Lease Obligations and Other Commitments - Schedule of Cash Activities Associated with our Leases (Details) - USD ($) $ in Thousands	3 Months Ended	9 Months Ended
Mar. 02, 2024	Feb. 25, 2023	Mar. 02, 2024	Feb. 25, 2023
Commitments and Contingencies Disclosure [Abstract]
Operating cash flows from operating leases	$ 354	$ 150	$ 977	$ 646

Amount of cash outflow from operating lease, excluding payments to bring another asset to condition and location necessary for its intended use.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 5
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479041/842-20-45-5

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (g)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147478964/842-20-50-4

Name:	us-gaap_OperatingLeasePayments
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration