




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  ):



 '''simple docstring'''


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

       """simple docstring"""






       super().__init__()
       lowerCamelCase_							=       initial_learning_rate
       lowerCamelCase_							=       warmup_steps
       lowerCamelCase_							=       power
       lowerCamelCase_							=       decay_schedule_fn
       lowerCamelCase_							=       name

 def __call__(							self   :    Dict		,				A_   :    Any    )  ->      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`.
             lowerCamelCase_							=       tf.cast(A_		,				tf.floataa    )
             lowerCamelCase_							=       tf.cast(self.warmup_steps		,				tf.floataa    )
             lowerCamelCase_							=       global_step_float / warmup_steps_float
             lowerCamelCase_							=       self.initial_learning_rate * tf.math.pow(A_		,				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=A_		,				)





 def 							a__					(							self   :    Union[str, Any]    )  ->      Dict:

       """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     (				lowercase      :			float      ,				lowercase      :			int      ,				lowercase      :			int      ,				lowercase      :			float = 0.0      ,				lowercase      :			float = 0.9      ,				lowercase      :			float = 0.999      ,				lowercase      :			float = 1e-8      ,				lowercase      :			Optional[float] = None      ,				lowercase      :			Optional[float] = None      ,				lowercase      :			float = 0.0      ,				lowercase      :			float = 1.0      ,				lowercase      :			Optional[List[str]] = None      ,				):


      '''simple docstring'''



      lowerCamelCase_							=       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_							=       WarmUp(
                initial_learning_rate=lowercase      ,				decay_schedule_fn=lowercase      ,				warmup_steps=lowercase      ,				)
      if weight_decay_rate > 0.0:
            lowerCamelCase_							=       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_							=       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     A(		UpperCamelCase  ):



 '''simple docstring'''


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

       """simple docstring"""






       super().__init__(A_		,				A_		,				A_		,				A_		,				A_		,				A_		,				**A_    )
       lowerCamelCase_							=       weight_decay_rate
       lowerCamelCase_							=       include_in_weight_decay
       lowerCamelCase_							=       exclude_from_weight_decay

 @classmethod
 def 							a__					(							cls   :    Optional[Any]		,				A_   :    List[Any]    )  ->      List[str]:

       """simple docstring"""






       lowerCamelCase_							=       {'WarmUp': WarmUp}
       return super(A_		,				cls    ).from_config(A_		,				custom_objects=A_    )

 def 							a__					(							self   :    Dict		,				A_   :    List[str]		,				A_   :    Optional[int]		,				A_   :    Optional[int]    )  ->      Optional[int]:

       """simple docstring"""






       super(A_		,				self    )._prepare_local(A_		,				A_		,				A_    )
       lowerCamelCase_							=       tf.constant(
           self.weight_decay_rate		,				name='adam_weight_decay_rate'    )

 def 							a__					(							self   :    int		,				A_   :    str		,				A_   :    Any		,				A_   :    List[Any]    )  ->      Tuple:

       """simple docstring"""






       lowerCamelCase_							=       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   :    int		,				A_   :    Any		,				A_   :    Optional[int]=None		,				**A_   :    Any    )  ->      Optional[Any]:

       """simple docstring"""






       lowerCamelCase_	,							lowerCamelCase_							=       list(zip(*A_    )    )
       return super(A_		,				self    ).apply_gradients(zip(A_		,				A_    )		,				name=A_		,				**A_    )

 def 							a__					(							self   :    Any		,				A_   :    Tuple		,				A_   :    List[str]		,				A_   :    List[str]    )  ->      str:

       """simple docstring"""






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

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

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

 def 							a__					(							self   :    Dict		,				A_   :    str		,				A_   :    Dict		,				A_   :    str=None    )  ->      Dict:

       """simple docstring"""






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

 def 							a__					(							self   :    Tuple		,				A_   :    List[Any]		,				A_   :    Union[str, Any]		,				A_   :    List[str]		,				A_   :    Tuple=None    )  ->      Union[str, Any]:

