Net Income Per Share - Schedule of Computation of Basic 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, Basic, by Common Class, Including Two Class Method [Line Items]
Net income available to shareholders	$ 34,206	$ 28,214
Allocation of net income for Basic:
Common Stock	$ 34,206	$ 28,214
Weighted average number of shares for Basic:
Common Stock (in shares)	20,278	20,272
Common Stock
Allocation of net income for Basic:
Common Stock	$ 27,384	$ 22,342
Weighted average number of shares for Basic:
Common Stock (in shares)	15,462	15,285
Earnings per share for Basic:
Common Stock (in dollars per share)	$ 1.77	$ 1.46
Class B Common Stock
Allocation of net income for Basic:
Common Stock	$ 6,822	$ 5,668
Weighted average number of shares for Basic:
Common Stock (in shares)	4,816	4,847
Earnings per share for Basic:
Common Stock (in dollars per share)	$ 1.42	$ 1.17
Unvested participating shares
Allocation of net income for Basic:
Common Stock	$ 0	$ 204
Weighted average number of shares for Basic:
Common Stock (in shares)	0	140