


import sys

from .dependency_versions_table import deps
from .utils.versions import require_version, require_version_core


# define which module versions we always want to check at run time
# (usually the ones defined in `install_requires` in setup.py)
#
# order specific notes:
# - tqdm must be checked before tokenizers

snake_case							:	Optional[int]					      =				'''python tqdm regex requests packaging filelock numpy tokenizers'''.split()
if sys.version_info < (3, 7):
						pkgs_to_check_at_runtime.append('''dataclasses''')
if sys.version_info < (3, 8):
						pkgs_to_check_at_runtime.append('''importlib_metadata''')

for pkg in pkgs_to_check_at_runtime:
						if pkg in deps:
												if pkg == "tokenizers":
																		# must be loaded here, or else tqdm check may fail
																		from .utils import is_tokenizers_available

																		if not is_tokenizers_available():
																								continue  # not required, check version only if installed

												require_version_core(deps[pkg])
						else:
												raise ValueError(f"""can't find {pkg} in {deps.keys()}, check dependency_versions_table.py""")






def 							__lowercase       (			__lowerCAmelCase							:    Any ,   __lowerCAmelCase							:    Optional[Any]=None       ):
							require_version(deps[pkg] ,   __lowerCAmelCase       )








from math import ceil, sqrt






def 							__lowercase       (			__lowerCAmelCase							:    int = 1_0_0_0_0_0_0       ):
							a__					=					0

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




