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Intangible Assets and Goodwill - Additional Information (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended 12 Months Ended
May 27, 2022
May 28, 2021
May 27, 2022
May 28, 2021
Aug. 27, 2021
Finite Lived Intangible Assets [Line Items]          
Intangible assets $ 1.1 $ 64.5 $ 1.1 $ 64.5  
Intangible assets estimated useful lives     17 years 6 months 6 years 8 months 12 days  
Amortization of intangible assets 5.9 $ 6.2 $ 18.2 $ 13.0  
Finite-lived intangible assets, expected amortization for remainder of 2022 5.6   5.6    
Finite-lived intangible assets, expected amortization for 2023 21.8   21.8    
Finite-lived intangible assets, expected amortization for 2024 17.8   17.8    
Finite-lived intangible assets, expected amortization for 2025 15.3   15.3    
Finite-lived intangible assets, expected amortization for 2026 8.5   8.5    
Finite-lived intangible assets, expected amortization, thereafter $ 14.1   14.1    
Memory Solutions          
Finite Lived Intangible Assets [Line Items]          
Goodwill, increase (decrease)     $ 0.8   $ 0.3