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Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands | Aug. 31, 2024 | Aug. 26, 2023
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Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | $ 435,754 | $ 439,584
Accumulated Amortization | 315,755 | 293,966
Net Carrying Amount | 119,999 | 145,618
Customer Contracts |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 314,446 | 315,448
Accumulated Amortization | 228,456 | 211,996
Net Carrying Amount | 85,990 | 103,452
Software |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 81,482 | 80,538
Accumulated Amortization | 51,023 | 45,117
Net Carrying Amount | 30,459 | 35,421
Other Intangible Assets |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 39,826 | 43,598
Accumulated Amortization | 36,276 | 36,853
Net Carrying Amount | $ 3,550 | $ 6,745

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