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Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands | Nov. 25, 2023 | Aug. 26, 2023
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Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | $ 435,683 | $ 439,584
Accumulated Amortization | 297,215 | 293,966
Net Carrying Amount | 138,468 | 145,618
Customer Contracts |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 314,542 | 315,448
Accumulated Amortization | 216,104 | 211,996
Net Carrying Amount | 98,438 | 103,452
Software |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 81,336 | 80,538
Accumulated Amortization | 46,407 | 45,117
Net Carrying Amount | 34,929 | 35,421
Other Intangible Assets |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 39,805 | 43,598
Accumulated Amortization | 34,704 | 36,853
Net Carrying Amount | $ 5,101 | $ 6,745

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