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Employee Benefit Plans - Narrative (Details) $ in Millions | 3 Months Ended | 9 Months Ended |
--- | --- | --- | ---
May 25, 2024 USD ($) RetirementPlan | May 27, 2023 USD ($) | May 25, 2024 USD ($) RetirementPlan | May 27, 2023 USD ($) | Aug. 26, 2023 USD ($)
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items] |  |  |  |  |
Contributions charged to expense under the plan | $ 5.1 | $ 4.4 | $ 15.2 | $ 14.3 |
SERP |  |  |  |  |
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items] |  |  |  |  |
Number of frozen non-contributory defined benefit pension plans | RetirementPlan | 1 |  | 1 |  |
Amounts charged to expense related to the plans | $ 0.4 | 0.4 | $ 1.3 | 1.3 |
Non-qualified Deferred Compensation Plan |  |  |  |  |
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items] |  |  |  |  |
Amounts charged to expense related to the plans | 0.2 | $ 0.1 | 0.6 | $ 0.3 |
NQDC Plan assets | 3.1 |  | 3.1 |  | $ 2.0
NQDC Plan liabilities | $ 1.3 |  | $ 1.3 |  | $ 0.5

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