




import os
import sys
import tempfile

import torch

from .state import AcceleratorState
from .utils import PrecisionType, PrepareForLaunch, is_mps_available, patch_environment

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE=() ,_SCREAMING_SNAKE_CASE=None ,_SCREAMING_SNAKE_CASE="no" ,_SCREAMING_SNAKE_CASE="29500"    )	-> Optional[int]:
       lowerCamelCase   :      Optional[Any]			 =					False
       lowerCamelCase   :      int			 =					False
       if any(key.startswith("KAGGLE"    ) for key in os.environ.keys()    ):
              lowerCamelCase   :      Dict			 =					True
       elif "IPython" in sys.modules:
              lowerCamelCase   :      Dict			 =					"google.colab" in str(sys.modules["IPython"].get_ipython()    )

       try:
              lowerCamelCase   :      Tuple			 =					PrecisionType(mixed_precision.lower()    )
       except ValueError:
              raise ValueError(
                  f'''Unknown mixed_precision mode: {args.mixed_precision.lower()}. Choose between {PrecisionType.list()}.'''    )

       if (in_colab or in_kaggle) and (os.environ.get("TPU_NAME" ,_SCREAMING_SNAKE_CASE    ) is not None):
              # TPU launch
              import torch_xla.distributed.xla_multiprocessing as xmp

              if len(AcceleratorState._shared_state    ) > 0:
                     raise ValueError(
                         "To train on TPU in Colab or Kaggle Kernel, the `Accelerator` should only be initialized inside "
                         "your training function. Restart your notebook and make sure no cells initializes an "
                         "`Accelerator`."    )
              if num_processes is None:
                     lowerCamelCase   :      Any			 =					8

              lowerCamelCase   :      Tuple			 =					PrepareForLaunch(_SCREAMING_SNAKE_CASE ,distributed_type="TPU"    )
              print(f'''Launching a training on {num_processes} TPU cores.'''    )
              xmp.spawn(_SCREAMING_SNAKE_CASE ,args=_SCREAMING_SNAKE_CASE ,nprocs=_SCREAMING_SNAKE_CASE ,start_method="fork"    )
       elif in_colab:
              # No need for a distributed launch otherwise as it's either CPU or one GPU.
              if torch.cuda.is_available():
                     print("Launching training on one GPU."    )
              else:
                     print("Launching training on one CPU."    )
              function(*_SCREAMING_SNAKE_CASE    )
       else:
              if num_processes is None:
                     raise ValueError(
                         "You have to specify the number of GPUs you would like to use, add `num_processes=...` to your call."    )

              if num_processes > 1:
                     # Multi-GPU launch
                     from torch.multiprocessing import start_processes
                     from torch.multiprocessing.spawn import ProcessRaisedException

                     if len(AcceleratorState._shared_state    ) > 0:
                            raise ValueError(
                                "To launch a multi-GPU training from your notebook, the `Accelerator` should only be initialized "
                                "inside your training function. Restart your notebook and make sure no cells initializes an "
                                "`Accelerator`."    )

                     if torch.cuda.is_initialized():
                            raise ValueError(
                                "To launch a multi-GPU training from your notebook, you need to avoid running any instruction "
                                "using `torch.cuda` in any cell. Restart your notebook and make sure no cells use any CUDA "
                                "function."    )

                     # torch.distributed will expect a few environment variable to be here. We set the ones common to each
                     # process here (the other ones will be set be the launcher).
                     with patch_environment(
                         world_size=_SCREAMING_SNAKE_CASE ,master_addr="127.0.01" ,master_port=_SCREAMING_SNAKE_CASE ,mixed_precision=_SCREAMING_SNAKE_CASE    ):
                            lowerCamelCase   :      List[str]			 =					PrepareForLaunch(_SCREAMING_SNAKE_CASE ,distributed_type="MULTI_GPU"    )
                            print(f'''Launching training on {num_processes} GPUs.'''    )
                            try:
                                   start_processes(_SCREAMING_SNAKE_CASE ,args=_SCREAMING_SNAKE_CASE ,nprocs=_SCREAMING_SNAKE_CASE ,start_method="fork"    )
                            except ProcessRaisedException as e:
                                   if "Cannot re-initialize CUDA in forked subprocess" in e.args[0]:
                                          raise RuntimeError(
                                              "CUDA has been initialized before the `notebook_launcher` could create a forked subprocess. "
                                              "This likely stems from an outside import causing issues once the `notebook_launcher()` is called. "
                                              "Please review your imports and test them when running the `notebook_launcher()` to identify "
                                              "which one is problematic."    ) from e

              else:
                     # No need for a distributed launch otherwise as it's either CPU, GPU or MPS.
                     if is_mps_available():
                            lowerCamelCase   :      List[str]			 =					"1"
                            print("Launching training on MPS."    )
                     elif torch.cuda.is_available():
                            print("Launching training on one GPU."    )
                     else:
                            print("Launching training on CPU."    )
                     function(*_SCREAMING_SNAKE_CASE    )


def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE=() ,_SCREAMING_SNAKE_CASE=2    )	-> List[Any]:
       from torch.multiprocessing import start_processes

       with tempfile.NamedTemporaryFile() as tmp_file:
              # torch.distributed will expect a few environment variable to be here. We set the ones common to each
              # process here (the other ones will be set be the launcher).
              with patch_environment(
                  world_size=_SCREAMING_SNAKE_CASE ,master_addr="127.0.01" ,master_port="29500" ,accelerate_mixed_precision="no" ,accelerate_debug_rdv_file=tmp_file.name ,accelerate_use_cpu="yes" ,):
                     lowerCamelCase   :      List[Any]			 =					PrepareForLaunch(_SCREAMING_SNAKE_CASE ,debug=_SCREAMING_SNAKE_CASE    )
                     start_processes(_SCREAMING_SNAKE_CASE ,args=_SCREAMING_SNAKE_CASE ,nprocs=_SCREAMING_SNAKE_CASE ,start_method="fork"    )








import itertools
import math




def 				a						(							snake_case__:					int					):


				'''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 				a						(							):


				'''simple docstring'''
				lowercase_       =					2
				while True:
								if is_prime(snake_case__					):
												yield num
								num += 1




def 				a						(							snake_case__:					int = 10_001					):


				'''simple docstring'''
				return next(itertools.islice(prime_generator()						,   nth - 1						,   snake_case__					)					)


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




