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Fair Value Measurements - Fair Value Hierarchy (Details) - USD ($) $ in Millions	Aug. 31, 2019	Jun. 01, 2019
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Noncontrolling Interest, Ownership Percentage by Noncontrolling Owners		5.00%
Mutual funds - equity
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - equity	$ 0.9	$ 0.9
Mutual funds - fixed income
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - fixed income	8.1	7.9
NAV | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - equity	0.0	0.0
Deferred compensation plan	0.0	0.0
Total	60.6	69.5
Foreign currency forward contracts	0.0
Total	0.0	0.0
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Deferred compensation plan	13.5	12.5
Total	14.4	13.4
Total	0.1	1.4
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Foreign currency forward contracts
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Foreign currency forward contracts	0.1	1.4
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Other Noncurrent Assets | Interest rate swap agreement
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Interest rate swap agreement - asset	0.0	1.0
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Other Assets
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - fixed income	8.1	8.9
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Other Liabilities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - fixed income	12.7	2.2
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Other Liabilities | Interest rate swap agreement
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Interest rate swap agreement - liability	12.7	2.2
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Mutual funds - equity
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - equity	0.9	0.9
Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring | Mutual funds - fixed income
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - fixed income	8.1	7.9
Management Estimate (Level 3) | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Deferred compensation plan	0.0	0.0
Total	0.0	0.0
Total	0.0	0.0
Management Estimate (Level 3) | Fair Value, Measurements, Recurring | Foreign currency forward contracts
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Foreign currency forward contracts	0.0	0.0
Management Estimate (Level 3) | Fair Value, Measurements, Recurring | Mutual funds - equity
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Mutual funds - equity	0.0	0.0
Money market funds | NAV | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Money market funds	60.6	69.5
Money market funds | Quoted Prices with Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Money market funds	0.0	0.0
Money market funds | Management Estimate (Level 3) | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Money market funds	$ 0.0	$ 0.0

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