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Income Taxes - Components of Income Tax Expense (Benefit) (Details) - USD ($) $ in Millions	12 Months Ended
	Jun. 02, 2018	Jun. 03, 2017	May 28, 2016
Income Tax Disclosure [Abstract]
Current: Domestic - Federal	$ 30.2	$ 28.7	$ 36.4
Domestic - State	4.3	2.3	6.4
Foreign	10.7	11.1	6.3
Current Income Tax Expense (Benefit)	45.2	42.1	49.1
Deferred: Domestic - Federal	(4.1)	9.2	7.5
Domestic - State	0.1	2.8	0.2
Foreign	1.2	1.0	2.7
Deferred Income Tax Expense (Benefit)	(2.8)	13.0	10.4
Income tax expense	$ 42.4	$ 55.1	$ 59.5

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