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Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
Feb. 26, 2022
Feb. 27, 2021
Feb. 26, 2022
Feb. 27, 2021
Accumulated Other Comprehensive Income [Roll Forward]        
Balance at beginning of period     $ 849.6  
Other comprehensive income (loss), net of tax $ 17.1 $ 18.6 (29.9) $ 57.3
Balance at end of period 1,455.9   1,455.9  
Cumulative Translation Adjustments        
Accumulated Other Comprehensive Income [Roll Forward]        
Balance at beginning of period     (3.9) (56.0)
Other comprehensive (loss) income, net of tax before reclassifications     (46.7) 42.8
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 income (loss), net of tax     (46.7) 42.8
Balance at end of period (50.6) (13.2) (50.6) (13.2)
Pension and Other Post-retirement Benefit Plans        
Accumulated Other Comprehensive Income [Roll Forward]        
Balance at beginning of period     (50.4) (59.2)
Other comprehensive (loss) income, net of tax before reclassifications     0.0 0.0
Reclassification from accumulated other comprehensive loss - Other, net     6.4 4.5
Tax benefit     (0.8) (0.8)
Net reclassifications     5.6 3.7
Other comprehensive income (loss), net of tax     5.6 3.7
Balance at end of period (44.8) (55.5) (44.8) (55.5)
Unrealized Gains on Available-for-sale Securities        
Accumulated Other Comprehensive Income [Roll Forward]        
Balance at beginning of period     0.0 0.1
Other comprehensive (loss) income, net of tax before reclassifications     0.0 (0.1)
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 income (loss), net of tax     0.0 (0.1)
Balance at end of period 0.0 0.0 0.0 0.0
Interest Rate Swap Agreements        
Accumulated Other Comprehensive Income [Roll Forward]        
Balance at beginning of period     (10.8) (18.9)
Other comprehensive (loss) income, net of tax before reclassifications     16.3 11.1
Reclassification from accumulated other comprehensive loss - Other, net     (3.1) (3.3)
Tax benefit     0.0 0.0
Net reclassifications     (3.1) (3.3)
Other comprehensive income (loss), net of tax     13.2 7.8
Balance at end of period 2.4 (11.1) 2.4 (11.1)
Accumulated Other Comprehensive Loss        
Accumulated Other Comprehensive Income [Roll Forward]        
Balance at beginning of period     (65.1) (134.0)
Other comprehensive (loss) income, net of tax before reclassifications     (30.4) 53.8
Reclassification from accumulated other comprehensive loss - Other, net     3.3 1.2
Tax benefit     (0.8) (0.8)
Net reclassifications     2.5 0.4
Other comprehensive income (loss), net of tax     (27.9) 54.2
Balance at end of period $ (93.0) $ (79.8) $ (93.0) $ (79.8)