Income Taxes - Additional Information (Details) - USD ($)	3 Months Ended		9 Months Ended
	Mar. 02, 2024	Feb. 25, 2023	Mar. 02, 2024	Feb. 25, 2023	May 27, 2023
Operating Loss Carryforwards [Line Items]
Income tax provision	$ 229,000	$ 1,655,000	$ 116,000	$ 5,281,000
Effective income tax provision rate			39.20%	22.50%
Federal statutory rate			21.00%
Liability for uncertain tax positions related to continuing operations, excluding interest and penalties	0		$ 0		$ 0
Deferred tax valuation allowance	1,400,000		1,400,000		1,400,000
Maximum
Operating Loss Carryforwards [Line Items]
Deferred tax liability, undistributed earnings of foreign subsidiaries	100,000		100,000		$ 100,000
State and Local Jurisdiction
Operating Loss Carryforwards [Line Items]
Valuation allowance pertaining to deferred tax assets	200,000		200,000
Foreign Tax Authority
Operating Loss Carryforwards [Line Items]
Valuation allowance pertaining to deferred tax assets	$ 1,200,000		$ 1,200,000