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Income Taxes - Effective Income Tax Rate Reconciliation (Details) - USD ($) $ in Millions	12 Months Ended
	May 30, 2020	Jun. 01, 2019	Jun. 02, 2018
Income Tax Disclosure [Abstract]
Income taxes computed at the United States Statutory rate	$ (2.8)	$ 41.0	$ 49.0
State and local income taxes, net of federal income tax benefit	1.4	4.9	3.3
Non-deductible goodwill impairment	17.1	0.0	0.0
Gain on consolidation of equity method investments	(5.5)	0.0	0.0
Remeasurement of U.S. deferred tax assets and liabilities due to the Tax Act	0.0	(0.2)	(8.9)
U.S. tax liability on undistributed foreign earnings due to the Tax Act	0.0	(2.6)	9.0
Foreign-derived intangible income	(1.4)	(3.1)	0.0
Global intangible low-taxed income	5.9	6.9	0.0
Foreign statutory rate differences	0.7	1.9	(4.0)
Manufacturing deduction under the American Jobs Creation Act of 2004	0.0	0.0	(2.7)
Research and development credit	(4.4)	(5.3)	(4.2)
Foreign offshore income claim	(1.7)	(0.7)	0.0
Foreign tax credit	(5.8)	(5.7)	(2.4)
Foreign withholding taxes and other miscellaneous foreign taxes	2.7	0.8	1.9
Other, net	(0.2)	1.7	1.4
Income tax expense	$ 6.0	$ 39.6	$ 42.4
Effective tax rate	(44.90%)	20.30%	25.20%

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