
import inspect
import os
import unittest

import torch

import accelerate
from accelerate import debug_launcher
from accelerate.test_utils import (
    execute_subprocess_async,
    require_cpu,
    require_huggingface_suite,
    require_multi_gpu,
    require_single_gpu,
)
from accelerate.utils import patch_environment




@require_huggingface_suite
class 				_lowerCamelCase (      unittest.TestCase ):





     """simple docstring"""







     def    __SCREAMING_SNAKE_CASE			(							self  )  ->   Any:




           """simple docstring"""







           UpperCamelCase__    :   Any					=				inspect.getfile(accelerate.test_utils  )
           UpperCamelCase__    :   List[Any]					=				os.path.sep.join(
               mod_file.split(os.path.sep  )[:-1] + ['''scripts''', '''external_deps''', '''test_metrics.py''']  )

           from accelerate.test_utils.scripts.external_deps import test_metrics  # noqa: F401

           UpperCamelCase__    :   List[Any]					=				test_metrics






     @require_cpu
     def    __SCREAMING_SNAKE_CASE			(							self  )  ->   int:




           """simple docstring"""







           debug_launcher(self.test_metrics.main						,						num_processes=1  )






     @require_cpu
     def    __SCREAMING_SNAKE_CASE			(							self  )  ->   List[Any]:




           """simple docstring"""







           debug_launcher(self.test_metrics.main  )






     @require_single_gpu
     def    __SCREAMING_SNAKE_CASE			(							self  )  ->   Tuple:




           """simple docstring"""







           self.test_metrics.main()






     @require_multi_gpu
     def    __SCREAMING_SNAKE_CASE			(							self  )  ->   Tuple:




           """simple docstring"""







           print(F'''Found {torch.cuda.device_count()} devices.'''  )
           UpperCamelCase__    :   Optional[int]					=				["torchrun", F'''--nproc_per_node={torch.cuda.device_count()}''', self.test_file_path]
           with patch_environment(omp_num_threads=1  ):
                 execute_subprocess_async(__SCREAMING_SNAKE_CASE						,						env=os.environ.copy()  )




import math


def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__		):
      UpperCamelCase__    :   List[str]					=				math.loga(math.sqrt(4 * positive_integer + 1		) / 2 + 1 / 2		)

      return exponent == int(UpperCamelCase__		)


def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__ = 1 / 1_2_3_4_5		):
      UpperCamelCase__    :   Dict					=				0
      UpperCamelCase__    :   Tuple					=				0

      UpperCamelCase__    :   Optional[Any]					=				3
      while True:
            UpperCamelCase__    :   Union[str, Any]					=				(integer**2 - 1) / 4
            # if candidate is an integer, then there is a partition for k
            if partition_candidate == int(UpperCamelCase__		):
                  UpperCamelCase__    :   int					=				int(UpperCamelCase__		)
                  total_partitions += 1
                  if check_partition_perfect(UpperCamelCase__		):
                        perfect_partitions += 1
            if perfect_partitions > 0:
                  if perfect_partitions / total_partitions < max_proportion:
                        return int(UpperCamelCase__		)
            integer += 1


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


