Summary of Significant Accounting Policies - Schedule of Computation of Basic Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended								12 Months Ended
	Aug. 29, 2020	May 30, 2020	Feb. 29, 2020	Nov. 30, 2019	Aug. 31, 2019	May 25, 2019	Feb. 23, 2019	Nov. 24, 2018	Aug. 29, 2020	Aug. 31, 2019	Aug. 25, 2018
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income available to shareholders	$ 31,563	$ 21,285	$ 34,680	$ 48,242	$ 45,988	$ 47,220	$ 47,606	$ 38,320	$ 135,770	$ 179,134	$ 163,895
Allocation of net income for Basic:
Common stock									$ 135,770	$ 179,134	$ 163,895
Weighted average number of shares for Basic:
Common stock (in shares)									18,919	19,082	19,811
Common Stock
Allocation of net income for Basic:
Common stock	$ 26,499	$ 17,871	$ 29,129	$ 40,526	$ 38,619	$ 39,563	$ 39,923	$ 32,137	$ 114,017	$ 150,247	$ 133,802
Weighted average number of shares for Basic:
Common stock (in shares)	15,250	15,255	15,293	15,308	15,340	15,341	15,428	15,432	15,276	15,385	15,454
Income per share for Basic:
Common stock (in dollars per share)	$ 1.74	$ 1.17	$ 1.90	$ 2.65	$ 2.52	$ 2.58	$ 2.59	$ 2.08	$ 7.46	$ 9.77	$ 8.66
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 5,064	$ 3,414	$ 5,551	$ 7,716	$ 7,369	$ 7,657	$ 7,683	$ 6,183	$ 21,753	$ 28,887	$ 30,093
Weighted average number of shares for Basic:
Common stock (in shares)	3,643	3,643	3,643	3,643	3,659	3,710	3,710	3,710	3,643	3,697	4,357
Income per share for Basic:
Common stock (in dollars per share)	$ 1.39	$ 0.94	$ 1.52	$ 2.12	$ 2.01	$ 2.06	$ 2.07	$ 1.67	$ 5.97	$ 7.81	$ 6.91