


from math import ceil, sqrt



def 	lowerCAmelCase       (						lowerCAmelCase_ = 1_000_000       )->       int:
				lowerCAmelCase_       :					Optional[Any]			 = 0

				for outer_width in range(3       ,      (limit // 4) + 2       ):
								if outer_width**2 > limit:
												lowerCAmelCase_       :					Optional[Any]			 = max(ceil(sqrt(outer_width**2 - limit       )       )       ,      1       )
								else:
												lowerCAmelCase_       :					Tuple			 = 1
								if (outer_width - hole_width_lower_bound) % 2:
												hole_width_lower_bound += 1

								answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

				return answer


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




'''simple docstring'''




import contextlib
import importlib
import io
import unittest

import transformers

# Try to import everything from transformers to ensure every object can be loaded.
from transformers import *  # noqa F406
from transformers.testing_utils import DUMMY_UNKNOWN_IDENTIFIER, require_flax, require_tf, require_torch
from transformers.utils import ContextManagers, find_labels, is_flax_available, is_tf_available, is_torch_available


if is_torch_available():
							from transformers import BertForPreTraining, BertForQuestionAnswering, BertForSequenceClassification

if is_tf_available():
							from transformers import TFBertForPreTraining, TFBertForQuestionAnswering, TFBertForSequenceClassification

if is_flax_available():
							from transformers import FlaxBertForPreTraining, FlaxBertForQuestionAnswering, FlaxBertForSequenceClassification


a   :			str					  =    DUMMY_UNKNOWN_IDENTIFIER
# An actual model hosted on huggingface.co

a   :			int					  =    """main"""
# Default branch name
a   :			Any					  =    """f2c752cfc5c0ab6f4bdec59acea69eefbee381c2"""
# One particular commit (not the top of `main`)
a   :			str					  =    """aaaaaaa"""
# This commit does not exist, so we should 404.

a   :			int					  =    """d9e9f15bc825e4b2c9249e9578f884bbcb5e3684"""
# Sha-1 of config.json on the top of `main`, for checking purposes
a   :			Any					  =    """4b243c475af8d0a7754e87d7d096c92e5199ec2fe168a2ee7998e3b8e9bcb1d3"""



@contextlib.contextmanager
def       __lowerCamelCase  (					)      ->			List[str]:
							print("""Welcome!"""		)
							yield
							print("""Bye!"""		)



@contextlib.contextmanager
def       __lowerCamelCase  (					)      ->			Optional[int]:
							print("""Bonjour!"""		)
							yield
							print("""Au revoir!"""		)

class 			UpperCamelCase_ (							unittest.TestCase			):





	def  _lowercase(  self    )			->			List[Any]:
								# If the spec is missing, importlib would not be able to import the module dynamically.
								assert transformers.__spec__ is not None
								assert importlib.util.find_spec("""transformers"""    ) is not None




class 			UpperCamelCase_ (							unittest.TestCase			):





	@unittest.mock.patch("""sys.stdout"""		,		new_callable=io.StringIO    )
	def  _lowercase(  self		,		A    )			->			Tuple:
								with ContextManagers([]    ):
															print("""Transformers are awesome!"""    )
								# The print statement adds a new line at the end of the output
								self.assertEqual(mock_stdout.getvalue()		,		"""Transformers are awesome!\n"""    )





	@unittest.mock.patch("""sys.stdout"""		,		new_callable=io.StringIO    )
	def  _lowercase(  self		,		A    )			->			Dict:
								with ContextManagers([context_en()]    ):
															print("""Transformers are awesome!"""    )
								# The output should be wrapped with an English welcome and goodbye
								self.assertEqual(mock_stdout.getvalue()		,		"""Welcome!\nTransformers are awesome!\nBye!\n"""    )





	@unittest.mock.patch("""sys.stdout"""		,		new_callable=io.StringIO    )
	def  _lowercase(  self		,		A    )			->			Union[str, Any]:
								with ContextManagers([context_fr(), context_en()]    ):
															print("""Transformers are awesome!"""    )
								# The output should be wrapped with an English and French welcome and goodbye
								self.assertEqual(mock_stdout.getvalue()		,		"""Bonjour!\nWelcome!\nTransformers are awesome!\nBye!\nAu revoir!\n"""    )





	@require_torch
	def  _lowercase(  self    )			->			Optional[int]:
								self.assertEqual(find_labels(A    )		,		["""labels"""]    )
								self.assertEqual(find_labels(A    )		,		["""labels""", """next_sentence_label"""]    )
								self.assertEqual(find_labels(A    )		,		["""start_positions""", """end_positions"""]    )

								class 			UpperCamelCase_ (							__magic_name__			):
									pass




								self.assertEqual(find_labels(A    )		,		["""labels"""]    )





	@require_tf
	def  _lowercase(  self    )			->			int:
								self.assertEqual(find_labels(A    )		,		["""labels"""]    )
								self.assertEqual(find_labels(A    )		,		["""labels""", """next_sentence_label"""]    )
								self.assertEqual(find_labels(A    )		,		["""start_positions""", """end_positions"""]    )

								class 			UpperCamelCase_ (							__magic_name__			):
									pass




								self.assertEqual(find_labels(A    )		,		["""labels"""]    )






	@require_flax
	def  _lowercase(  self    )			->			Any:
								# Flax models don't have labels
								self.assertEqual(find_labels(A    )		,		[]    )
								self.assertEqual(find_labels(A    )		,		[]    )
								self.assertEqual(find_labels(A    )		,		[]    )

								class 			UpperCamelCase_ (							__magic_name__			):
									pass




								self.assertEqual(find_labels(A    )		,		[]    )

