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Fair Value Measurements - Fair Value Hierarchy (Details) - USD ($) $ in Millions	Feb. 29, 2020	Jun. 01, 2019
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	8.0	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	14.7	69.5
Foreign currency forward contracts	0.0	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	12.6	12.5
Total	13.5	13.4
Total	0.3	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	0.3	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	8.0	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	17.3	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	17.3	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	8.0	7.9
Money market funds | NAV | Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Money market funds	14.7	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

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- Definition

Fair value portion of probable future economic benefits obtained or controlled by an entity as a result of past transactions or events.

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Amount of investment in debt and equity securities categorized neither as held-to-maturity nor trading.

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Carrying amount as of the balance sheet date of assets held under deferred compensation agreements.

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Fair value portion of liability contracts related to the exchange of different currencies, including, but not limited to, foreign currency options, forward (delivery or nondelivery) contracts, and swaps entered into.

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Fair value of financial and nonfinancial obligations.

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