Shareholders' Equity - Narrative (Details)					12 Months Ended
	Oct. 20, 2021 USD ($) $ / shares	Oct. 19, 2021 $ / shares	Oct. 23, 2019 $ / shares	Oct. 22, 2019 $ / shares	Aug. 28, 2021 USD ($) $ / shares shares	Aug. 29, 2020 $ / shares shares	Aug. 31, 2019 vote $ / shares shares	Jan. 02, 2019 USD ($)
Class Of Stock [Line Items]
Shares repurchased (in shares) | shares					60,950	117,767	197,150
Total cost of shares repurchased divided by the total number of shares repurchased					$ 184.13	$ 184.67	$ 154.78
Stock repurchase, remaining to repurchase outstanding shares value | $					$ 36,500,000
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					0	0	67,000
Quarterly dividend amount (in dollars per share)	$ 0.24	$ 0.20	$ 0.20	$ 0.09