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 29, 2021	May 30, 2020	May 29, 2021	May 30, 2020
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 42,016	$ 21,285	$ 116,497	$ 104,207
As reported - Basic (in shares)	18,881	18,898	18,881	18,928
As reported – Diluted	$ 42,016	$ 21,285	$ 116,497	$ 104,207
As reported - Diluted (in shares)	19,051	18,995	19,041	19,074
As reported - Diluted (in dollars per share)	$ 2.21	$ 1.12	$ 6.12	$ 5.46
Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 35,270	$ 17,871	$ 97,792	$ 87,519
As reported - Basic (in shares)	15,238	15,255	15,238	15,285
As reported - Basic (in dollars per share)	$ 2.31	$ 1.17	$ 6.42	$ 5.73
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	170	97	160	146
Class B Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 6,746	$ 3,414	$ 18,705	$ 16,688
As reported - Basic (in shares)	3,643	3,643	3,643	3,643
As reported - Basic (in dollars per share)	$ 1.85	$ 0.94	$ 5.13	$ 4.58