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Goodwill and Other Intangible Assets -Schedule of Goodwill and Identified Intangible Assets (Details) - USD ($)
$ in Thousands
 3 Months Ended 12 Months Ended
Dec. 29, 2024
Sep. 29, 2024
Goodwill [Roll Forward]    
Goodwill, beginning of period $ 328,040 $ 329,504
Allocated to sold operations (4,182) (1,464)
Goodwill, end of period 323,858 328,040
Amortizable intangible assets:    
Total intangibles, net 390,458 398,115
Mastheads    
Non-amortized intangible assets:    
Mastheads 10,917 10,917
Customer and newspaper subscriber lists    
Amortizable intangible assets:    
Customer and newspaper subscriber lists 262,146 262,242
Less accumulated amortization (206,463) (203,084)
Amortizable intangible assets, net $ 55,683 $ 59,158