


from __future__ import annotations






def 							__lowercase       (			__lowerCAmelCase							:    float ,   __lowerCAmelCase							:    float ,   __lowerCAmelCase							:    float ,   ):
							if (stress, tangential_force, area).count(0       ) != 1:
														raise ValueError('You cannot supply more or less than 2 values'       )
							elif stress < 0:
														raise ValueError('Stress cannot be negative'       )
							elif tangential_force < 0:
														raise ValueError('Tangential Force cannot be negative'       )
							elif area < 0:
														raise ValueError('Area cannot be negative'       )
							elif stress == 0:
														return (
														    "stress",
														    tangential_force / area,
														)
							elif tangential_force == 0:
														return (
														    "tangential_force",
														    stress * area,
														)
							else:
														return (
														    "area",
														    tangential_force / stress,
														)


if __name__ == "__main__":
						import doctest

						doctest.testmod()








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() = }""")




