


'''simple docstring'''

import math



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					Dict )		->       List[Any]:





   '''simple docstring'''







   UpperCamelCase__			    =    0
   if n % 2 == 0:
      count += 1
      while n % 2 == 0:
         UpperCamelCase__			    =    int(n / 2 )
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

   UpperCamelCase__			    =    3

   while i <= int(math.sqrt(_UpperCamelCase ) ):
      if n % i == 0:
         count += 1
         while n % i == 0:
            UpperCamelCase__			    =    int(n / i )
      UpperCamelCase__			    =    i + 2

   # this condition checks the prime
   # number n is greater than 2

   if n > 2:
      count += 1
   return count


if __name__ == "__main__":
       __lowercase:		List[Any]    						=  51_242_183
       print(F"""The number of distinct prime factors is/are {exact_prime_factor_count(n)}""")
       print(F"""The value of log(log(n)) is {math.log(math.log(n)):.4f}""")



'''simple docstring'''

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


__lowercase:		Tuple    						=  {
    "configuration_imagegpt": ["IMAGEGPT_PRETRAINED_CONFIG_ARCHIVE_MAP", "ImageGPTConfig", "ImageGPTOnnxConfig"]
}

try:
       if not is_vision_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       __lowercase:		List[str]    						=  ["ImageGPTFeatureExtractor"]
       __lowercase:		Tuple    						=  ["ImageGPTImageProcessor"]

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       __lowercase:		str    						=  [
           "IMAGEGPT_PRETRAINED_MODEL_ARCHIVE_LIST",
           "ImageGPTForCausalImageModeling",
           "ImageGPTForImageClassification",
           "ImageGPTModel",
           "ImageGPTPreTrainedModel",
           "load_tf_weights_in_imagegpt",
       ]


if TYPE_CHECKING:
       from .configuration_imagegpt import IMAGEGPT_PRETRAINED_CONFIG_ARCHIVE_MAP, ImageGPTConfig, ImageGPTOnnxConfig

       try:
              if not is_vision_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .feature_extraction_imagegpt import ImageGPTFeatureExtractor
              from .image_processing_imagegpt import ImageGPTImageProcessor

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_imagegpt import (
                  IMAGEGPT_PRETRAINED_MODEL_ARCHIVE_LIST,
                  ImageGPTForCausalImageModeling,
                  ImageGPTForImageClassification,
                  ImageGPTModel,
                  ImageGPTPreTrainedModel,
                  load_tf_weights_in_imagegpt,
              )

else:
       import sys

       __lowercase:		List[str]    						=  _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)