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. 30, 2019	Nov. 24, 2018
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income available to shareholders	$ 48,242	$ 38,320
Allocation of net income for Basic:
Common stock	$ 48,242	$ 38,320
Weighted average number of shares for Basic:
Common stock (in shares)	18,951	19,142
Common Stock
Allocation of net income for Basic:
Common stock	$ 40,526	$ 32,137
Weighted average number of shares for Basic:
Common stock (in shares)	15,308	15,432
Income per share for Basic:
Common stock (in dollars per share)	$ 2.65	$ 2.08
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 7,716	$ 6,183
Weighted average number of shares for Basic:
Common stock (in shares)	3,643	3,710
Income per share for Basic:
Common stock (in dollars per share)	$ 2.12	$ 1.67