Accumulated Other Comprehensive Loss - Summary of Changes in Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Mar. 31, 2024	Apr. 02, 2023	Mar. 31, 2024	Apr. 02, 2023
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning Balance	$ (217,641)	$ (217,676)	$ (211,024)	$ (219,947)
Reclassifications:
Other comprehensive income	(1,089)	(3,801)	(1,547)	(3,688)
Ending Balance	(220,114)	(218,473)	(220,114)	(218,473)
Accumulated Foreign Currency Adjustment Including Portion Attributable to Noncontrolling Interest
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning Balance	12,805	17,511	13,028	16,733
Other comprehensive income before reclassifications	(1,043)	(3,451)	(1,408)	(3,198)
Net other comprehensive income before reclassifications	(1,043)	(3,451)	(1,408)	(3,198)
Reclassifications:
Other comprehensive income	(1,043)	(3,451)	(1,408)	(3,198)
Other comprehensive income attributable to non-controlling interest	(416)	(1,147)	(558)	(1,672)
Ending Balance	12,178	15,207	12,178	15,207
Retirement and Postretirement Benefit Plans
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning Balance	1,073	1,715	1,166	1,855
Other comprehensive income before reclassifications		(371)		(371)
Other Comprehensive Income Before Reclassifications, Income Tax		87		87
Net other comprehensive income before reclassifications		(284)		(284)
Reclassifications:
Unrecognized net loss	(61)	(86)	(182)	(269)
Reclassifications, Income tax	15	20	43	63
Net reclassifications	(46)	(66)	(139)	(206)
Other comprehensive income	(46)	(350)	(139)	(490)
Ending Balance	1,027	1,365	1,027	1,365
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning Balance	13,878	19,226	14,194	18,588
Other comprehensive income before reclassifications	(1,043)	(3,822)	(1,408)	(3,569)
Other Comprehensive Income Before Reclassifications, Income Tax		87		87
Net other comprehensive income before reclassifications	(1,043)	(3,735)	(1,408)	(3,482)
Reclassifications:
Unrecognized net loss	(61)	(86)	(182)	(269)
Reclassifications, Income tax	15	20	43	63
Net reclassifications	(46)	(66)	(139)	(206)
Other comprehensive income	(1,089)	(3,801)	(1,547)	(3,688)
Other comprehensive income attributable to non-controlling interest	(416)	(1,147)	(558)	(1,672)
Ending Balance	$ 13,205	$ 16,572	$ 13,205	$ 16,572