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Other Non-Current Assets - Schedule of Unaudited, Condensed Income Statement Information for Unconsolidated Affiliates (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
Schedule Of Equity Method Investments [Line Items]                      
Net sales                 $ 623,527 $ 815,758 $ 667,592
Gross profit $ 6,025 $ 9,653 $ (8,000) $ 6,563 $ 18,354 $ 19,144 $ 16,890 $ 26,097 14,241 80,485 93,494
Net income                 (46,344) 15,171 29,073
Distributions received                   750 750
Equity Method Investment, Nonconsolidated Investee or Group of Investees [Member]                      
Schedule Of Equity Method Investments [Line Items]                      
Net sales                 29,123 31,745 19,649
Gross profit                 2,337 1,928 3,423
Income from operations                 604 148 1,777
Net income                 544 127 1,782
Depreciation and amortization                 $ 111 $ 121 $ 151
[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.