Income Per Share - Schedule of Computation of Diluted Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 25, 2023	Feb. 26, 2022	Feb. 25, 2023	Feb. 26, 2022
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 17,810	$ 18,451	$ 51,767	$ 52,156
As reported - Basic (in shares)	18,677	18,845	18,674	18,860
As reported – Diluted	$ 17,810	$ 18,451	$ 51,767	$ 52,156
As reported - Diluted (in shares)	18,767	18,967	18,757	18,999
As reported - Diluted (in dollars per share)	$ 0.95	$ 0.97	$ 2.76	$ 2.75
Common Stock
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 14,962	$ 15,492	$ 43,488	$ 43,792
As reported - Basic (in shares)	15,087	15,210	15,084	15,225
As reported - Basic (in dollars per share)	$ 0.99	$ 1.02	$ 2.88	$ 2.88
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0	$ 0
As reported – Diluted	$ 17,810	$ 18,451	$ 51,767	$ 52,156
Add: effect of dilutive potential common shares (in shares)	90	122	83	139
Class B Common Stock
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 2,848	$ 2,959	$ 8,279	$ 8,364
As reported - Basic (in shares)	3,590	3,635	3,590	3,635
As reported - Basic (in dollars per share)	$ 0.79	$ 0.81	$ 2.31	$ 2.30