

from collections import defaultdict
from math import ceil, sqrt



def 			_A	(      SCREAMING_SNAKE_CASE = 1_0_0_0_0_0_0	,SCREAMING_SNAKE_CASE = 1_0      ):
	UpperCAmelCase__:	Union[str, Any]									= defaultdict(UpperCAmelCase_      )

	for outer_width in range(3	,(t_limit // 4) + 2      ):
		if outer_width * outer_width > t_limit:
			UpperCAmelCase__:	Any									= max(
			    ceil(sqrt(outer_width * outer_width - t_limit      )      )	,1      )
		else:
			UpperCAmelCase__:	int									= 1

		hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

		for hole_width in range(UpperCAmelCase_	,outer_width - 1	,2      ):
			count[outer_width * outer_width - hole_width * hole_width] += 1

	return sum(1 for n in count.values() if 1 <= n <= 1_0      )


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




"""simple docstring"""







import warnings

from ...utils import logging
from .image_processing_deit import DeiTImageProcessor


UpperCamelCase     =							logging.get_logger(__name__)






class       UpperCamelCase__			(   _lowerCAmelCase      ):

			"""simple docstring"""


			def __init__(      self						,	*SCREAMING_SNAKE_CASE__						,	**SCREAMING_SNAKE_CASE__		)      ->	None:
				warnings.warn(
				    "The class DeiTFeatureExtractor is deprecated and will be removed in version 5 of Transformers. Please"
				    " use DeiTImageProcessor instead."						,	SCREAMING_SNAKE_CASE__						,	)
				super().__init__(*SCREAMING_SNAKE_CASE__						,	**SCREAMING_SNAKE_CASE__		)




