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Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Nov. 27, 2021
Nov. 28, 2020
Nov. 27, 2021
Nov. 28, 2020
Accumulated Other Comprehensive Income [Roll Forward]        
Balance at beginning of period     $ 849.6  
Other comprehensive (loss) income, net of tax before reclassifications $ (60.9) $ 4.9 (52.1) $ 35.1
Other comprehensive (loss) income, net of tax before reclassifications 0.0 0.0    
Net current period other comprehensive (loss) income (55.1) 7.2 (45.0) 38.7
Balance at end of period 1,436.4   1,436.4  
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     (50.1) 32.3
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 (loss) income     (50.1) 32.3
Balance at end of period (54.0) (23.7) (54.0) (23.7)
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     4.7 3.0
Tax benefit     (0.6) (0.5)
Net reclassifications     4.1 2.5
Net current period other comprehensive (loss) income     4.1 2.5
Balance at end of period (46.3) (56.7) (46.3) (56.7)
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
Net current period other comprehensive (loss) income     0.0 (0.1)
Balance at end of period 0.0 0.0 0.0 0.0
Interest Rate Swap Agreement        
Accumulated Other Comprehensive Income [Roll Forward]        
Balance at beginning of period     (10.8) (18.9)
Other comprehensive (loss) income, net of tax before reclassifications     4.9 3.4
Reclassification from accumulated other comprehensive loss - Other, net       (2.2)
Tax benefit     0.0 0.0
Net reclassifications     (1.9) (2.2)
Net current period other comprehensive (loss) income     3.0 1.2
Balance at end of period (7.8) (17.7) (7.8) (17.7)
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     (45.2) 35.6
Reclassification from accumulated other comprehensive loss - Other, net     2.8 0.8
Tax benefit     (0.6) (0.5)
Net reclassifications     2.2 0.3
Net current period other comprehensive (loss) income     (43.0) 35.9
Balance at end of period $ (108.1) $ (98.1) $ (108.1) $ (98.1)