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Income Taxes - Components of Income Tax Expense (Benefit) (Details) - USD ($)
$ in Millions
 12 Months Ended
May 30, 2020
Jun. 01, 2019
Jun. 02, 2018
Income Tax Disclosure [Abstract]      
Current: Domestic - Federal $ 12.0 $ 19.0 $ 30.2
Domestic - State 5.7 6.4 4.3
Foreign 13.3 12.9 10.7
Current Income Tax Expense (Benefit) 31.0 38.3 45.2
Deferred: Domestic - Federal (16.8) 1.0 (4.1)
Domestic - State (3.9) (0.2) 0.1
Foreign (4.3) 0.5 1.2
Deferred Income Tax Expense (Benefit) (25.0) 1.3 (2.8)
Income tax expense $ 6.0 $ 39.6 $ 42.4