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Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands | May 25, 2024 | Aug. 26, 2023
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Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | $ 435,470 | $ 439,584
Accumulated Amortization | 309,593 | 293,966
Net Carrying Amount | 125,877 | 145,618
Customer Contracts |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 314,705 | 315,448
Accumulated Amortization | 224,319 | 211,996
Net Carrying Amount | 90,386 | 103,452
Software |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 80,945 | 80,538
Accumulated Amortization | 49,546 | 45,117
Net Carrying Amount | 31,399 | 35,421
Other Intangible Assets |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross Carrying Amount | 39,820 | 43,598
Accumulated Amortization | 35,728 | 36,853
Net Carrying Amount | $ 4,092 | $ 6,745

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