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Commitments and Contingencies (Details)
$ in Millions
3 Months Ended
Oct. 06, 2022
Oct. 01, 2021
individual
Nov. 30, 2022
USD ($)
Nov. 30, 2021
USD ($)
Commitments and Contingencies Disclosure [Abstract]        
Standard warranty term     5 years  
Movement in Standard Product Warranty Accrual [Roll Forward]        
Beginning balance     $ 27.3 $ 20.3
Warranty and recall costs     3.7 4.4
Payments and other deductions     (8.6) (4.5)
Ending balance     $ 22.4 $ 20.2
Shareholder Derivative Complaint        
Loss Contingencies [Line Items]        
Number of former executives alleged to be in violation | individual   3    
Status report submission period 45 days