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Employee and Retiree Benefits - Deferred Compensation Narrative (Details) - USD ($) $ in Millions | 12 Months Ended
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Aug. 27, 2022 | Aug. 28, 2021 | Aug. 29, 2020
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items] |  |  |
Matching contribution amount | $ 12.0 | $ 5.6 | $ 3.4
Employer discretionary contribution amount | $ 12.1 | 6.1 | 0.0
Key Employees | Non-Qualified Deferred Compensation Program (1981) |  |  |
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items] |  |  |
Vesting age | 55 years |  |
Requisite service period | 5 years |  |
Requisite service period prior to December 1992 | 20 years |  |
Deferred compensation expense | $ 0.6 | 0.8 | $ 0.9
Officers and Managers | Supplemental Employee Retirement Plan (SERP) |  |  |
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items] |  |  |
Contractual amount of years after retirement | 15 years |  |
Officers and Key Employees | Executive Deferred Compensation Plan 2007 |  |  |
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items] |  |  |
Maximum salary deferral | 50.00% |  |
Maximum cash incentive award deferral | 100.00% |  |
Deferred compensation assets | $ 1.4 | $ 1.0 |

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