Net Income Per Share - Schedule of Computation of Diluted Earnings Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 24, 2018	Feb. 25, 2017	Feb. 24, 2018	Feb. 25, 2017
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 58,378	$ 22,516	$ 92,584	$ 50,730
As reported - Basic (in shares)	20,297	20,290	20,287	20,281
Add: Undistributed earnings allocated to unvested participating shares	$ 0	$ 158	$ 0	$ 357
Less: Undistributed earnings reallocated to unvested participating shares	0	(150)	0	(338)
Diluted EPS – Common Stock	$ 58,378	$ 22,362	$ 92,584	$ 50,381
Diluted EPS – Common Stock (in shares)	20,463	20,263	20,434	20,250
Diluted EPS – Common Stock (in dollars per share)	$ 2.85	$ 1.10	$ 4.53	$ 2.49
Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 46,744	$ 17,836	$ 74,126	$ 40,178
As reported - Basic (in shares)	15,481	15,305	15,471	15,295
As reported - Basic (in dollars per share)	$ 3.02	$ 1.17	$ 4.79	$ 2.63
Add: effect of dilutive potential common shares	$ 0	$ 0	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	166	112	147	109
Class B Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 11,634	$ 4,518	$ 18,458	$ 10,184
As reported - Basic (in shares)	4,816	4,846	4,816	4,846
As reported - Basic (in dollars per share)	$ 2.42	$ 0.93	$ 3.83	$ 2.10
Add: effect of dilutive potential common shares	$ 11,634	$ 4,518	$ 18,458	$ 10,184
Add: effect of dilutive potential common shares (in shares)	4,816	4,846	4,816	4,846