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Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Millions
 3 Months Ended
Sep. 02, 2023
Sep. 03, 2022
Accumulated Other Comprehensive Income [Roll Forward]    
Balance at beginning of period $ 1,432.6  
Other comprehensive income (loss), net of tax before reclassifications 4.3 $ (57.8)
Reclassification from accumulated other comprehensive loss - Other, net 7.3 0.1
Tax benefit 0.0 (0.1)
Net reclassifications 7.3 0.0
Net current period other comprehensive income (loss) 11.6 (57.8)
Balance at end of period 1,422.3  
Accumulated Other Comprehensive Loss    
Accumulated Other Comprehensive Income [Roll Forward]    
Balance at beginning of period (95.1) (107.1)
Net current period other comprehensive income (loss) 11.6 (57.8)
Balance at end of period (83.5) (164.9)
Cumulative Translation Adjustments    
Accumulated Other Comprehensive Income [Roll Forward]    
Balance at beginning of period (114.0) (93.9)
Other comprehensive income (loss), net of tax before reclassifications 3.9 (72.5)
Reclassification from accumulated other comprehensive loss - Other, net 0.0 0.0
Tax benefit 0.0 0.0
Net reclassifications 0.0 0.0
Net current period other comprehensive income (loss) 3.9 (72.5)
Balance at end of period (110.1) (166.4)
Pension and Other Post-retirement Benefit Plans    
Accumulated Other Comprehensive Income [Roll Forward]    
Balance at beginning of period (23.8) (36.9)
Other comprehensive income (loss), net of tax before reclassifications 0.0 0.0
Reclassification from accumulated other comprehensive loss - Other, net (0.1) 0.5
Tax benefit 0.0 (0.1)
Net reclassifications (0.1) 0.4
Net current period other comprehensive income (loss) (0.1) 0.4
Balance at end of period (23.9) (36.5)
Interest Rate Swap Agreement    
Accumulated Other Comprehensive Income [Roll Forward]    
Balance at beginning of period 42.7 23.7
Other comprehensive income (loss), net of tax before reclassifications 0.4 14.7
Reclassification from accumulated other comprehensive loss - Other, net 7.4 (0.4)
Tax benefit 0.0 0.0
Net reclassifications 7.4 (0.4)
Net current period other comprehensive income (loss) 7.8 14.3
Balance at end of period $ 50.5 $ 38.0