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Accumulated Other Comprehensive Loss - Summary of Changes in Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Thousands
 3 Months Ended 9 Months Ended
Mar. 30, 2025
Mar. 31, 2024
Mar. 30, 2025
Mar. 31, 2024
Accumulated Other Comprehensive Income Loss [Line Items]        
Beginning Balance $ (228,155) $ (217,641) $ (225,615) $ (211,024)
Reclassifications:        
Other comprehensive loss (income) 41 (1,089) 3,754 (1,547)
Ending Balance (234,601) (220,114) (234,601) (220,114)
Accumulated Foreign Currency Adjustment Including Portion Attributable to Noncontrolling Interest        
Accumulated Other Comprehensive Income Loss [Line Items]        
Beginning Balance 17,146 12,805 14,716 13,028
Other comprehensive loss before reclassifications 77 (1,043) 4,082 (1,408)
Income Tax     0  
Net other comprehensive loss before reclassifications 77 (1,043) 4,082 (1,408)
Reclassifications:        
Other comprehensive loss (income) 77 (1,043) 4,082 (1,408)
Other comprehensive loss attributable to non-controlling interest 32 (416) 1,607 (558)
Ending Balance 17,191 12,178 17,191 12,178
Retirement and Postretirement Benefit Plans        
Accumulated Other Comprehensive Income Loss [Line Items]        
Beginning Balance 681 1,073 973 1,166
Other comprehensive loss before reclassifications     0  
Income Tax     0  
Net other comprehensive loss before reclassifications     0  
Reclassifications:        
Unrecognized net loss (46) (61) (421) (182)
Reclassifications, Income tax 10 15 93 43
Net reclassifications (36) (46) (328) (139)
Other comprehensive loss (income) (36) (46) (328) (139)
Ending Balance 645 1,027 645 1,027
Accumulated Other Comprehensive Loss        
Accumulated Other Comprehensive Income Loss [Line Items]        
Beginning Balance 17,827 13,878 15,689 14,194
Other comprehensive loss before reclassifications 77 (1,043) 4,082 (1,408)
Income Tax     0  
Net other comprehensive loss before reclassifications 77 (1,043) 4,082 (1,408)
Reclassifications:        
Unrecognized net loss (46) (61) (421) (182)
Reclassifications, Income tax 10 15 93 43
Net reclassifications (36) (46) (328) (139)
Other comprehensive loss (income) 41 (1,089) 3,754 (1,547)
Other comprehensive loss attributable to non-controlling interest 32 (416) 1,607 (558)
Ending Balance $ 17,836 $ 13,205 $ 17,836 $ 13,205