



'''simple docstring'''




from dataclasses import dataclass, field
from typing import Tuple

from ..utils import cached_property, is_torch_available, is_torch_tpu_available, logging, requires_backends
from .benchmark_args_utils import BenchmarkArguments


if is_torch_available():
						import torch

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


UpperCamelCase__       :	int    = logging.get_logger(__name__)






@dataclass
class 						_UpperCamelCase  (							lowerCamelCase__    ):


			'''simple docstring'''

			_A      :		Any			    =		[
			    '''no_inference''',
			    '''no_cuda''',
			    '''no_tpu''',
			    '''no_speed''',
			    '''no_memory''',
			    '''no_env_print''',
			    '''no_multi_process''',
			]

			def __init__(							self     : int							,     **lowerCAmelCase__     : Tuple						):





					"""simple docstring"""






					for deprecated_arg in self.deprecated_args:
							if deprecated_arg in kwargs:
									__SCREAMING_SNAKE_CASE       :		Optional[int]           =		deprecated_arg[3:]
									setattr(self							,     lowerCAmelCase__							,     not kwargs.pop(lowerCAmelCase__						)						)
									logger.warning(
									    F"{deprecated_arg} is depreciated. Please use --no_{positive_arg} or"
									    F" {positive_arg}={kwargs[positive_arg]}"						)

					__SCREAMING_SNAKE_CASE       :		Dict           =		kwargs.pop("""torchscript"""							,     self.torchscript						)
					__SCREAMING_SNAKE_CASE       :		Tuple           =		kwargs.pop("""torch_xla_tpu_print_metrics"""							,     self.torch_xla_tpu_print_metrics						)
					__SCREAMING_SNAKE_CASE       :		int           =		kwargs.pop("""fp16_opt_level"""							,     self.fpaa_opt_level						)
					super().__init__(**lowerCAmelCase__						)

			_A      :		bool			    =		field(default=lowerCamelCase__    ,					metadata={'''help''': '''Trace the models using torchscript'''}    )
			_A      :		bool			    =		field(default=lowerCamelCase__    ,					metadata={'''help''': '''Print Xla/PyTorch tpu metrics'''}    )
			_A      :		str			    =		field(
			    default='''O1'''    ,					metadata={
			        '''help''': (
			            '''For fp16: Apex AMP optimization level selected in [\'O0\', \'O1\', \'O2\', and \'O3\']. '''
			            '''See details at https://nvidia.github.io/apex/amp.html'''
			        )
			    }    ,					)

			@cached_property
			def UpperCamelCase__					(							self     : Optional[int]						):





					"""simple docstring"""






					requires_backends(self							,     ["""torch"""]						)
					logger.info("""PyTorch: setting up devices"""						)
					if not self.cuda:
							__SCREAMING_SNAKE_CASE       :		List[str]           =		torch.device("""cpu"""						)
							__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		0
					elif is_torch_tpu_available():
							__SCREAMING_SNAKE_CASE       :		Any           =		xm.xla_device()
							__SCREAMING_SNAKE_CASE       :		Any           =		0
					else:
							__SCREAMING_SNAKE_CASE       :		Tuple           =		torch.device("""cuda""" if torch.cuda.is_available() else """cpu"""						)
							__SCREAMING_SNAKE_CASE       :		int           =		torch.cuda.device_count()
					return device, n_gpu

			@property
			def UpperCamelCase__					(							self     : int						):





					"""simple docstring"""






					return is_torch_tpu_available() and self.tpu

			@property
			def UpperCamelCase__					(							self     : Union[str, Any]						):





					"""simple docstring"""






					requires_backends(self							,     ["""torch"""]						)
					# TODO(PVP): currently only single GPU is supported
					return torch.cuda.current_device()

			@property
			def UpperCamelCase__					(							self     : Optional[int]						):





					"""simple docstring"""






					requires_backends(self							,     ["""torch"""]						)
					return self._setup_devices[0]

			@property
			def UpperCamelCase__					(							self     : Tuple						):





					"""simple docstring"""






					requires_backends(self							,     ["""torch"""]						)
					return self._setup_devices[1]



			@property
			def UpperCamelCase__					(							self     : str						):





					"""simple docstring"""






					return self.n_gpu > 0




'''simple docstring'''




from math import ceil, sqrt


def 				lowerCAmelCase_   (	_lowerCamelCase:   int = 1_00_00_00					):
		__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		0

		for outer_width in range(3       ,      (limit // 4) + 2					):
				if outer_width**2 > limit:
						__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		max(ceil(sqrt(outer_width**2 - limit					)					)       ,      1					)
				else:
						__SCREAMING_SNAKE_CASE       :		Union[str, Any]           =		1
				if (outer_width - hole_width_lower_bound) % 2:
						hole_width_lower_bound += 1

				answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

		return answer


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