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Restructuring and Integration Expense - Schedule of Restructuring Rollforward (Details) - USD ($)
$ in Millions
 3 Months Ended 12 Months Ended
Sep. 02, 2023
Sep. 03, 2022
Jun. 03, 2023
Restructuring Reserve [Roll Forward]      
Restructuring Costs $ 5.2 $ 0.5  
2023 Restructuring Plan      
Restructuring Reserve [Roll Forward]      
Restructuring Costs     $ 34.0
Severance and Employee Benefit | 2024 Restructuring Plan      
Restructuring Reserve [Roll Forward]      
Beginning balance 0.0    
Restructuring Costs 5.2    
Amounts Paid (1.8)    
Ending balance 3.4   0.0
Severance and Employee Benefit | 2023 Restructuring Plan      
Restructuring Reserve [Roll Forward]      
Beginning balance 7.3    
Restructuring Costs 0.0   27.9
Amounts Paid (3.8)    
Ending balance $ 3.5   $ 7.3