



"""simple docstring"""
import os
import sys
import tempfile

import torch

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


def 	_SCREAMING_SNAKE_CASE  (__lowerCAmelCase       ,     __lowerCAmelCase=()       ,     __lowerCAmelCase=None       ,     __lowerCAmelCase="no"       ,     __lowerCAmelCase="29500"							)       ->  Any:







  '''simple docstring'''


  lowercase_	    =       False
  lowercase_	    =       False
  if any(key.startswith("""KAGGLE"""							) for key in os.environ.keys()							):
    lowercase_	    =       True
  elif "IPython" in sys.modules:
    lowercase_	    =       '''google.colab''' in str(sys.modules["""IPython"""].get_ipython()							)

  try:
    lowercase_	    =       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"""       ,     lowerCAmelCase__							) 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:
      lowercase_	    =       8

    lowercase_	    =       PrepareForLaunch(lowerCAmelCase__       ,     distributed_type="""TPU"""							)
    print(F'''Launching a training on {num_processes} TPU cores.'''							)
    xmp.spawn(lowerCAmelCase__       ,     args=lowerCAmelCase__       ,     nprocs=lowerCAmelCase__       ,     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(*lowerCAmelCase__							)
  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=lowerCAmelCase__       ,     master_addr="""127.0.01"""       ,     master_port=lowerCAmelCase__       ,     mixed_precision=lowerCAmelCase__							):
        lowercase_	    =       PrepareForLaunch(lowerCAmelCase__       ,     distributed_type="""MULTI_GPU"""							)
        print(F'''Launching training on {num_processes} GPUs.'''							)
        try:
          start_processes(lowerCAmelCase__       ,     args=lowerCAmelCase__       ,     nprocs=lowerCAmelCase__       ,     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():
        lowercase_	    =       '''1'''
        print("""Launching training on MPS."""							)
      elif torch.cuda.is_available():
        print("""Launching training on one GPU."""							)
      else:
        print("""Launching training on CPU."""							)
      function(*lowerCAmelCase__							)


def 	_SCREAMING_SNAKE_CASE  (__lowerCAmelCase       ,     __lowerCAmelCase=()       ,     __lowerCAmelCase=2							)       ->  List[Any]:







  '''simple docstring'''


  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=lowerCAmelCase__       ,     master_addr="""127.0.01"""       ,     master_port="""29500"""       ,     accelerate_mixed_precision="""no"""       ,     accelerate_debug_rdv_file=tmp_file.name       ,     accelerate_use_cpu="""yes"""       ,     ):
      lowercase_	    =       PrepareForLaunch(lowerCAmelCase__       ,     debug=lowerCAmelCase__							)
      start_processes(lowerCAmelCase__       ,     args=lowerCAmelCase__       ,     nprocs=lowerCAmelCase__       ,     start_method="""fork"""							)



from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt




def    __UpperCamelCase     (				lowerCAmelCase__							:				int  ):
 __a :  int						=  int(number**0.5  )
 return number == sq * sq




def    __UpperCamelCase     (				lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				int  ,   lowerCAmelCase__							:				int  ):
 __a :  int						=  x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
 __a :  int						=  x_den * y_den * z_den
 __a :  int						=  gcd(lowerCAmelCase__  ,   lowerCAmelCase__  )
 top //= hcf
 bottom //= hcf
 return top, bottom




def    __UpperCamelCase     (				lowerCAmelCase__							:				int = 3_5  ):
 __a :  set						=  set()
 __a :  int
 __a :  Fraction						=  Fraction(0  )
 __a :  tuple[int, int]

 for x_num in range(1  ,   order + 1  ):
  for x_den in range(x_num + 1  ,   order + 1  ):
   for y_num in range(1  ,   order + 1  ):
    for y_den in range(y_num + 1  ,   order + 1  ):
     # n=1
     __a :  Any						=  x_num * y_den + x_den * y_num
     __a :  Dict						=  x_den * y_den
     __a :  int						=  gcd(lowerCAmelCase__  ,   lowerCAmelCase__  )
     z_num //= hcf
     z_den //= hcf
     if 0 < z_num < z_den <= order:
      __a :  str						=  add_three(
          lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  )
      unique_s.add(lowerCAmelCase__  )

     # n=2
     __a :  Union[str, Any]						=  (
         x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
     )
     __a :  Optional[Any]						=  x_den * x_den * y_den * y_den
     if is_sq(lowerCAmelCase__  ) and is_sq(lowerCAmelCase__  ):
      __a :  Any						=  int(sqrt(lowerCAmelCase__  )  )
      __a :  Optional[Any]						=  int(sqrt(lowerCAmelCase__  )  )
      __a :  int						=  gcd(lowerCAmelCase__  ,   lowerCAmelCase__  )
      z_num //= hcf
      z_den //= hcf
      if 0 < z_num < z_den <= order:
       __a :  str						=  add_three(
           lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  )
       unique_s.add(lowerCAmelCase__  )

                    # n=-1
     __a :  List[str]						=  x_num * y_num
     __a :  List[str]						=  x_den * y_num + x_num * y_den
     __a :  str						=  gcd(lowerCAmelCase__  ,   lowerCAmelCase__  )
     z_num //= hcf
     z_den //= hcf
     if 0 < z_num < z_den <= order:
      __a :  Optional[int]						=  add_three(
          lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  )
      unique_s.add(lowerCAmelCase__  )

     # n=2
     __a :  List[str]						=  x_num * x_num * y_num * y_num
     __a :  Optional[int]						=  (
         x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
     )
     if is_sq(lowerCAmelCase__  ) and is_sq(lowerCAmelCase__  ):
      __a :  Union[str, Any]						=  int(sqrt(lowerCAmelCase__  )  )
      __a :  List[str]						=  int(sqrt(lowerCAmelCase__  )  )
      __a :  Optional[int]						=  gcd(lowerCAmelCase__  ,   lowerCAmelCase__  )
      z_num //= hcf
      z_den //= hcf
      if 0 < z_num < z_den <= order:
       __a :  int						=  add_three(
           lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__  )
       unique_s.add(lowerCAmelCase__  )

 for num, den in unique_s:
  total += Fraction(lowerCAmelCase__  ,   lowerCAmelCase__  )

 return total.denominator + total.numerator


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