

"""simple docstring"""





from ..utils import DummyObject, requires_backends







class 				SCREAMING_SNAKE_CASE					(		metaclass=a_       ):






					"""simple docstring"""



					lowercase__				 =       ["flax", "transformers"]







					def __init__(       self			:				int   ,*lowercase_			:				List[str]   ,**lowercase_			:				Union[str, Any]		):
						requires_backends(self   ,['''flax''', '''transformers''']		)







					@classmethod
					def        __lowerCAmelCase (       cls			:				List[Any]   ,*lowercase_			:				int   ,**lowercase_			:				Union[str, Any]		):
						requires_backends(cls   ,['''flax''', '''transformers''']		)







					@classmethod
					def        __lowerCAmelCase (       cls			:				Dict   ,*lowercase_			:				Tuple   ,**lowercase_			:				str		):
						requires_backends(cls   ,['''flax''', '''transformers''']		)







class 				SCREAMING_SNAKE_CASE					(		metaclass=a_       ):






					"""simple docstring"""



					lowercase__				 =       ["flax", "transformers"]







					def __init__(       self			:				Optional[int]   ,*lowercase_			:				str   ,**lowercase_			:				Optional[Any]		):
						requires_backends(self   ,['''flax''', '''transformers''']		)







					@classmethod
					def        __lowerCAmelCase (       cls			:				List[str]   ,*lowercase_			:				List[str]   ,**lowercase_			:				Optional[Any]		):
						requires_backends(cls   ,['''flax''', '''transformers''']		)







					@classmethod
					def        __lowerCAmelCase (       cls			:				List[Any]   ,*lowercase_			:				Union[str, Any]   ,**lowercase_			:				List[str]		):
						requires_backends(cls   ,['''flax''', '''transformers''']		)







class 				SCREAMING_SNAKE_CASE					(		metaclass=a_       ):






					"""simple docstring"""



					lowercase__				 =       ["flax", "transformers"]







					def __init__(       self			:				int   ,*lowercase_			:				List[Any]   ,**lowercase_			:				str		):
						requires_backends(self   ,['''flax''', '''transformers''']		)







					@classmethod
					def        __lowerCAmelCase (       cls			:				List[str]   ,*lowercase_			:				Union[str, Any]   ,**lowercase_			:				Any		):
						requires_backends(cls   ,['''flax''', '''transformers''']		)







					@classmethod
					def        __lowerCAmelCase (       cls			:				int   ,*lowercase_			:				Optional[Any]   ,**lowercase_			:				Union[str, Any]		):
						requires_backends(cls   ,['''flax''', '''transformers''']		)







class 				SCREAMING_SNAKE_CASE					(		metaclass=a_       ):






					"""simple docstring"""



					lowercase__				 =       ["flax", "transformers"]







					def __init__(       self			:				Union[str, Any]   ,*lowercase_			:				List[str]   ,**lowercase_			:				Optional[Any]		):
						requires_backends(self   ,['''flax''', '''transformers''']		)







					@classmethod
					def        __lowerCAmelCase (       cls			:				int   ,*lowercase_			:				Dict   ,**lowercase_			:				Optional[Any]		):
						requires_backends(cls   ,['''flax''', '''transformers''']		)







					@classmethod
					def        __lowerCAmelCase (       cls			:				Optional[Any]   ,*lowercase_			:				str   ,**lowercase_			:				Optional[int]		):
						requires_backends(cls   ,['''flax''', '''transformers''']		)







"""simple docstring"""





from collections import defaultdict
from math import ceil, sqrt

def   __SCREAMING_SNAKE_CASE  (      A_ = 1_00_00_00						,     A_ = 10 ):
	lowerCAmelCase__	:						defaultdict  				=	defaultdict(A_ )

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

		hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

		for hole_width in range(A_						,     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() = }''')




