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. 27, 2021	Nov. 28, 2020
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income available to shareholders	$ 33,705	$ 41,896
Allocation of net income for Basic:
Net income allocated for common stockholder basic	$ 33,705	$ 41,896
Weighted average number of shares for Basic:
Common stock (in shares)	18,872	18,890
Common Stock
Allocation of net income for Basic:
Net income allocated for common stockholder basic	$ 28,291	$ 35,171
Weighted average number of shares for Basic:
Common stock (in shares)	15,229	15,247
Income per share for Basic:
Common stock (in dollars per share)	$ 1.86	$ 2.31
Class B Common Stock
Allocation of net income for Basic:
Net income allocated for common stockholder basic	$ 5,414	$ 6,725
Weighted average number of shares for Basic:
Common stock (in shares)	3,643	3,643
Income per share for Basic:
Common stock (in dollars per share)	$ 1.49	$ 1.85