       """simple docstring"""






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

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

       """simple docstring"""






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





 def 							a__					(							self   :    Any		,				A_   :    Union[str, Any]    )  ->      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(A_		,				A_    ) is not None:
                         return True

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







class     A(		UpperCamelCase  ):



 '''simple docstring'''


 def __init__(							self   :    Any    )  ->      Tuple:

       """simple docstring"""






       lowerCamelCase_							=       []
       lowerCamelCase_							=       None

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

       """simple docstring"""






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

       return self._accum_steps.value()

 @property
 def 							a__					(							self   :    List[Any]    )  ->      Union[str, 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   :    List[Any]		,				A_   :    int    )  ->      int:

       """simple docstring"""






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

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

       self._accum_steps.assign_add(1    )





 def 							a__					(							self   :    List[Any]    )  ->      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(A_    )    )








'''simple docstring'''





def 							lowerCamelCase	(					):





    '''simple docstring'''


    return [list(range(1_000 - i  ,-1_000 - i  ,-1							)							) for i in range(1_000							)]


SCREAMING_SNAKE_CASE__          =  generate_large_matrix()
SCREAMING_SNAKE_CASE__          =  (
    [[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3]],
    [[3, 2], [1, 0]],
    [[7, 7, 6]],
    [[7, 7, 6], [-1, -2, -3]],
    grid,
)




def 							lowerCamelCase	(					_snake_case	:    list[list[int]]							):





    '''simple docstring'''


    assert all(row == sorted(_snake_case  ,reverse=_snake_case							) for row in grid							)
    assert all(list(_snake_case							) == sorted(_snake_case  ,reverse=_snake_case							) for col in zip(*_snake_case							)							)




def 							lowerCamelCase	(					_snake_case	:    list[int]							):





    '''simple docstring'''


    lowercase__									=    0
    lowercase__									=    len(_snake_case							) - 1

    # Edge cases such as no values or all numbers are negative.
    if not array or array[0] < 0:
        return 0

    while right + 1 > left:
        lowercase__									=    (left + right) // 2
        lowercase__									=    array[mid]

        # Num must be negative and the index must be greater than or equal to 0.
        if num < 0 and array[mid - 1] >= 0:
            return mid

        if num >= 0:
            lowercase__									=    mid + 1
        else:
            lowercase__									=    mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
    return len(_snake_case							)




def 							lowerCamelCase	(					_snake_case	:    list[list[int]]							):





    '''simple docstring'''


    lowercase__									=    0
    lowercase__									=    len(grid[0]							)

    for i in range(len(_snake_case							)							):
        lowercase__									=    find_negative_index(grid[i][:bound]							)
        total += bound
    return (len(_snake_case							) * len(grid[0]							)) - total




def 							lowerCamelCase	(					_snake_case	:    list[list[int]]							):





    '''simple docstring'''


    return len([number for row in grid for number in row if number < 0]							)




def 							lowerCamelCase	(					_snake_case	:    list[list[int]]							):





    '''simple docstring'''


    lowercase__									=    0
    for row in grid:
        for i, number in enumerate(_snake_case							):
            if number < 0:
                total += len(_snake_case							) - i
                break
    return total




def 							lowerCamelCase	(					):





    '''simple docstring'''


    from timeit import timeit

    print("Running benchmarks"							)
    lowercase__									=    (
        "from __main__ import count_negatives_binary_search, "
        "count_negatives_brute_force, count_negatives_brute_force_with_break, grid"
    )
    for func in (
        "count_negatives_binary_search",  # took 0.7727 seconds
        "count_negatives_brute_force_with_break",  # took 4.6505 seconds
        "count_negatives_brute_force",  # took 12.8160 seconds
    ):
        lowercase__									=    timeit(f'''{func}(grid=grid)'''  ,setup=_snake_case  ,number=500							)
        print(f'''{func}() took {time:0.4f} seconds'''							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 benchmark()




