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Income Taxes - Components of Income Tax Expense (Benefit) (Details) - USD ($)
$ in Millions
 12 Months Ended
Jun. 03, 2023
May 28, 2022
May 29, 2021
Income Tax Disclosure [Abstract]      
Domestic - Federal $ 4.2 $ (3.8) $ 13.2
Domestic - State 2.2 0.2 5.2
Foreign 42.3 38.1 22.8
Current income tax expense (benefit) 48.7 34.5 41.2
Domestic - Federal (32.5) (12.2) 10.4
Domestic - State (4.4) (5.0) 1.4
Foreign (7.3) (6.2) (4.7)
Deferred income tax expense (benefit) (44.2) (23.4) 7.1
Income tax expense $ 4.5 $ 11.1 $ 48.3