




import warnings

from ..trainer import Trainer
from ..utils import logging


UpperCamelCase__					    =    logging.get_logger(__name__)
class     a__					(      snake_case__   ):






						def __init__(     self	,    _A=None	,    **_A    ):




											"""simple docstring"""



											warnings.warn(
											    "`SageMakerTrainer` is deprecated and will be removed in v5 of Transformers. You can use `Trainer` "
											    "instead."	,    _A	,    )
											super().__init__(args=_A	,    **_A    )










from math import ceil, sqrt







def 			_a   (		SCREAMING_SNAKE_CASE_							:       int = 1_00_00_00  ):
					__lowerCAmelCase            = 0

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




