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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 |  |

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