Accumulated Other Comprehensive Loss - Summary of Changes in Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Mar. 27, 2022	Mar. 28, 2021	Mar. 27, 2022	Mar. 28, 2021
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning balance	$ (217,071)	$ (201,473)	$ (213,433)	$ (175,441)
Other Comprehensive Income (Loss) Before Reclassifications	(1,291)	697	(35)	(5,419)
Income Tax	606		606
Net Other Comprehensive Income (Loss) Before Reclassifications	(685)	697	571	(5,419)
Reclassifications:
Prior Service Credits		2		6
Unrecognized Net Loss	(102)	(94)	(310)	(277)
Total Reclassifications Before Tax	(102)	(92)	(310)	(271)
Reclassifications, Income Tax	23	23	72	63
Net Reclassifications	(79)	(69)	(238)	(208)
Other Comprehensive Income	(764)	628	333	(5,627)
Ending balance	(221,854)	(207,494)	(221,854)	(207,494)
Foreign Currency Translation Adjustments
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning balance	15,438	15,654	14,685	20,136
Other Comprehensive Income (Loss) Before Reclassifications	(1,291)	697	(35)	(5,419)
Income Tax	606		606
Net Other Comprehensive Income (Loss) Before Reclassifications	(685)	697	571	(5,419)
Reclassifications:
Other Comprehensive Income	(685)	697	571	(5,419)
Other Comprehensive Income Attributable to Non- Controlling Interest	(373)	409	130	(1,225)
Ending balance	15,126	15,942	15,126	15,942
Retirement and Postretirement Benefit Plans
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning balance	1,953	1,838	2,112	1,977
Reclassifications:
Prior Service Credits		2		6
Unrecognized Net Loss	(102)	(94)	(310)	(277)
Total Reclassifications Before Tax	(102)	(92)	(310)	(271)
Reclassifications, Income Tax	23	23	72	63
Net Reclassifications	(79)	(69)	(238)	(208)
Other Comprehensive Income	(79)	(69)	(238)	(208)
Ending balance	1,874	1,769	1,874	1,769
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning balance	17,391	17,492	16,797	22,113
Reclassifications:
Ending balance	17,000	17,711	17,000	17,711
AOCI Including Portion Attributable to Noncontrolling Interest
Reclassifications:
Other Comprehensive Income	(764)	628	333	(5,627)
AOCI Attributable to Noncontrolling Interest
Reclassifications:
Other Comprehensive Income Attributable to Non- Controlling Interest	$ (373)	$ 409	$ 130	$ (1,225)