





import math

import tensorflow as tf
from packaging import version


def _A       (   __magic_name__	):
   lowercase__			       =  tf.convert_to_tensor(__lowerCAmelCase	)
   lowercase__			       =  0.5 * (1.0 + tf.math.erf(x / tf.cast(tf.sqrt(2.0	)  , x.dtype	)	))

   return x * cdf


def _A       (   __magic_name__	):
   lowercase__			       =  tf.convert_to_tensor(__lowerCAmelCase	)
   lowercase__			       =  tf.cast(math.pi  , x.dtype	)
   lowercase__			       =  tf.cast(0.044_715  , x.dtype	)
   lowercase__			       =  0.5 * (1.0 + tf.tanh(tf.sqrt(2.0 / pi	) * (x + coeff * tf.pow(__lowerCAmelCase  , 3	))	))

   return x * cdf


def _A       (   __magic_name__	):
   lowercase__			       =  tf.convert_to_tensor(__lowerCAmelCase	)

   return x * tf.tanh(tf.math.softplus(__lowerCAmelCase	)	)


def _A       (   __magic_name__	):
   lowercase__			       =  tf.convert_to_tensor(__lowerCAmelCase	)
   lowercase__			       =  tf.cast(0.044_715  , x.dtype	)
   lowercase__			       =  tf.cast(0.7_978_845_608  , x.dtype	)

   return 0.5 * x * (1.0 + tf.tanh(x * coeffa * (1.0 + coeffa * x * x)	))


def _A       (   __magic_name__	):
   lowercase__			       =  tf.convert_to_tensor(__lowerCAmelCase	)
   lowercase__			       =  tf.cast(1.702  , x.dtype	)
   return x * tf.math.sigmoid(coeff * x	)


def _A       (   __magic_name__	):
   return tf.clip_by_value(_gelu(__lowerCAmelCase	)  , -10  , 10	)


def _A       (   __magic_name__  , __magic_name__=-1	):
   lowercase__			       =  tf.split(__lowerCAmelCase  , 2  , axis=__lowerCAmelCase	)
   return a * tf.math.sigmoid(__lowerCAmelCase	)


if version.parse(tf.version.VERSION) >= version.parse("""2.4"""):


  def _A       (   __magic_name__	):
     return tf.keras.activations.gelu(__lowerCAmelCase  , approximate=__lowerCAmelCase	)

  _snake_case           =			tf.keras.activations.gelu







  _snake_case           =			approximate_gelu_wrap
else:
  _snake_case           =			_gelu
  _snake_case           =			_gelu_new


_snake_case           =			{
    """gelu""": gelu,
    """gelu_10""": gelu_aa,
    """gelu_fast""": gelu_fast,
    """gelu_new""": gelu_new,
    """glu""": glu,
    """mish""": mish,
    """quick_gelu""": quick_gelu,
    """relu""": tf.keras.activations.relu,
    """sigmoid""": tf.keras.activations.sigmoid,
    """silu""": tf.keras.activations.swish,
    """swish""": tf.keras.activations.swish,
    """tanh""": tf.keras.activations.tanh,
}







def _A       (   __magic_name__	):

   if activation_string in ACTaFN:
      return ACTaFN[activation_string]
   else:
      raise KeyError(f'''function {activation_string} not found in ACT2FN mapping {list(ACTaFN.keys()	)}'''	)











import math


def _A       (   __magic_name__	):
   lowercase__			       =  math.loga(math.sqrt(4 * positive_integer + 1	) / 2 + 1 / 2	)

   return exponent == int(__magic_name__	)


def _A       (   __magic_name__ = 1 / 1_2345	):
   lowercase__			       =  0
   lowercase__			       =  0

   lowercase__			       =  3
   while True:
      lowercase__			       =  (integer**2 - 1) / 4
      # if candidate is an integer, then there is a partition for k
      if partition_candidate == int(__magic_name__	):
         lowercase__			       =  int(__magic_name__	)
         total_partitions += 1
         if check_partition_perfect(__magic_name__	):
            perfect_partitions += 1
      if perfect_partitions > 0:
         if perfect_partitions / total_partitions < max_proportion:
            return int(__magic_name__	)
      integer += 1


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






