



"""simple docstring"""







from collections import defaultdict
from math import ceil, sqrt

def       _lowerCamelCase				(							UpperCAmelCase_ :       int = 1000000,	UpperCAmelCase_ :       int = 10     )	-> int:






	"""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 <= 10     )


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






"""simple docstring"""


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_flax_available, is_torch_available


A_    							=					{
    """configuration_gpt_neo""": ["""GPT_NEO_PRETRAINED_CONFIG_ARCHIVE_MAP""", """GPTNeoConfig""", """GPTNeoOnnxConfig"""],
}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A_    							=					[
						    """GPT_NEO_PRETRAINED_MODEL_ARCHIVE_LIST""",
						    """GPTNeoForCausalLM""",
						    """GPTNeoForQuestionAnswering""",
						    """GPTNeoForSequenceClassification""",
						    """GPTNeoForTokenClassification""",
						    """GPTNeoModel""",
						    """GPTNeoPreTrainedModel""",
						    """load_tf_weights_in_gpt_neo""",
						]

try:
						if not is_flax_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A_    							=					[
						    """FlaxGPTNeoForCausalLM""",
						    """FlaxGPTNeoModel""",
						    """FlaxGPTNeoPreTrainedModel""",
						]


if TYPE_CHECKING:
						from .configuration_gpt_neo import GPT_NEO_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTNeoConfig, GPTNeoOnnxConfig

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_gpt_neo import (
												    GPT_NEO_PRETRAINED_MODEL_ARCHIVE_LIST,
												    GPTNeoForCausalLM,
												    GPTNeoForQuestionAnswering,
												    GPTNeoForSequenceClassification,
												    GPTNeoForTokenClassification,
												    GPTNeoModel,
												    GPTNeoPreTrainedModel,
												    load_tf_weights_in_gpt_neo,
												)

						try:
												if not is_flax_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_flax_gpt_neo import FlaxGPTNeoForCausalLM, FlaxGPTNeoModel, FlaxGPTNeoPreTrainedModel


else:
						import sys

						A_    							=					_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



