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Other Intangible Assets - Components of Gross and Net Acquired Intangible Assets (Details) - USD ($) $ in Thousands | Dec. 30, 2023 | Sep. 30, 2023 | Dec. 24, 2022
--- | --- | --- | ---
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | $ 737,800 | $ 737,800 | $ 737,800
Accumulated Amortization | (207,600) | (199,400) | (173,900)
Accumulated Impairment | (41,200) | (41,200) | (29,800)
Net Carrying Value | 489,058 | 497,228 | 534,207
Marketing-related intangible assets |  |  |
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | 274,600 | 274,600 | 274,600
Accumulated Amortization | (21,700) | (21,500) | (20,900)
Accumulated Impairment | (29,400) | (29,400) | (26,000)
Net Carrying Value | 223,500 | 223,700 | 227,700
Other acquired intangible assets |  |  |
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | 46,800 | 46,800 | 46,800
Accumulated Amortization | (31,500) | (30,500) | (27,600)
Accumulated Impairment | (1,500) | (1,500) | (1,200)
Net Carrying Value | 13,800 | 14,800 | 18,100
Amortizable | Marketing-related intangible assets |  |  |
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | 22,100 | 22,100 | 22,100
Accumulated Amortization | (21,700) | (21,500) | (20,900)
Accumulated Impairment | 0 | 0 | 0
Net Carrying Value | 400 | 600 | 1,200
Amortizable | Customer-related intangible assets |  |  |
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | 416,400 | 416,400 | 416,400
Accumulated Amortization | (154,400) | (147,400) | (125,400)
Accumulated Impairment | (10,300) | (10,300) | (2,500)
Net Carrying Value | 251,800 | 258,800 | 288,400
Amortizable | Other acquired intangible assets |  |  |
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | 39,700 | 39,700 | 39,700
Accumulated Amortization | (31,500) | (30,500) | (27,600)
Accumulated Impairment | (300) | (300) | 0
Net Carrying Value | 7,900 | 8,900 | 12,200
Nonamortizable | Marketing-related intangible assets |  |  |
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | 252,500 | 252,500 | 252,500
Accumulated Amortization | 0 | 0 | 0
Accumulated Impairment | (29,400) | (29,400) | (26,000)
Net Carrying Value | 223,100 | 223,100 | 226,500
Nonamortizable | Other acquired intangible assets |  |  |
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | 7,100 | 7,100 | 7,100
Accumulated Amortization | 0 | 0 | 0
Accumulated Impairment | (1,200) | (1,200) | (1,200)
Net Carrying Value | $ 5,900 | $ 5,900 | $ 5,900

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