'''simple docstring'''





import itertools
import math





def 	lowerCAmelCase_				(					snake_case_       : int			)    ->      bool:


     '''simple docstring'''




     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(snake_case_			) + 1			)					,    6			):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True





def 	lowerCAmelCase_				(					)    ->      Optional[int]:


     '''simple docstring'''




     UpperCAmelCase_           =   2
     while True:
          if is_prime(snake_case_			):
               yield num
          num += 1





def 	lowerCAmelCase_				(					snake_case_       : int = 1_00_01			)    ->      int:


     '''simple docstring'''




     return next(itertools.islice(prime_generator()					,    nth - 1					,    snake_case_			)			)


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





from typing import TYPE_CHECKING

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


UpperCamelCase  							=						{
    '''configuration_groupvit''': [
        '''GROUPVIT_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''GroupViTConfig''',
        '''GroupViTOnnxConfig''',
        '''GroupViTTextConfig''',
        '''GroupViTVisionConfig''',
    ],
}

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      UpperCamelCase  							=						[
          '''GROUPVIT_PRETRAINED_MODEL_ARCHIVE_LIST''',
          '''GroupViTModel''',
          '''GroupViTPreTrainedModel''',
          '''GroupViTTextModel''',
          '''GroupViTVisionModel''',
      ]

try:
      if not is_tf_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      UpperCamelCase  							=						[
          '''TF_GROUPVIT_PRETRAINED_MODEL_ARCHIVE_LIST''',
          '''TFGroupViTModel''',
          '''TFGroupViTPreTrainedModel''',
          '''TFGroupViTTextModel''',
          '''TFGroupViTVisionModel''',
      ]

if TYPE_CHECKING:
      from .configuration_groupvit import (
          GROUPVIT_PRETRAINED_CONFIG_ARCHIVE_MAP,
          GroupViTConfig,
          GroupViTOnnxConfig,
          GroupViTTextConfig,
          GroupViTVisionConfig,
      )

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_groupvit import (
                GROUPVIT_PRETRAINED_MODEL_ARCHIVE_LIST,
                GroupViTModel,
                GroupViTPreTrainedModel,
                GroupViTTextModel,
                GroupViTVisionModel,
            )

      try:
            if not is_tf_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_tf_groupvit import (
                TF_GROUPVIT_PRETRAINED_MODEL_ARCHIVE_LIST,
                TFGroupViTModel,
                TFGroupViTPreTrainedModel,
                TFGroupViTTextModel,
                TFGroupViTVisionModel,
            )

else:
      import sys

      UpperCamelCase  							=						_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)



