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Accumulated Other Comprehensive Loss, Net (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
Jun. 30, 2024
Jun. 30, 2023
Jun. 30, 2024
Jun. 30, 2023
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Beginning balance $ 1,542.6 $ 1,247.3 $ 1,379.1 $ 1,070.1
Other comprehensive income, net of tax (7.9) 6.7 14.3 47.1
Ending balance 1,607.8 1,329.9 1,607.8 1,329.9
Foreign Currency Translation Adjustment        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Beginning balance     (31.2)  
Other comprehensive income, net of tax     (6.9)  
Ending balance (38.1)   (38.1)  
Pension Benefits Adjustment        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Beginning balance     (2.2)  
Other comprehensive income, net of tax     0.0  
Ending balance (2.2)   (2.2)  
Cash Flow Hedge        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Beginning balance     (18.4)  
Other comprehensive income, net of tax     21.2  
Ending balance 2.8   2.8  
Accumulated Other Comprehensive Loss, net        
AOCI Attributable to Parent, Net of Tax [Roll Forward]        
Beginning balance (29.6) (50.2) (51.8) (90.6)
Other comprehensive income, net of tax (7.9) 6.7 14.3 47.1
Ending balance $ (37.5) $ (43.5) $ (37.5) $ (43.5)