





from functools import lru_cache

def    __snake_case  (    _lowerCAmelCase       :       Union[str, Any]		)       ->  str:
   A_    : Any								=	2
   A_    : Dict								=	set()
   while i * i <= n:
      if n % i:
         i += 1
      else:
         n //= i
         factors.add(UpperCamelCase__		)
   if n > 1:
      factors.add(UpperCamelCase__		)
   return factors

@lru_cache
def    __snake_case  (    _lowerCAmelCase       :       Union[str, Any]		)       ->  List[Any]:
   return len(unique_prime_factors(UpperCamelCase__		)		)

def    __snake_case  (    _lowerCAmelCase       :       int		)       ->  str:
   return len(set(UpperCamelCase__		)		) in (0, 1)

def    __snake_case  (    _lowerCAmelCase       :       Any		)       ->  Optional[Any]:
   A_    : Optional[int]								=	2

   while True:
      # Increment each value of a generated range
      A_    : Dict								=	[base + i for i in range(UpperCamelCase__		)]

      # Run elements through out unique_prime_factors function
      # Append our target number to the end.
      A_    : List[str]								=	[upf_len(UpperCamelCase__		) for x in group]
      checker.append(UpperCamelCase__		)

      # If all numbers in the list are equal, return the group variable.
      if equality(UpperCamelCase__		):
         return group

      # Increment our base variable by 1
      base += 1

def    __snake_case  (    _lowerCAmelCase       :       List[str] = 4		)       ->  List[str]:
   A_    : int								=	run(UpperCamelCase__		)
   return results[0] if len(UpperCamelCase__		) else None


if __name__ == "__main__":
 print(solution())

"""simple docstring"""




import os
import socket
from contextlib import contextmanager

import torch

from ..commands.config.default import write_basic_config  # noqa: F401
from ..state import PartialState
from .dataclasses import DistributedType
from .imports import is_deepspeed_available, is_tpu_available
from .transformer_engine import convert_model
from .versions import is_torch_version


if is_deepspeed_available():
				from deepspeed import DeepSpeedEngine

if is_tpu_available(check_device=False):
				import torch_xla.core.xla_model as xm






def      UpperCAmelCase    (		UpperCamelCase__ ):






							"""simple docstring"""





							if is_torch_version('<'				,			'2.0.0' ) or not hasattr(UpperCamelCase__				,			'_dynamo' ):
														return False
							return isinstance(UpperCamelCase__				,			torch._dynamo.eval_frame.OptimizedModule )






def      UpperCAmelCase    (		UpperCamelCase__				,			UpperCamelCase__ = True ):






							"""simple docstring"""





							A__		   =							(torch.nn.parallel.DistributedDataParallel, torch.nn.DataParallel)

							A__		   =							is_compiled_module(UpperCamelCase__ )
							if is_compiled:
														A__		   =							model
														A__		   =							model._orig_mod

							if is_deepspeed_available():
														options += (DeepSpeedEngine,)

							while isinstance(UpperCamelCase__				,			UpperCamelCase__ ):
														A__		   =							model.module

							if not keep_fpaa_wrapper:
														A__		   =							getattr(UpperCamelCase__				,			'forward' )
														A__		   =							model.__dict__.pop('_original_forward'				,			UpperCamelCase__ )
														if original_forward is not None:
																					while hasattr(UpperCamelCase__				,			'__wrapped__' ):
																												A__		   =							forward.__wrapped__
																												if forward == original_forward:
																																			break
																					A__		   =							forward
														if getattr(UpperCamelCase__				,			'_converted_to_transformer_engine'				,			UpperCamelCase__ ):
																					convert_model(UpperCamelCase__				,			to_transformer_engine=UpperCamelCase__ )

							if is_compiled:
														A__		   =							model
														A__		   =							compiled_model

							return model






def      UpperCAmelCase    (		):






							"""simple docstring"""





							PartialState().wait_for_everyone()






def      UpperCAmelCase    (		UpperCamelCase__				,			UpperCamelCase__ ):






							"""simple docstring"""





							if PartialState().distributed_type == DistributedType.TPU:
														xm.save(UpperCamelCase__				,			UpperCamelCase__ )
							elif PartialState().local_process_index == 0:
														torch.save(UpperCamelCase__				,			UpperCamelCase__ )






@contextmanager
def      UpperCAmelCase    (		**UpperCamelCase__ ):






							"""simple docstring"""





							for key, value in kwargs.items():
														A__		   =							str(UpperCamelCase__ )

							yield

							for key in kwargs:
														if key.upper() in os.environ:
																					del os.environ[key.upper()]






def      UpperCAmelCase    (		UpperCamelCase__ ):






							"""simple docstring"""





							if not hasattr(UpperCamelCase__				,			'__qualname__' ) and not hasattr(UpperCamelCase__				,			'__name__' ):
														A__		   =							getattr(UpperCamelCase__				,			'__class__'				,			UpperCamelCase__ )
							if hasattr(UpperCamelCase__				,			'__qualname__' ):
														return obj.__qualname__
							if hasattr(UpperCamelCase__				,			'__name__' ):
														return obj.__name__
							return str(UpperCamelCase__ )






def      UpperCAmelCase    (		UpperCamelCase__				,			UpperCamelCase__ ):






							"""simple docstring"""





							for key, value in source.items():
														if isinstance(UpperCamelCase__				,			UpperCamelCase__ ):
																					A__		   =							destination.setdefault(UpperCamelCase__				,			{} )
																					merge_dicts(UpperCamelCase__				,			UpperCamelCase__ )
														else:
																					A__		   =							value

							return destination






def      UpperCAmelCase    (		UpperCamelCase__ = None ):






							"""simple docstring"""





							if port is None:
														A__		   =							29_500
							with socket.socket(socket.AF_INET				,			socket.SOCK_STREAM ) as s:
														return s.connect_ex(('localhost', port) ) == 0





