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Fair Value Measurements - Fair Value Hierarchy (Details) - USD ($) $ in Millions | Dec. 02, 2017 | Jun. 03, 2017
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Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | $ 8.5 | $ 8.6
Fixed Income Securities |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | 7.6 | 7.7
Mutual funds - equity |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | 0.9 | 0.9
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Deferred compensation plan | 14.3 | 12.8
Total | 28.4 | 25.2
Contingent consideration | 0.0 | 0.0
Total | 0.9 | 0.6
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Foreign Exchange Forward |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Foreign currency forward contracts | 0.4 | 0.5
Foreign currency forward contracts | 0.5 | 0.6
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Interest Rate Swap |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Interest rate swap agreement | 5.2 | 3.3
Interest rate swap agreement | 0.4 | 0.0
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Fixed Income Securities |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | 7.6 | 7.7
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Mutual funds - equity |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | 0.9 | 0.9
Fair Value, Inputs, 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
Contingent consideration | 0.5 | 0.5
Total | 0.5 | 0.5
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring | Foreign Exchange Forward |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Foreign currency forward contracts | 0.0 | 0.0
Foreign currency forward contracts | 0.0 | 0.0
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring | Interest Rate Swap |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Interest rate swap agreement | 0.0 | 0.0
Interest rate swap agreement | 0.0 | 0.0
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring | Fixed Income Securities |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | 0.0 | 0.0
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring | Mutual funds - equity |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | $ 0.0 | $ 0.0

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- Definition Amount of investment in debt and equity securities categorized neither as held-to-maturity nor trading. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 320 -SubTopic 10 -Section 25 -Paragraph 1 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=65884222&loc=d3e22054-111558 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 320 -SubTopic 10 -Section 50 -Paragraph 5 -Subparagraph (aa) -URI http://asc.fasb.org/extlink&oid=73527792&loc=d3e27232-111563 Reference 3: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 320 -SubTopic 10 -Section 45 -Paragraph 1 -URI http://asc.fasb.org/extlink&oid=66010992&loc=d3e26610-111562 + Details
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