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 25, 2019	May 26, 2018	May 25, 2019	May 26, 2018
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 47,220	$ 36,359	$ 133,146	$ 128,943
As reported - Basic (in shares)	19,051	19,533	19,110	20,036
As reported – Diluted	$ 47,220	$ 36,359	$ 133,146	$ 128,943
As reported - Diluted (in shares)	19,168	19,687	19,220	20,178
As reported - Diluted (in dollars per share)	$ 2.46	$ 1.85	$ 6.93	$ 6.39
Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 39,563	$ 30,034	$ 111,626	$ 104,324
As reported - Basic (in shares)	15,341	15,446	15,400	15,463
As reported - Basic (in dollars per share)	$ 2.58	$ 1.94	$ 7.25	$ 6.75
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	117	154	110	142
Class B Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 7,657	$ 6,325	$ 21,520	$ 24,619
As reported - Basic (in shares)	3,710	4,087	3,710	4,573
As reported - Basic (in dollars per share)	$ 2.06	$ 1.55	$ 5.80	$ 5.38