Lease Obligations and Other Commitments - Components of Lease Costs (Details) - USD ($) $ in Thousands	3 Months Ended	9 Months Ended
Mar. 02, 2024	Feb. 25, 2023	Mar. 02, 2024	Feb. 25, 2023
Lease, Cost [Abstract]
Consolidated operating lease expense	$ 457	$ 434	$ 1,328	$ 1,300

Amount of operating lease expense. Excludes sublease income.

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 4
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479041/842-20-45-4

Name:	us-gaap_OperatingLeaseExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration