Goodwill and Other Intangible Assets (Schedule of Goodwill and Other Intangible Assets) (Details) - USD ($) $ in Thousands	12 Months Ended
	May 30, 2020	Jun. 01, 2019	Jun. 02, 2018
Goodwill [Roll Forward]
Goodwill, Balance	$ 35,525	$ 35,525
Goodwill, Balance	35,525	35,525	$ 35,525
Finite-lived Intangible Assets [Roll Forward]
Other intangibles, Amortization	(2,946)	(2,795)	(2,800)
Other Intangibles, Finite-Lived, Balance	22,096
Intangible Assets (Excluding Goodwill) [Roll Forward]
Other intangibles, Balance	23,762	26,307
Other intangibles, Additions	2,000	250
Other intangibles, Balance	22,816	23,762	26,307
Water Rights
Indefinite-lived Intangible Assets [Roll Forward]
Other Intangibles, Indefinite-Lived, Balance	720	720
Other Intangibles, Indefinite-Lived, Balance	720	720	720
Franchise rights
Finite-lived Intangible Assets [Roll Forward]
Other Intangibles, Finite-Lived, Balance	19,955	21,583
Other intangibles, Amortization	(1,628)	(1,628)
Other Intangibles, Finite-Lived, Balance	18,327	19,955	21,583
Customer relationships
Finite-lived Intangible Assets [Roll Forward]
Other Intangibles, Finite-Lived, Balance	2,504	3,582
Other intangibles, Amortization	(1,150)	(1,078)
Other Intangibles, Finite-Lived, Additions	1,000
Other Intangibles, Finite-Lived, Balance	2,354	2,504	3,582
Non-compete agreements
Finite-lived Intangible Assets [Roll Forward]
Other Intangibles, Finite-Lived, Balance	297	86
Other intangibles, Amortization	(118)	(39)
Other Intangibles, Finite-Lived, Additions	1,000	250
Other Intangibles, Finite-Lived, Balance	1,179	297	86
Trademark
Finite-lived Intangible Assets [Roll Forward]
Other Intangibles, Finite-Lived, Balance	286	336
Other intangibles, Amortization	(50)	(50)
Other Intangibles, Finite-Lived, Balance	$ 236	$ 286	$ 336