Income Per Share - Schedule of Computation of Diluted Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended		9 Months Ended
	May 31, 2025	May 25, 2024	May 31, 2025	May 25, 2024
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 39,680	$ 38,057	$ 107,244	$ 100,839
As reported - Basic (in shares)	18,547	18,652	18,570	18,684
As reported - Diluted	$ 39,680	$ 38,057	$ 107,244	$ 100,839
As reported - Diluted (in shares)	18,607	18,705	18,633	18,738
As reported - Diluted (in dollars per share)	$ 2.13	$ 2.03	$ 5.76	$ 5.38
Common Stock
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 33,346	$ 31,962	$ 90,126	$ 84,716
As reported - Basic (in shares)	14,990	15,062	15,007	15,094
As reported - Basic (in dollars per share)	$ 2.22	$ 2.12	$ 6.01	$ 5.61
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	60	53	63	54
As reported - Diluted (in dollars per share)	$ 2.13	$ 2.03	$ 5.76	$ 5.38
Class B Common Stock
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 6,334	$ 6,095	$ 17,118	$ 16,123
As reported - Basic (in shares)	3,557	3,590	3,563	3,590
As reported - Basic (in dollars per share)	$ 1.78	$ 1.7	$ 4.80	$ 4.49