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 25, 2019	Feb. 23, 2019	Nov. 24, 2018	May 26, 2018	Feb. 24, 2018	Nov. 25, 2017	May 25, 2019	May 26, 2018
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]
Net income available to shareholders	$ 47,220	$ 47,606	$ 38,320	$ 36,359	$ 58,378	$ 34,206	$ 133,146	$ 128,943
Allocation of net income for Basic:
Common stock	$ 47,220			$ 36,359			$ 133,146	$ 128,943
Weighted average number of shares for Basic:
Common stock (in shares)	19,051			19,533			19,110	20,036
Common Stock
Allocation of net income for Basic:
Common stock	$ 39,563			$ 30,034			$ 111,626	$ 104,324
Weighted average number of shares for Basic:
Common stock (in shares)	15,341			15,446			15,400	15,463
Income per share for Basic:
Common stock (in dollars per share)	$ 2.58			$ 1.94			$ 7.25	$ 6.75
Class B Common Stock
Allocation of net income for Basic:
Common stock	$ 7,657			$ 6,325			$ 21,520	$ 24,619
Weighted average number of shares for Basic:
Common stock (in shares)	3,710			4,087			3,710	4,573
Income per share for Basic:
Common stock (in dollars per share)	$ 2.06			$ 1.55			$ 5.80	$ 5.38