Accumulated Other Comprehensive Loss - Summary of Changes in Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Dec. 31, 2023	Jan. 01, 2023	Dec. 31, 2023	Jan. 01, 2023
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning Balance	$ (215,301)	$ (219,409)	$ (211,024)	$ (219,947)
Reclassifications:
Other comprehensive income (loss)	(1,061)	(499)	(458)	113
Ending Balance	(217,641)	(217,676)	(217,641)	(217,676)
Accumulated Foreign Currency Adjustment Including Portion Attributable to Noncontrolling Interest
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning Balance	13,407	17,471	13,028	16,733
Other comprehensive income (loss) before reclassifications	(1,014)	(429)	(365)	253
Net other comprehensive loss before reclassifications	(1,014)	(429)	(365)	253
Reclassifications:
Other comprehensive income (loss)	(1,014)	(429)	(365)	253
Other comprehensive income (loss) attributable to non- controlling interest	(412)	(469)	(142)	(525)
Ending Balance	12,805	17,511	12,805	17,511
Retirement and Postretirement Benefit Plans
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning Balance	1,120	1,785	1,166	1,855
Reclassifications:
Unrecognized net loss	(61)	(92)	(121)	(183)
Reclassifications, Income tax	14	22	28	43
Net reclassifications	(47)	(70)	(93)	(140)
Other comprehensive income (loss)	(47)	(70)	(93)	(140)
Ending Balance	1,073	1,715	1,073	1,715
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning Balance	14,527	19,256	14,194	18,588
Other comprehensive income (loss) before reclassifications	(1,014)	(429)	(365)	253
Net other comprehensive loss before reclassifications	(1,014)	(429)	(365)	253
Reclassifications:
Unrecognized net loss	(61)	(92)	(121)	(183)
Reclassifications, Income tax	14	22	28	43
Net reclassifications	(47)	(70)	(93)	(140)
Other comprehensive income (loss)	(1,061)	(499)	(458)	113
Other comprehensive income (loss) attributable to non- controlling interest	(412)	(469)	(142)	(525)
Ending Balance	$ 13,878	$ 19,226	$ 13,878	$ 19,226