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Transactions with Related Parties (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 28, 2024 | Sep. 30, 2023 | Sep. 24, 2022
Related Party Transaction [Line Items] |  |  |
Accounts payable | $ 212,606 | $ 190,902 |
Contract Packaging, Inc. |  |  |
Related Party Transaction [Line Items] |  |  |
Percentage of shares held by CPI in Tech Pac | 20.00% | 20.00% | 20.00%
Accounts payable | $ 1,400 | $ 1,600 |
Contract Packaging, Inc. | Tech Pac |  |  |
Related Party Transaction [Line Items] |  |  |
Purchases products from related party | $ 37,000 | $ 31,000 | $ 41,000

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