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Employee Benefit Plans - Schedule of Funded Status and Amounts Recognized in the Balance Sheet (Details) - USD ($)
$ in Millions
 12 Months Ended
Jun. 02, 2018
Jun. 03, 2017
May 28, 2016
Change in benefit obligation:      
Benefit obligation at beginning of year $ 114.8    
Benefit obligation at end of year 106.9 $ 114.8  
Change in plan assets:      
Fair value of plan assets at beginning of year 80.5    
Fair value of plan assets at end of year 94.6 80.5  
Components of the amounts recognized in the Consolidated Balance Sheets:      
Non-current liabilities (15.6) (38.5)  
Post-Retirement Benefits      
Change in benefit obligation:      
Benefit obligation at beginning of year 5.0 5.9  
Interest cost 0.1 0.2 $ 0.2
Foreign exchange impact 0.0 0.0  
Actuarial (gain) loss (0.5) (0.4)  
Benefits paid (0.6) (0.7)  
Benefit obligation at end of year 4.0 5.0 5.9
Change in plan assets:      
Fair value of plan assets at beginning of year 0.0 0.0  
Actual return on plan assets 0.0 0.0  
Foreign exchange impact 0.0 0.0  
Employer contributions 0.6 0.7  
Benefits paid (0.6) (0.7)  
Fair value of plan assets at end of year 0.0 0.0 0.0
Funded status:      
Under funded status at end of year (4.0) (5.0)  
Components of the amounts recognized in the Consolidated Balance Sheets:      
Current liabilities (0.6) (0.7)  
Non-current liabilities (3.4) (4.3)  
Components of the amounts recognized in Accumulated other comprehensive loss before the effect of income taxes:      
Unrecognized net actuarial loss (gain) (1.1) (0.6)  
Accumulated other comprehensive loss (1.1) (0.6)  
Domestic      
Change in benefit obligation:      
Benefit obligation at beginning of year 1.0 1.0  
Interest cost 0.1 0.1 0.0
Foreign exchange impact 0.0 0.0  
Actuarial (gain) loss 0.0 0.0  
Benefits paid (0.1) (0.1)  
Benefit obligation at end of year 1.0 1.0 1.0
Change in plan assets:      
Fair value of plan assets at beginning of year 0.0 0.0  
Actual return on plan assets 0.0 0.0  
Foreign exchange impact 0.0 0.0  
Employer contributions 0.1 0.1  
Benefits paid (0.1) (0.1)  
Fair value of plan assets at end of year 0.0 0.0 0.0
Funded status:      
Under funded status at end of year (1.0) (1.0)  
Components of the amounts recognized in the Consolidated Balance Sheets:      
Current liabilities (0.1) (0.1)  
Non-current liabilities (0.9) (0.9)  
Components of the amounts recognized in Accumulated other comprehensive loss before the effect of income taxes:      
Unrecognized net actuarial loss (gain) 0.3 0.3  
Accumulated other comprehensive loss 0.3 0.3  
International      
Change in benefit obligation:      
Benefit obligation at beginning of year 113.8 104.4  
Interest cost 2.7 2.7 3.8
Foreign exchange impact 4.2 (12.5)  
Actuarial (gain) loss (12.2) 23.4  
Benefits paid (2.6) (4.2)  
Benefit obligation at end of year 105.9 113.8 104.4
Change in plan assets:      
Fair value of plan assets at beginning of year 80.5 85.0  
Actual return on plan assets 1.2 9.6  
Foreign exchange impact 2.8 (10.3)  
Employer contributions 12.7 0.4  
Benefits paid (2.6) (4.2)  
Fair value of plan assets at end of year 94.6 80.5 $ 85.0
Funded status:      
Under funded status at end of year (11.3) (33.3)  
Components of the amounts recognized in the Consolidated Balance Sheets:      
Current liabilities 0.0 0.0  
Non-current liabilities (11.3) (33.3)  
Components of the amounts recognized in Accumulated other comprehensive loss before the effect of income taxes:      
Unrecognized net actuarial loss (gain) 40.8 50.9  
Accumulated other comprehensive loss $ 40.8 $ 50.9