from math import ceil, sqrt
def    A			(					_lowercase = 1_000_000		):
						SCREAMING_SNAKE_CASE							:					Optional[int]           =							0

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






import os

try:
					from .build_directory_md import good_file_paths
except ImportError:
					from build_directory_md import good_file_paths  # type: ignore

__UpperCamelCase	: Dict    		=  list(good_file_paths())
assert filepaths, "good_file_paths() failed!"

__UpperCamelCase	: Tuple    		=  [file for file in filepaths if file != file.lower()]
if upper_files:
					print(f"""{len(upper_files)} files contain uppercase characters:""")
					print('\n'.join(upper_files) + '\n')

__UpperCamelCase	: List[Any]    		=  [file for file in filepaths if ' ' in file]
if space_files:
					print(f"""{len(space_files)} files contain space characters:""")
					print('\n'.join(space_files) + '\n')

__UpperCamelCase	: List[Any]    		=  [file for file in filepaths if '-' in file]
if hyphen_files:
					print(f"""{len(hyphen_files)} files contain hyphen characters:""")
					print('\n'.join(hyphen_files) + '\n')

__UpperCamelCase	: List[Any]    		=  [file for file in filepaths if os.sep not in file]
if nodir_files:
					print(f"""{len(nodir_files)} files are not in a directory:""")
					print('\n'.join(nodir_files) + '\n')

__UpperCamelCase	: Optional[Any]    		=  len(upper_files + space_files + hyphen_files + nodir_files)
if bad_files:
					import sys

					sys.exit(bad_files)





