

from collections import defaultdict
from math import ceil, sqrt
def 						__lowerCamelCase	(       __snake_case					:		int = 1_000_000,		__snake_case					:		int = 10	)	->							int:






						"""simple docstring"""





						A__					:       defaultdict     =defaultdict(__snake_case	)

						for outer_width in range(3,		(t_limit // 4) + 2	):
												if outer_width * outer_width > t_limit:
																		A__					:       Optional[Any]     =max(
																		    ceil(sqrt(outer_width * outer_width - t_limit	)	),		1	)
												else:
																		A__					:       Union[str, Any]     =1

												hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

												for hole_width in range(__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() = }""")




'''simple docstring'''



from typing import Dict

from .base import GenericTensor, Pipeline



class lowerCamelCase			(  lowercase_						):



			'''simple docstring'''






			def lowercase__						(				self	:						List[str]		,      lowerCAmelCase_	:						Tuple=None		,      lowerCAmelCase_	:						Dict=None		,      lowerCAmelCase_	:						Any=None		,      **lowerCAmelCase_	:						Union[str, Any]			)      ->		Optional[Any]:





									'''simple docstring'''
									if tokenize_kwargs is None:
															A__					:       List[Any]     ={}

									if truncation is not None:
															if "truncation" in tokenize_kwargs:
																					raise ValueError(
																					    """truncation parameter defined twice (given as keyword argument as well as in tokenize_kwargs)"""			)
															A__					:       str     =truncation

									A__					:       Optional[int]     =tokenize_kwargs

									A__					:       List[Any]     ={}
									if return_tensors is not None:
															A__					:       Any     =return_tensors

									return preprocess_params, {}, postprocess_params


			def lowercase__						(				self	:						int		,      lowerCAmelCase_	:						Union[str, Any]		,      **lowerCAmelCase_	:						Dict			)      ->		Dict[str, GenericTensor]:





									'''simple docstring'''
									A__					:       List[str]     =self.framework
									A__					:       Union[str, Any]     =self.tokenizer(lowerCAmelCase_		,      return_tensors=lowerCAmelCase_		,      **lowerCAmelCase_			)
									return model_inputs


			def lowercase__						(				self	:						Optional[int]		,      lowerCAmelCase_	:						Dict			)      ->		Optional[Any]:





									'''simple docstring'''
									A__					:       Union[str, Any]     =self.model(**lowerCAmelCase_			)
									return model_outputs


			def lowercase__						(				self	:						Tuple		,      lowerCAmelCase_	:						Tuple		,      lowerCAmelCase_	:						Any=False			)      ->		List[Any]:





									'''simple docstring'''
									# [0] is the first available tensor, logits or last_hidden_state.
									if return_tensors:
															return model_outputs[0]
									if self.framework == "pt":
															return model_outputs[0].tolist()
									elif self.framework == "tf":
															return model_outputs[0].numpy().tolist()



			def __call__(				self	:						int		,      *lowerCAmelCase_	:						Any		,      **lowerCAmelCase_	:						Union[str, Any]			)      ->		List[str]:





									'''simple docstring'''
									return super().__call__(*lowerCAmelCase_		,      **lowerCAmelCase_			)

