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Investments and Fair Value Measurements - Fair Value of Contingent Consideration (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Feb. 24, 2024
Feb. 25, 2023
Feb. 24, 2024
Feb. 25, 2023
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]        
Beginning fair value - contingent consideration $ 19.2 $ 40.2 $ 18.4 $ 39.8
Fair value adjustments 0.3 1.6 1.1 2.0
Ending fair value - contingent consideration $ 19.5 $ 41.8 $ 19.5 $ 41.8