Income Per Share - Schedule of Computation of Basic Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended						9 Months Ended
	May 29, 2021	Feb. 27, 2021	Nov. 28, 2020	May 30, 2020	Feb. 29, 2020	Nov. 30, 2019	May 29, 2021	May 30, 2020
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income available to shareholders	$ 42,016	$ 32,585	$ 41,896	$ 21,285	$ 34,680	$ 48,242	$ 116,497	$ 104,207
Allocation of net income for Basic:
Common stock	$ 42,016			$ 21,285			$ 116,497	$ 104,207
Weighted average number of shares for Basic:
Common stock (in shares)	18,881			18,898			18,881	18,928
Common Stock
Allocation of net income for Basic:
Common stock	$ 35,270			$ 17,871			$ 97,792	$ 87,519
Weighted average number of shares for Basic:
Common stock (in shares)	15,238			15,255			15,238	15,285
Income per share for Basic:
Common stock (in dollars per share)	$ 2.31			$ 1.17			$ 6.42	$ 5.73
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 6,746			$ 3,414			$ 18,705	$ 16,688
Weighted average number of shares for Basic:
Common stock (in shares)	3,643			3,643			3,643	3,643
Income per share for Basic:
Common stock (in dollars per share)	$ 1.85			$ 0.94			$ 5.13	$ 4.58