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Transactions with Related Parties (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2023
Sep. 24, 2022
Sep. 25, 2021
Related Party Transaction [Line Items]      
Accounts payable $ 190,902 $ 215,681  
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 $ 1,600 $ 1,000  
Contract Packaging, Inc. | Tech Pac      
Related Party Transaction [Line Items]      
Purchases products from related party $ 31,000 $ 41,000 $ 42,600