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Restructuring Expenses (Details) - USD ($)
$ in Millions
 12 Months Ended 24 Months Ended 36 Months Ended
May 30, 2020
Jun. 01, 2019
Jun. 02, 2018
May 30, 2020
May 30, 2020
Restructuring Cost and Reserve [Line Items]          
Restructuring expenses $ 26.4 $ 10.2 $ 5.7    
International Contract          
Restructuring Cost and Reserve [Line Items]          
Restructuring expenses 4.8 2.5 3.9    
North America Contract          
Restructuring Cost and Reserve [Line Items]          
Restructuring expenses 18.7 7.7 1.8    
Retail          
Restructuring Cost and Reserve [Line Items]          
Restructuring expenses 2.9 $ 0.0 $ 0.0    
Facilities Consolidation Plan | International Contract          
Restructuring Cost and Reserve [Line Items]          
Restructuring & impairment expenses 1.4       $ 7.8
Assets Held-for-sale, Long Lived, Fair Value Disclosure 7.8     $ 7.8 7.8
Facilities Consolidation Plan | International Contract | Exit or Disposal Activities          
Restructuring Cost and Reserve [Line Items]          
Effect on Future Earnings, Amount 3.0        
Profit Improvement Plan | North America Contract          
Restructuring Cost and Reserve [Line Items]          
Effect on Future Earnings, Amount 10.0        
Restructuring expenses 1.7     11.1  
Nemschoff Plan | North America Contract          
Restructuring Cost and Reserve [Line Items]          
Restructuring expenses 3.2        
Restructuring and Related Cost, Expected Cost 5.0     $ 5.0 $ 5.0
North American Sales and Global Product Teams Plan          
Restructuring Cost and Reserve [Line Items]          
Restructuring expenses 2.6        
Retail Plan | Retail | Severance and employee related expenses          
Restructuring Cost and Reserve [Line Items]          
Restructuring expenses 2.2        
May 2020 Restructuring Plan | Severance and employee related expenses          
Restructuring Cost and Reserve [Line Items]          
Effect on Future Earnings, Amount 40.0        
Restructuring expenses $ 15.3