Business Segment Information - Reconciliations of Segment Gross Profit to Consolidated (loss) income Before Income Taxes (Details) - USD ($) $ in Thousands	3 Months Ended																12 Months Ended
	Jul. 02, 2023	[1]	Apr. 02, 2023	[1]	Jan. 01, 2023	[1]	Oct. 02, 2022	[1]	Jul. 03, 2022	[2]	Mar. 27, 2022	[2]	Dec. 26, 2021	[2]	Sep. 26, 2021	[2]	Jul. 02, 2023	Jul. 03, 2022	Jun. 27, 2021
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit	$ 6,025		$ 9,653		$ (8,000)		$ 6,563		$ 18,354		$ 19,144		$ 16,890		$ 26,097		$ 14,241	$ 80,485	$ 93,494
Selling, general and administrative expenses																	47,345	52,489	51,334
Benefit for bad debts																	(89)	(445)	(1,316)
Other operating expenses (income), net																	7,856	(158)	4,865
Operating (loss) income																	(40,871)	28,599	38,611
Interest income																	(2,109)	(1,524)	(603)
Interest expense																	7,577	3,085	3,323
Equity in earnings of unconsolidated affiliates																	(896)	(605)	(739)
Recovery of non-income taxes, net																		815	(9,717)
(Loss) income before income taxes																	(45,443)	26,828	46,347
Americas [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit																	(14,659)	24,468	36,406
Brazil [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit																	12,162	27,141	31,695
Asia [Member]
Segment Reporting Reconciling Item For Operating Profit Loss From Segment To Consolidated [Line Items]
Gross profit																	$ 16,738	$ 28,876	$ 25,393

[1] Gross profit for our domestic operations for all fiscal quarters of fiscal 2023 was impacted by lower production volumes driving weaker fixed cost absorption in connection with lower sales volumes.

[2] Gross profit for our domestic operations for all fiscal quarters of fiscal 2022 includes adverse pressures from (i) higher raw material costs, (ii) rising input costs, and (iii) the weakening of labor productivity.