





"""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 					A__				(			UpperCamelCase					,  UpperCamelCase=()					,  UpperCamelCase=None					,  UpperCamelCase="no"					,  UpperCamelCase="29500"       ):
							A		=  False
							A		=  False
							if any(key.startswith("KAGGLE"       ) for key in os.environ.keys()       ):
														A		=  True
							elif "IPython" in sys.modules:
														A		=  "google.colab" in str(sys.modules["IPython"].get_ipython()       )

							try:
														A		=  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"					,  UpperCamelCase       ) 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:
																					A		=  8

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






def 					A__				(			UpperCamelCase					,  UpperCamelCase=()					,  UpperCamelCase=2       ):
							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=UpperCamelCase					,  master_addr="127.0.01"					,  master_port="29500"					,  accelerate_mixed_precision="no"					,  accelerate_debug_rdv_file=tmp_file.name					,  accelerate_use_cpu="yes"					,  ):
																					A		=  PrepareForLaunch(UpperCamelCase					,  debug=UpperCamelCase       )
																					start_processes(UpperCamelCase					,  args=UpperCamelCase					,  nprocs=UpperCamelCase					,  start_method="fork"       )









"""simple docstring"""
from math import isqrt, loga






def 					A__				(			UpperCamelCase       ):
							A		=  [True] * max_number
							for i in range(2					,  isqrt(max_number - 1       ) + 1       ):
														if is_prime[i]:
																					for j in range(i**2					,  UpperCamelCase					,  UpperCamelCase       ):
																												A		=  False

							return [i for i in range(2					,  UpperCamelCase       ) if is_prime[i]]






def 					A__				(			UpperCamelCase = 800_800					,  UpperCamelCase = 800_800       ):
							A		=  degree * loga(UpperCamelCase       )
							A		=  int(UpperCamelCase       )
							A		=  calculate_prime_numbers(UpperCamelCase       )

							A		=  0
							A		=  0
							A		=  len(UpperCamelCase       ) - 1
							while left < right:
														while (
														    prime_numbers[right] * loga(prime_numbers[left]       )
														    + prime_numbers[left] * loga(prime_numbers[right]       )
														    > upper_bound
														):
																					right -= 1
														hybrid_integers_count += right - left
														left += 1

							return hybrid_integers_count


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


