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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
Jul. 02, 2023
Jul. 03, 2022
Accumulated Other Comprehensive Income Loss [Line Items]    
Beginning balance $ (219,947) $ (212,797)
Other comprehensive loss before reclassifications (5,257) 1,630
Other comprehensive loss before reclassifications, Income Tax (504) 625
Net other comprehensive loss before Reclassifications (5,761) 2,255
Reclassifications:    
Sale of interest in VAST LLC (830)  
Actuarial losses (342) (409)
Total reclassifications before tax (1,172) (409)
Retirement and Postretirement Plans Reclassifications, Income Tax 80 96
Net reclassifications (1,092) (313)
Other Comprehensive Loss (6,853) 1,942
Ending balance (211,024) (219,947)
Foreign Currency Translation Adjustments    
Accumulated Other Comprehensive Income Loss [Line Items]    
Beginning balance 16,733 14,683
Other comprehensive loss before reclassifications (4,698) 1,712
Other comprehensive loss before reclassifications, Income Tax (636) 606
Net other comprehensive loss before Reclassifications (5,334) 2,318
Reclassifications:    
Sale of interest in VAST LLC (830)  
Total reclassifications before tax (830)  
Net reclassifications (830)  
Other Comprehensive Loss (6,164) 2,318
Other comprehensive loss attributable to non-controlling interest (2,459) 268
Ending balance 13,028 16,733
Retirement and Postretirement Benefit Plans    
Accumulated Other Comprehensive Income Loss [Line Items]    
Beginning balance 1,855 2,231
Other comprehensive loss before reclassifications (559) (82)
Other comprehensive loss before reclassifications, Income Tax 132 19
Net other comprehensive loss before Reclassifications (427) (63)
Reclassifications:    
Actuarial losses (342) (409)
Total reclassifications before tax (342) (409)
Retirement and Postretirement Plans Reclassifications, Income Tax 80 96
Net reclassifications (262) (313)
Other Comprehensive Loss (689) (376)
Ending balance 1,166 1,855
Accumulated Other Comprehensive Loss    
Accumulated Other Comprehensive Income Loss [Line Items]    
Beginning balance 18,588 16,914
Reclassifications:    
Ending balance 14,194 18,588
AOCI Including Portion Attributable to Noncontrolling Interest    
Reclassifications:    
Other Comprehensive Loss (6,853) 1,942
AOCI Attributable to Noncontrolling Interest    
Reclassifications:    
Other comprehensive loss attributable to non-controlling interest $ (2,459) $ 268