
import math

import tensorflow as tf
from packaging import version
def 					lowerCamelCase__		(				_lowerCamelCase  )						->int:
 _UpperCAmelCase 				=tf.convert_to_tensor(UpperCamelCase__  )
 _UpperCAmelCase 				=0.5 * (1.0 + tf.math.erf(x / tf.cast(tf.sqrt(2.0  )			,		x.dtype  )  ))

 return x * cdf
def 					lowerCamelCase__		(				_lowerCamelCase  )						->Tuple:
 _UpperCAmelCase 				=tf.convert_to_tensor(UpperCamelCase__  )
 _UpperCAmelCase 				=tf.cast(math.pi			,		x.dtype  )
 _UpperCAmelCase 				=tf.cast(0.044_715			,		x.dtype  )
 _UpperCAmelCase 				=0.5 * (1.0 + tf.tanh(tf.sqrt(2.0 / pi  ) * (x + coeff * tf.pow(UpperCamelCase__			,		3  ))  ))

 return x * cdf
def 					lowerCamelCase__		(				_lowerCamelCase  )						->Any:
 _UpperCAmelCase 				=tf.convert_to_tensor(UpperCamelCase__  )

 return x * tf.tanh(tf.math.softplus(UpperCamelCase__  )  )
def 					lowerCamelCase__		(				_lowerCamelCase  )						->Union[str, Any]:
 _UpperCAmelCase 				=tf.convert_to_tensor(UpperCamelCase__  )
 _UpperCAmelCase 				=tf.cast(0.044_715			,		x.dtype  )
 _UpperCAmelCase 				=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 					lowerCamelCase__		(				_lowerCamelCase  )						->List[str]:
 _UpperCAmelCase 				=tf.convert_to_tensor(UpperCamelCase__  )
 _UpperCAmelCase 				=tf.cast(1.702			,		x.dtype  )
 return x * tf.math.sigmoid(coeff * x  )
def 					lowerCamelCase__		(				_lowerCamelCase  )						->Dict:
 return tf.clip_by_value(_gelu(UpperCamelCase__  )			,		-10			,		10  )
def 					lowerCamelCase__		(				_lowerCamelCase			,		_lowerCamelCase=-1  )						->str:
 _UpperCAmelCase				,      _UpperCAmelCase 				=tf.split(UpperCamelCase__			,		2			,		axis=UpperCamelCase__  )
 return a * tf.math.sigmoid(UpperCamelCase__  )


if version.parse(tf.version.VERSION) >= version.parse('2.4'):
       def 					lowerCamelCase__		(				_lowerCamelCase  )						->List[str]:
        return tf.keras.activations.gelu(UpperCamelCase__			,		approximate=UpperCamelCase__  )

       snake_case__      :		List[str]				=       tf.keras.activations.gelu



       snake_case__      :		List[str]				=       approximate_gelu_wrap
else:
       snake_case__      :		Tuple				=       _gelu
       snake_case__      :		Optional[int]				=       _gelu_new


snake_case__      :		Union[str, Any]				=       {
    '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 					lowerCamelCase__		(				_lowerCamelCase  )						->Any:
 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 itertools
import math


def       UpperCamelCase__(			UpperCamelCase__     :			int    )->bool:

       if 1 < number < 4:
              # 2 and 3 are primes
              return True
       elif number < 2 or number % 2 == 0 or number % 3 == 0:
              # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
              return False

       # All primes number are in format of 6k +/- 1
       for i in range(5					,	int(math.sqrt(UpperCamelCase__    ) + 1    )					,	6    ):
              if number % i == 0 or number % (i + 2) == 0:
                     return False
       return True


def       UpperCamelCase__(			)->Tuple:
       A__		   =		2
       while True:
              if is_prime(UpperCamelCase__    ):
                     yield num
              num += 1


def       UpperCamelCase__(			UpperCamelCase__     :			int = 1_00_01    )->int:
       return next(itertools.islice(prime_generator()					,	nth - 1					,	UpperCamelCase__    )    )


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





