Income Per Share - Schedule of Computation of Basic Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended
	Nov. 24, 2018	Nov. 25, 2017
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income available to shareholders	$ 38,320	$ 34,206
Allocation of net income for Basic:
Common stock	$ 38,320	$ 34,206
Weighted average number of shares for Basic:
Common stock (in shares)	19,142	20,278
Common Stock
Allocation of net income for Basic:
Common stock	$ 32,137	$ 27,384
Weighted average number of shares for Basic:
Common stock (in shares)	15,432	15,462
Income per share for Basic:
Common stock (in dollars per share)	$ 2.08	$ 1.77
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 6,183	$ 6,822
Weighted average number of shares for Basic:
Common stock (in shares)	3,710	4,816
Income per share for Basic:
Common stock (in dollars per share)	$ 1.67	$ 1.42