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Other Intangible Assets - Components of Gross and Net Acquired Intangible Assets (Details) - USD ($) $ in Thousands | Jun. 29, 2024 | Sep. 30, 2023 | Jun. 24, 2023
--- | --- | --- | ---
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | $ 737,900 | $ 737,800 | $ 737,800
Accumulated Amortization | (223,800) | (199,400) | (191,200)
Accumulated Impairment | (41,200) | (41,200) | (34,500)
Net Carrying Value | 472,854 | 497,228 | 512,175
Marketing-related intangible assets |  |  |
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | 274,700 | 274,600 | 274,600
Accumulated Amortization | (22,000) | (21,500) | (21,300)
Accumulated Impairment | (29,400) | (29,400) | (26,000)
Net Carrying Value | 223,200 | 223,700 | 227,300
Other acquired intangible assets |  |  |
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | 46,800 | 46,800 | 46,800
Accumulated Amortization | (33,400) | (30,500) | (29,500)
Accumulated Impairment | (1,500) | (1,500) | (1,200)
Net Carrying Value | 11,900 | 14,800 | 16,100
Amortizable | Marketing-related intangible assets |  |  |
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | 22,100 | 22,100 | 22,100
Accumulated Amortization | (22,000) | (21,500) | (21,300)
Accumulated Impairment | 0 | 0 | 0
Net Carrying Value | 100 | 600 | 800
Amortizable | Customer-related intangible assets |  |  |
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | 416,400 | 416,400 | 416,400
Accumulated Amortization | (168,400) | (147,400) | (140,300)
Accumulated Impairment | (10,300) | (10,300) | (7,300)
Net Carrying Value | 237,700 | 258,800 | 268,800
Amortizable | Other acquired intangible assets |  |  |
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Gross | 39,700 | 39,700 | 39,700
Accumulated Amortization | (33,400) | (30,500) | (29,500)
Accumulated Impairment | (300) | (300) | 0
Net Carrying Value | 6,000 | 8,900 | 10,200
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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