






"""simple docstring"""





import unittest

from accelerate import debug_launcher
from accelerate.test_utils import require_cpu, test_ops, test_script
@require_cpu
class    __lowerCamelCase    (  unittest.TestCase  ):

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Optional[Any]:
       debug_launcher(test_script.main      )







   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Optional[int]:
       debug_launcher(test_ops.main      )












"""simple docstring"""





from collections import defaultdict
from math import ceil, sqrt







def   lowerCAmelCase_( SCREAMING_SNAKE_CASE = 1_00_00_00 ,	SCREAMING_SNAKE_CASE = 10					)					->	int:
    """simple docstring"""

    UpperCamelCase__         =    defaultdict(SCREAMING_SNAKE_CASE					)

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

        hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

        for hole_width in range(SCREAMING_SNAKE_CASE ,	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 <= 10					)


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




