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. 23, 2019	Feb. 24, 2018	Feb. 23, 2019	Feb. 24, 2018
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 47,606	$ 58,378	$ 85,926	$ 92,584
As reported - Basic (in shares)	19,138	20,297	19,140	20,287
As reported – Diluted	$ 47,606	$ 58,378	$ 85,926	$ 92,584
As reported - Diluted (in shares)	19,232	20,463	19,258	20,434
As reported - Diluted (in dollars per share)	$ 2.48	$ 2.85	$ 4.46	$ 4.53
Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 39,923	$ 46,744	$ 72,061	$ 74,126
As reported - Basic (in shares)	15,428	15,481	15,430	15,471
As reported - Basic (in dollars per share)	$ 2.59	$ 3.02	$ 4.67	$ 4.79
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	94	166	118	147
Class B Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 7,683	$ 11,634	$ 13,865	$ 18,458
As reported - Basic (in shares)	3,710	4,816	3,710	4,816
As reported - Basic (in dollars per share)	$ 2.07	$ 2.42	$ 3.74	$ 3.83