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
	Nov. 25, 2017	Nov. 26, 2016
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 34,206	$ 28,214
As reported - Basic (in shares)	20,278	20,272
Add: Undistributed earnings allocated to unvested participating shares	$ 0	$ 199
Less: Undistributed earnings reallocated to unvested participating shares	0	(189)
Diluted EPS – Common Stock	$ 34,206	$ 28,020
Diluted EPS – Common Stock (in shares)	20,434	20,249
Diluted EPS – Common Stock (in dollars per share)	$ 1.67	$ 1.38
Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 27,384	$ 22,342
As reported - Basic (in shares)	15,462	15,285
As reported - Basic (in dollars per share)	$ 1.77	$ 1.46
Add: effect of dilutive potential common shares	$ 0	$ 0
Add: effect of dilutive potential common shares (in shares)	156	117
Class B Common Stock
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items]
As reported - Basic	$ 6,822	$ 5,668
As reported - Basic (in shares)	4,816	4,847
As reported - Basic (in dollars per share)	$ 1.42	$ 1.17
Add: effect of dilutive potential common shares	$ 6,822	$ 5,668
Add: effect of dilutive potential common shares (in shares)	4,816	4,847