Shareholders' Equity - Narrative (Details)						12 Months Ended
	Jul. 15, 2022 USD ($) $ / shares shares	Oct. 20, 2021 $ / shares	Oct. 19, 2021 $ / shares	Oct. 23, 2019 $ / shares	Oct. 22, 2019 $ / shares	Aug. 27, 2022 USD ($) $ / shares shares	Aug. 28, 2021 $ / shares shares	Aug. 29, 2020 $ / shares shares	Aug. 31, 2019 Vote	Oct. 18, 2021 USD ($)	Jan. 02, 2019 USD ($)
Class Of Stock [Line Items]
Shares repurchased (in shares) | shares						213,419	60,950	117,767
Total cost of shares repurchased divided by the total number of shares repurchased						$ 179.98	$ 184.13	$ 184.67
Stock repurchase, remaining to repurchase outstanding shares value | $						$ 63,600,000
Maximum
Class Of Stock [Line Items]
Stock repurchase authorized, Value | $										$ 100,000,000.0	$ 100,000,000.0
Common Stock
Class Of Stock [Line Items]
Voting rights | Vote									1
Dividend rate									125.00%
Quarterly dividend amount (in dollars per share)		$ 0.30	$ 0.25	$ 0.25	$ 0.1125
Class B Common Stock
Class Of Stock [Line Items]
Voting rights | Vote									10
Number of shares converted (in shares) | shares						17,000	0	0
Quarterly dividend amount (in dollars per share)		$ 0.24	$ 0.20	$ 0.20	$ 0.09
Shares repurchased (in shares) | shares	35,714
Total cost of shares repurchased divided by the total number of shares repurchased	$ 168.00
Shares repurchased, Value | $	$ 6,000,000.0