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. 28, 2026	Mar. 01, 2025	Feb. 28, 2026	Mar. 01, 2025
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 20,484	$ 24,459	$ 54,847	$ 67,564
As reported - Basic (in shares)	18,074	18,567	18,108	18,577
As reported - Diluted	$ 20,484	$ 24,459	$ 54,847	$ 67,564
As reported - Diluted (in shares)	18,143	18,649	18,159	18,653
As reported - Diluted (in dollars per share)	$ 1.13	$ 1.31	$ 3.02	$ 3.62
Common Stock
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 17,133	$ 20,559	$ 45,887	$ 56,778
As reported - Basic (in shares)	14,523	15,009	14,557	15,011
As reported - Basic (in dollars per share)	$ 1.18	$ 1.37	$ 3.15	$ 3.78
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	69	82	51	76
As reported - Diluted (in dollars per share)	$ 1.13	$ 1.31	$ 3.02	$ 3.62
Class B Common Stock
Earnings Per Share Diluted [Line Items]
As reported - Basic	$ 3,351	$ 3,900	$ 8,960	$ 10,786
As reported - Basic (in shares)	3,551	3,558	3,551	3,566
As reported - Basic (in dollars per share)	$ 0.94	$ 1.1	$ 2.52	$ 3.02