Share-based Compensation - Summary of Share-Based Award Activity for Stock Options and Stock Appreciation Rights (Details)	12 Months Ended
	Aug. 27, 2022 $ / shares shares
Number of Shares
Outstanding at beginning of period (in shares) | shares	394,174
Granted | shares	34,754
Expired | shares	(168)
Exercised | shares	(53,226)
Forfeited | shares	(7,186)
Outstanding at end of period (in shares) | shares	368,348
Exercisable at end of period (in shares) | shares	250,223
Weighted Average Exercise Price
Outstanding at beginning of period (in dollars per share) | $ / shares	$ 144.07
Granted | $ / shares	199.80
Expired | $ / shares	201.24
Exercised | $ / shares	123.07
Forfeited | $ / shares	164.72
Outstanding at end of period (in dollars per share) | $ / shares	151.93
Exercisable at end of period (in dollars per share) | $ / shares	$ 141.68