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Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Millions
 3 Months Ended
Sep. 03, 2022
Aug. 28, 2021
Accumulated Other Comprehensive Income [Roll Forward]    
Balance at beginning of period $ 1,427.1  
Other comprehensive (loss) income, net of tax before reclassifications (57.8) $ (16.7)
Reclassification from accumulated other comprehensive loss - Other, net 0.1 1.7
Tax benefit (0.1) (0.2)
Net reclassifications 0.0 1.5
Other comprehensive (loss), net of tax (57.8) (15.2)
Balance at end of period 1,374.8  
Accumulated Other Comprehensive Loss    
Accumulated Other Comprehensive Income [Roll Forward]    
Balance at beginning of period (107.1) (65.1)
Other comprehensive (loss), net of tax (57.8) (15.2)
Balance at end of period (164.9) (80.3)
Cumulative Translation Adjustments    
Accumulated Other Comprehensive Income [Roll Forward]    
Balance at beginning of period (93.9) (3.9)
Other comprehensive (loss) income, net of tax before reclassifications (72.5) (16.5)
Reclassification from accumulated other comprehensive loss - Other, net 0.0 0.0
Tax benefit 0.0 0.0
Net reclassifications 0.0 0.0
Other comprehensive (loss), net of tax (72.5) (16.5)
Balance at end of period (166.4) (20.4)
Pension and Other Post-retirement Benefit Plans    
Accumulated Other Comprehensive Income [Roll Forward]    
Balance at beginning of period (36.9) (50.4)
Other comprehensive (loss) income, net of tax before reclassifications 0.0 0.0
Reclassification from accumulated other comprehensive loss - Other, net 0.5 2.5
Tax benefit (0.1) (0.2)
Net reclassifications 0.4 2.3
Other comprehensive (loss), net of tax 0.4 2.3
Balance at end of period (36.5) (48.1)
Interest Rate Swap Agreement    
Accumulated Other Comprehensive Income [Roll Forward]    
Balance at beginning of period 23.7 (10.8)
Other comprehensive (loss) income, net of tax before reclassifications 14.7 (0.2)
Reclassification from accumulated other comprehensive loss - Other, net (0.4) (0.8)
Tax benefit 0.0 0.0
Net reclassifications (0.4) (0.8)
Other comprehensive (loss), net of tax 14.3 (1.0)
Balance at end of period $ 38.0 $ (11.8)