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Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Millions
 3 Months Ended
Sep. 01, 2018
Sep. 02, 2017
Jun. 03, 2018
Jun. 04, 2017
Accumulated Other Comprehensive Income (Loss)        
Balance at beginning of year $ 664.8      
Other comprehensive income (loss) (7.8) $ 3.6    
Balance at end of period 673.2 608.7    
Cumulative Translation Adjustments        
Accumulated Other Comprehensive Income (Loss)        
Balance at beginning of year (34.1) (36.8)    
Cumulative effect of accounting change     $ 0.0  
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax (7.9) 4.4    
Reclassification from Accumulated Other Comprehensive Income, Current Period, before Tax 0.0 0.0    
Tax benefit 0.0 0.0    
Reclassification from Accumulated Other Comprehensive Income, Current Period, Net of Tax 0.0 0.0    
Other comprehensive income (loss) (7.9) 4.4    
Balance at end of period (42.0) (32.4)    
Pension and Other Post-retirement Benefit Plans        
Accumulated Other Comprehensive Income (Loss)        
Balance at beginning of year (37.2) (47.6)    
Cumulative effect of accounting change     0.0  
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax 0.0 0.0    
Reclassification from Accumulated Other Comprehensive Income, Current Period, before Tax 0.8 1.0    
Tax benefit (0.1) (0.2)    
Reclassification from Accumulated Other Comprehensive Income, Current Period, Net of Tax 0.7 0.8    
Other comprehensive income (loss) 0.7 0.8    
Balance at end of period (36.5) (46.8)    
Unrealized Gains on Available-for-sale Securities        
Accumulated Other Comprehensive Income (Loss)        
Balance at beginning of year 0.1 0.1    
Cumulative effect of accounting change     (0.1)  
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax (0.1) 0.0    
Reclassification from Accumulated Other Comprehensive Income, Current Period, before Tax 0.0 0.0    
Tax benefit 0.0 0.0    
Reclassification from Accumulated Other Comprehensive Income, Current Period, Net of Tax 0.0 0.0    
Other comprehensive income (loss) (0.1) 0.0    
Balance at end of period (0.1) 0.1    
Interest Rate Swap Agreement        
Accumulated Other Comprehensive Income (Loss)        
Balance at beginning of year 9.9 2.1    
Cumulative effect of accounting change     0.0  
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax (0.5) (1.6)    
Reclassification from Accumulated Other Comprehensive Income, Current Period, before Tax 0.0 0.0    
Tax benefit 0.0 0.0    
Reclassification from Accumulated Other Comprehensive Income, Current Period, Net of Tax 0.0 0.0    
Other comprehensive income (loss) (0.5) (1.6)    
Balance at end of period 9.4 0.5    
Accumulated Other Comprehensive Loss        
Accumulated Other Comprehensive Income (Loss)        
Balance at beginning of year (61.3) (82.2)    
Cumulative effect of accounting change     $ (0.1) $ 0.0
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax (8.5) 2.8    
Reclassification from Accumulated Other Comprehensive Income, Current Period, before Tax 0.8 1.0    
Tax benefit (0.1) (0.2)    
Reclassification from Accumulated Other Comprehensive Income, Current Period, Net of Tax 0.7 0.8    
Other comprehensive income (loss) (7.8) 3.6    
Balance at end of period $ (69.2) $ (78.6)