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		9 Months Ended
	May 27, 2017	May 28, 2016	May 27, 2017	May 28, 2016
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income available to shareholders	$ 24,362	$ 30,144	$ 75,092	$ 89,532
Allocation of net income for Basic:
Common Stock	$ 24,362	$ 30,144	$ 75,092	$ 89,532
Weighted average number of shares for Basic:
Common Stock (in shares)	20,308	20,177	20,290	20,139
Common Stock
Allocation of net income for Basic:
Common Stock	$ 19,307	$ 23,939	$ 59,486	$ 71,172
Weighted average number of shares for Basic:
Common Stock (in shares)	15,326	15,253	15,305	15,238
Earnings per share for Basic:
Common Stock (in dollars per share)	$ 1.26	$ 1.57	$ 3.89	$ 4.67
Class B Common Stock
Allocation of net income for Basic:
Common Stock	$ 4,883	$ 6,061	$ 15,068	$ 17,956
Weighted average number of shares for Basic:
Common Stock (in shares)	4,846	4,827	4,846	4,805
Earnings per share for Basic:
Common Stock (in dollars per share)	$ 1.01	$ 1.26	$ 3.11	$ 3.74
Unvested participating shares
Allocation of net income for Basic:
Common Stock	$ 172	$ 144	$ 538	$ 404
Weighted average number of shares for Basic:
Common Stock (in shares)	136	97	139	96