

from math import ceil, sqrt





def 	__a     (      A__			:  int = 1000000       ):
    SCREAMING_SNAKE_CASE										=   0

    for outer_width in range(3			,  (limit // 4) + 2       ):
        if outer_width**2 > limit:
            SCREAMING_SNAKE_CASE										=   max(ceil(sqrt(outer_width**2 - limit       )       )			,  1       )
        else:
            SCREAMING_SNAKE_CASE										=   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() = }')


from dataclasses import dataclass, field
from typing import Tuple

from ..utils import cached_property, is_tf_available, logging, requires_backends
from .benchmark_args_utils import BenchmarkArguments


if is_tf_available():
    import tensorflow as tf


__A			:					Dict						=			logging.get_logger(__name__)





@dataclass
class 			_SCREAMING_SNAKE_CASE (   __snake_case		):







   '''simple docstring'''




   lowerCamelCase__				=      [
       "no_inference",
       "no_cuda",
       "no_tpu",
       "no_speed",
       "no_memory",
       "no_env_print",
       "no_multi_process",
   ]





   def __init__(       self					:			List[Any]     , **__lowerCamelCase					:			Any			):
       for deprecated_arg in self.deprecated_args:
           if deprecated_arg in kwargs:
               SCREAMING_SNAKE_CASE										=   deprecated_arg[3:]
               SCREAMING_SNAKE_CASE										=   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										=   kwargs.pop("tpu_name"     , self.tpu_name			)
       SCREAMING_SNAKE_CASE										=   kwargs.pop("device_idx"     , self.device_idx			)
       SCREAMING_SNAKE_CASE										=   kwargs.pop("eager_mode"     , self.eager_mode			)
       SCREAMING_SNAKE_CASE										=   kwargs.pop("use_xla"     , self.use_xla			)
       super().__init__(**__lowerCamelCase			)

   lowerCamelCase__				=      field(
       default=__snake_case					,       metadata={"help": "Name of TPU"}					,       )
   lowerCamelCase__				=      field(
       default=0					,       metadata={"help": "CPU / GPU device index. Defaults to 0."}					,       )
   lowerCamelCase__				=      field(default=__snake_case					,       metadata={"help": "Benchmark models in eager model."}		)
   lowerCamelCase__				=      field(
       default=__snake_case					,       metadata={
           "help": "Benchmark models using XLA JIT compilation. Note that `eager_model` has to be set to `False`."
       }					,       )





   @cached_property
   def      _snake_case		(       self					:			Optional[int]			):
       requires_backends(self     , ["tf"]			)
       SCREAMING_SNAKE_CASE										=   None
       if self.tpu:
           try:
               if self.tpu_name:
                   SCREAMING_SNAKE_CASE										=   tf.distribute.cluster_resolver.TPUClusterResolver(self.tpu_name			)
               else:
                   SCREAMING_SNAKE_CASE										=   tf.distribute.cluster_resolver.TPUClusterResolver()
           except ValueError:
               SCREAMING_SNAKE_CASE										=   None
       return tpu





   @cached_property
   def      _snake_case		(       self					:			Any			):
       requires_backends(self     , ["tf"]			)
       if self.is_tpu:
           tf.config.experimental_connect_to_cluster(self._setup_tpu			)
           tf.tpu.experimental.initialize_tpu_system(self._setup_tpu			)

           SCREAMING_SNAKE_CASE										=   tf.distribute.TPUStrategy(self._setup_tpu			)
       else:
           # currently no multi gpu is allowed
           if self.is_gpu:
               # TODO: Currently only single GPU is supported
               tf.config.set_visible_devices(self.gpu_list[self.device_idx]     , "GPU"			)
               SCREAMING_SNAKE_CASE										=   tf.distribute.OneDeviceStrategy(device=f"/gpu:{self.device_idx}"			)
           else:
               tf.config.set_visible_devices([]     , "GPU"			)  # disable GPU
               SCREAMING_SNAKE_CASE										=   tf.distribute.OneDeviceStrategy(device=f"/cpu:{self.device_idx}"			)

       return strategy





   @property
   def      _snake_case		(       self					:			Any			):
       requires_backends(self     , ["tf"]			)
       return self._setup_tpu is not None





   @property
   def      _snake_case		(       self					:			Optional[Any]			):
       requires_backends(self     , ["tf"]			)
       return self._setup_strategy





   @property
   def      _snake_case		(       self					:			List[str]			):
       requires_backends(self     , ["tf"]			)
       return tf.config.list_physical_devices("GPU"			)





   @property
   def      _snake_case		(       self					:			Any			):
       requires_backends(self     , ["tf"]			)
       if self.cuda:
           return len(self.gpu_list			)
       return 0





   @property
   def      _snake_case		(       self					:			Dict			):
       return self.n_gpu > 0