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Organization and Summary of Significant Accounting Policies - Summary of Changes in Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Thousands
 12 Months Ended
Jun. 30, 2024
Jul. 02, 2023
Accumulated Other Comprehensive Income Loss [Line Items]    
Beginning Balance $ (211,024) $ (219,947)
Other comprehensive income (loss) before reclassifications 2,784 (5,257)
Other comprehensive income (loss) before reclassifications, Income Tax 2 (504)
Net other comprehensive income (loss) before Reclassifications 2,786 (5,761)
Reclassifications:    
Sale of interest in VAST LLC   (830)
Actuarial losses (242) (342)
Total reclassifications before tax (242) (1,172)
Retirement and Postretirement Plans Reclassifications, Income Tax 57 80
Net reclassifications (185) (1,092)
Other Comprehensive income (loss) 2,601 (6,853)
Ending Balance (225,615) (211,024)
Foreign Currency Translation Adjustments    
Accumulated Other Comprehensive Income Loss [Line Items]    
Beginning Balance 13,028 16,733
Other comprehensive income (loss) before reclassifications 2,794 (4,698)
Other comprehensive income (loss) before reclassifications, Income Tax   (636)
Net other comprehensive income (loss) before Reclassifications 2,794 (5,334)
Reclassifications:    
Sale of interest in VAST LLC   (830)
Total reclassifications before tax   (830)
Net reclassifications   (830)
Other Comprehensive income (loss) 2,794 (6,164)
Other comprehensive income (loss) attributable to non-controlling interest 1,106 (2,459)
Ending Balance 14,716 13,028
Retirement and Postretirement Benefit Plans    
Accumulated Other Comprehensive Income Loss [Line Items]    
Beginning Balance 1,166 1,855
Other comprehensive income (loss) before reclassifications (10) (559)
Other comprehensive income (loss) before reclassifications, Income Tax 2 132
Net other comprehensive income (loss) before Reclassifications (8) (427)
Reclassifications:    
Actuarial losses (242) (342)
Total reclassifications before tax (242) (342)
Retirement and Postretirement Plans Reclassifications, Income Tax 57 80
Net reclassifications (185) (262)
Other Comprehensive income (loss) (193) (689)
Ending Balance 973 1,166
Accumulated Other Comprehensive Loss    
Accumulated Other Comprehensive Income Loss [Line Items]    
Beginning Balance 14,194 18,588
Reclassifications:    
Ending Balance 15,689 14,194
AOCI Including Portion Attributable to Noncontrolling Interest    
Reclassifications:    
Other Comprehensive income (loss) 2,601 (6,853)
AOCI Attributable to Noncontrolling Interest    
Reclassifications:    
Other comprehensive income (loss) attributable to non-controlling interest $ 1,106 $ (2,459)