Accumulated Other Comprehensive Loss - Summary of Changes in Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jan. 01, 2023	Dec. 26, 2021	Jan. 01, 2023	Dec. 26, 2021
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning balance	$ (219,409)	$ (212,797)	$ (219,947)	$ (212,797)
Other Comprehensive Income (Loss) Before Reclassifications	(429)	544	253	1,256
Net Other Comprehensive Income (Loss) Before Reclassifications	(429)	544	253	1,256
Reclassifications:
Unrecognized Net Loss	(92)	(99)	(183)	(201)
Reclassifications, Income Tax	22	23	43	47
Net Reclassifications	(70)	(76)	(140)	(154)
Other Comprehensive Income (Loss)	(499)	468	113	1,102
Ending balance	(217,676)	(216,424)	(217,676)	(216,424)
Accumulated Foreign Currency Adjustment Including Portion Attributable to Noncontrolling Interest
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning balance	17,471	15,245	(16,733)	14,683
Other Comprehensive Income (Loss) Before Reclassifications	(429)	544	253	1,256
Net Other Comprehensive Income (Loss) Before Reclassifications	(429)	544	253	1,256
Reclassifications:
Other Comprehensive Income (Loss)	(429)	544	253	1,256
Other Comprehensive Income (Loss) Attributable to Non- Controlling Interest	(469)	353	(525)	503
Ending balance	17,511	15,436	17,511	15,436
Retirement and Postretirement Benefit Plans
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning balance	1,785	2,153	(1,855)	2,231
Reclassifications:
Unrecognized Net Loss	(92)	(99)	(183)	(201)
Reclassifications, Income Tax	22	23	43	47
Net Reclassifications	(70)	(76)	(140)	(154)
Other Comprehensive Income (Loss)	(70)	(76)	(140)	(154)
Ending balance	1,715	2,077	1,715	2,077
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income Loss [Line Items]
Beginning balance	19,256	17,398	18,588	16,914
Reclassifications:
Ending balance	19,226	17,513	19,226	17,513
AOCI Including Portion Attributable to Noncontrolling Interest
Reclassifications:
Other Comprehensive Income (Loss)	(499)	468	113	1,102
AOCI Attributable to Noncontrolling Interest
Reclassifications:
Other Comprehensive Income (Loss) Attributable to Non- Controlling Interest	$ (469)	$ 353	$ (525)	$ 503