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Fair Value of Financial Instruments Fair Value of Financial Instruments (Details) £ in Millions, $ in Millions			12 Months Ended
	Jun. 12, 2017 USD ($)	Sep. 13, 2016 USD ($)	May 30, 2020 USD ($)	Jun. 01, 2019 USD ($)	Jun. 02, 2018 USD ($)	Jun. 03, 2017 USD ($)	Jun. 01, 2019 GBP (£)	Sep. 02, 2018 USD ($)	Jun. 03, 2018 USD ($)	Jun. 02, 2018 GBP (£)	Jun. 04, 2017 USD ($)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Cumulative effect of accounting change									$ 1.9		$ (0.2)
Derivative Liability, Notional Amount				$ 38.1	$ 37.3
Derivative Asset, Notional Amount | £							£ 19.2			£ 19.9
Other Comprehensive Income (Loss), Derivatives Qualifying as Hedges, Net of Tax				(12.8)	7.5	$ 2.1
Equity Securities without Readily Determinable Fair Value, Upward Price Adjustment, Annual Amount				2.1	0.0	0.0
Equity Securities without Readily Determinable Fair Value, Amount				$ 3.6
Interest rate swap agreement
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Derivative Asset, Notional Amount	$ 75.0	$ 150.0
Debt Conversion, Converted Instrument, Rate	238.70%	1.949%
Foreign Exchange Forward | Not Designated as Hedging Instrument
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Derivative, Term of Contract				30 days
Quoted Prices With Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring [Member] | Interest rate swap agreement
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Derivative Liability, Notional Amount					0.0
Interest Rate Swap Agreement				$ (1.2)
Other Noncurrent Assets | Quoted Prices With Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring [Member] | Interest rate swap agreement
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Interest Rate Swap Agreement				1.0	15.0
Other Noncurrent Liabilities | Quoted Prices With Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring [Member] | Interest rate swap agreement
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Interest Rate Swap Agreement				2.2	0.0
Accumulated Other Comprehensive Income (Loss)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Cumulative effect of accounting change									1.4
Accumulated Net Gain (Loss) from Cash Flow Hedges Attributable to Parent
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Cumulative effect of accounting change								$ 1.5
Reclassification from Accumulated Other Comprehensive Income, Current Period, before Tax				$ 0.5	$ 0.3	$ 0.0
Accounting Standard Update 2016-01 | Accumulated Other Comprehensive Income (Loss)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Cumulative effect of accounting change									$ 0.1
Scenario, Forecast
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Derivative Instruments, Gain (Loss) Reclassification from Accumulated OCI to Income, Estimated Net Amount to be Transferred			$ 0.3

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Amount after tax of increase (decrease) to equity or (increase) decrease to net assets, resulting from the cumulative effect adjustment of a new accounting principle applied in the period of adoption.

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Nominal or face amount used to calculate payments on the derivative asset.

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Period the derivative contract is outstanding, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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Amount of investment in equity security without readily determinable fair value.

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