






"""simple docstring"""


from ..utils import DummyObject, requires_backends


class 					snake_case		(							metaclass=_lowerCAmelCase						):


   '''simple docstring'''

   A_						:	Union[str, Any]						 = ["speech"]


   def __init__(	self :     Dict,       *_lowerCamelCase :     Any,       **_lowerCamelCase :     Any  ):

     '''simple docstring'''
     requires_backends(self,       ['''speech''']  )





class 					snake_case		(							metaclass=_lowerCAmelCase						):


   '''simple docstring'''

   A_						:	Dict						 = ["speech"]


   def __init__(	self :     List[str],       *_lowerCamelCase :     Any,       **_lowerCamelCase :     Any  ):

     '''simple docstring'''
     requires_backends(self,       ['''speech''']  )












"""simple docstring"""


from collections import defaultdict
from math import ceil, sqrt



def 					lowerCAmelCase				(    __UpperCamelCase = 1_0_0_0_0_0_0		,       __UpperCamelCase = 1_0 ):




  """simple docstring"""







  __A									= defaultdict(__UpperCamelCase )

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




