



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						(       _A			:				List[str]    )->       Optional[Any]:





						"""simple docstring"""





						if is_torch_version("<"			,							"2.0.0"    ) or not hasattr(_A			,							"_dynamo"    ):
												return False
						return isinstance(_A			,							torch._dynamo.eval_frame.OptimizedModule    )
def  UpperCamelCase						(       _A			:				str			,							_A			:				bool = True    )->       Optional[Any]:





						"""simple docstring"""





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

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

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

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

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

						if is_compiled:
												A__							=       model
												A__							=       compiled_model

						return model
def  UpperCamelCase						(       )->       List[str]:





						"""simple docstring"""





						PartialState().wait_for_everyone()
def  UpperCamelCase						(       _A			:				Optional[int]			,							_A			:				Union[str, Any]    )->       Union[str, Any]:





						"""simple docstring"""





						if PartialState().distributed_type == DistributedType.TPU:
												xm.save(_A			,							_A    )
						elif PartialState().local_process_index == 0:
												torch.save(_A			,							_A    )
@contextmanager
def  UpperCamelCase						(       **_A			:				Union[str, Any]    )->       Union[str, Any]:





						"""simple docstring"""





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

						yield

						for key in kwargs:
												if key.upper() in os.environ:
																		del os.environ[key.upper()]
def  UpperCamelCase						(       _A			:				Tuple    )->       List[Any]:





						"""simple docstring"""





						if not hasattr(_A			,							"__qualname__"    ) and not hasattr(_A			,							"__name__"    ):
												A__							=       getattr(_A			,							"__class__"			,							_A    )
						if hasattr(_A			,							"__qualname__"    ):
												return obj.__qualname__
						if hasattr(_A			,							"__name__"    ):
												return obj.__name__
						return str(_A    )
def  UpperCamelCase						(       _A			:				Any			,							_A			:				Union[str, Any]    )->       Tuple:





						"""simple docstring"""





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

						return destination
def  UpperCamelCase						(       _A			:				int = None    )->       bool:





						"""simple docstring"""





						if port is None:
												A__							=       29500
						with socket.socket(socket.AF_INET			,							socket.SOCK_STREAM    ) as s:
												return s.connect_ex(("localhost", port)    ) == 0










import math
from collections.abc import Iterator
from itertools import takewhile
def  UpperCamelCase						(       _A			:				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(_A    ) + 1    )			,							6    ):
												if number % i == 0 or number % (i + 2) == 0:
																		return False
						return True
def  UpperCamelCase						(       )->       Iterator[int]:





						"""simple docstring"""





						A__							=       2
						while True:
												if is_prime(_A    ):
																		yield num
												num += 1
def  UpperCamelCase						(       _A			:				int = 2000000    )->       int:





						"""simple docstring"""





						return sum(takewhile(lambda _A    : x < n			,							prime_generator()    )    )


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





