[Any]											=					global_step_float / warmup_steps_float
                 UpperCamelCase__     : Any											=					self.initial_learning_rate * tf.math.pow(__SCREAMING_SNAKE_CASE    ,    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=__SCREAMING_SNAKE_CASE    ,    )






     def  __SCREAMING_SNAKE_CASE      (				self	)	-> Optional[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 				SCREAMING_SNAKE_CASE_   (      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			,		):
      UpperCamelCase__     : Tuple											=					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__     : List[str]											=					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 					_lowerCamelCase			(   UpperCamelCase_			):





     """simple docstring"""







     def __init__(				self    ,    __SCREAMING_SNAKE_CASE = 0.001    ,    __SCREAMING_SNAKE_CASE = 0.9    ,    __SCREAMING_SNAKE_CASE = 0.999    ,    __SCREAMING_SNAKE_CASE = 1e-7    ,    __SCREAMING_SNAKE_CASE = False    ,    __SCREAMING_SNAKE_CASE = 0.0    ,    __SCREAMING_SNAKE_CASE = None    ,    __SCREAMING_SNAKE_CASE = None    ,    __SCREAMING_SNAKE_CASE = "AdamWeightDecay"    ,    **__SCREAMING_SNAKE_CASE    ,    )	-> Tuple:




           """simple docstring"""







           super().__init__(__SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    **__SCREAMING_SNAKE_CASE	)
           UpperCamelCase__     : List[Any]											=					weight_decay_rate
           UpperCamelCase__     : Tuple											=					include_in_weight_decay
           UpperCamelCase__     : str											=					exclude_from_weight_decay






     @classmethod
     def  __SCREAMING_SNAKE_CASE      (				cls    ,    __SCREAMING_SNAKE_CASE	)	-> Dict:




           """simple docstring"""







           UpperCamelCase__     : Any											=					{'''WarmUp''': WarmUp}
           return super(__SCREAMING_SNAKE_CASE    ,    cls	).from_config(__SCREAMING_SNAKE_CASE    ,    custom_objects=__SCREAMING_SNAKE_CASE	)






     def  __SCREAMING_SNAKE_CASE      (				self    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE	)	-> Dict:




           """simple docstring"""







           super(__SCREAMING_SNAKE_CASE    ,    self	)._prepare_local(__SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE	)
           UpperCamelCase__     : Union[str, Any]											=					tf.constant(
               self.weight_decay_rate    ,    name='''adam_weight_decay_rate'''	)






     def  __SCREAMING_SNAKE_CASE      (				self    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE	)	-> List[str]:




           """simple docstring"""







           UpperCamelCase__     : Union[str, Any]											=					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  __SCREAMING_SNAKE_CASE      (				self    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE=None    ,    **__SCREAMING_SNAKE_CASE	)	-> Optional[Any]:




           """simple docstring"""







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






     def  __SCREAMING_SNAKE_CASE      (				self    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE	)	-> Tuple:




           """simple docstring"""







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

           UpperCamelCase__     : int											=					apply_state or {}
           UpperCamelCase__     : Any											=					apply_state.get((var_device, var_dtype)	)
           if coefficients is None:
                 UpperCamelCase__     : List[str]											=					self._fallback_apply_state(__SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE	)
                 UpperCamelCase__     : Optional[Any]											=					coefficients

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






     def  __SCREAMING_SNAKE_CASE      (				self    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE=None	)	-> Any:




           """simple docstring"""







           UpperCamelCase__					,UpperCamelCase__     : Dict											=					self._get_lr(var.device    ,    var.dtype.base_dtype    ,    __SCREAMING_SNAKE_CASE	)
           UpperCamelCase__     : Tuple											=					self._decay_weights_op(__SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE	)
           with tf.control_dependencies([decay]	):
                 return super(__SCREAMING_SNAKE_CASE    ,    self	)._resource_apply_dense(__SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    **__SCREAMING_SNAKE_CASE	)






     def  __SCREAMING_SNAKE_CASE      (				self    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE=None	)	-> Optional[int]:




           """simple docstring"""







           UpperCamelCase__					,UpperCamelCase__     : Any											=					self._get_lr(var.device    ,    var.dtype.base_dtype    ,    __SCREAMING_SNAKE_CASE	)
           UpperCamelCase__     : Optional[int]											=					self._decay_weights_op(__SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE	)
           with tf.control_dependencies([decay]	):
                 return super(__SCREAMING_SNAKE_CASE    ,    self	)._resource_apply_sparse(__SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE    ,    **__SCREAMING_SNAKE_CASE	)






     def  __SCREAMING_SNAKE_CASE      (				self	)	-> Any:




           """simple docstring"""







           UpperCamelCase__     : int											=					super().get_config()
           config.update({'''weight_decay_rate''': self.weight_decay_rate}	)
           return config






     def  __SCREAMING_SNAKE_CASE      (				self    ,    __SCREAMING_SNAKE_CASE	)	-> Union[str, 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(__SCREAMING_SNAKE_CASE    ,    __SCREAMING_SNAKE_CASE	) is not None:
                             return True

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




class 					_lowerCamelCase			(   UpperCamelCase_			):





     """simple docstring"""







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




           """simple docstring"""







           UpperCamelCase__     : Dict											=					[]
           UpperCamelCase__     : List[Any]											=					None






     @property
     def  __SCREAMING_SNAKE_CASE      (				self	)	-> List[Any]:




           """simple docstring"""







           if self._accum_steps is None:
                 UpperCamelCase__     : Optional[Any]											=					tf.Variable(
                     tf.constant(0    ,    dtype=tf.intaa	)    ,    trainable=__SCREAMING_SNAKE_CASE    ,    synchronization=tf.VariableSynchronization.ON_READ    ,    aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA    ,    )

           return self._accum_steps.value()






     @property
     def  __SCREAMING_SNAKE_CASE      (				self	)	-> List[str]:




           """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    ,    __SCREAMING_SNAKE_CASE	)	-> List[str]:




           """simple docstring"""







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

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

           self._accum_steps.assign_add(1	)






     def  __SCREAMING_SNAKE_CASE      (				self	)	-> Tuple:




           """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(__SCREAMING_SNAKE_CASE	)	)




def 				SCREAMING_SNAKE_CASE_   (      UpperCamelCase__ = 2_0_0_0_0_0_0		):
      UpperCamelCase__     : Dict											=					[0 for i in range(n + 1		)]
      UpperCamelCase__     : Any											=					1
      UpperCamelCase__     : int											=					1

      for i in range(2			,		int(n**0.5		) + 1		):
            if primality_list[i] == 0:
                  for j in range(i * i			,		n + 1			,		UpperCamelCase__		):
                        UpperCamelCase__     : Any											=					1
      UpperCamelCase__     : Optional[Any]											=					0
      for i in range(UpperCamelCase__		):
            if primality_list[i] == 0:
                  sum_of_primes += i
      return sum_of_primes


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


