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Accumulated Other Comprehensive Loss, Net (Details) - USD ($)
$ in Millions
 3 Months Ended
Dec. 31, 2024
Dec. 31, 2023
AOCI Attributable to Parent, Net of Tax [Roll Forward]    
Beginning balance $ 1,709.1 $ 1,379.1
Other comprehensive loss, net of tax (25.2) 27.6
Ending balance 1,777.4 1,482.8
Foreign Currency Translation Adjustment    
AOCI Attributable to Parent, Net of Tax [Roll Forward]    
Beginning balance (31.3)  
Other comprehensive loss, net of tax (18.3)  
Ending balance (49.6)  
Pension Benefits Adjustment    
AOCI Attributable to Parent, Net of Tax [Roll Forward]    
Beginning balance (1.2)  
Other comprehensive loss, net of tax 0.0  
Ending balance (1.2)  
Cash Flow Hedge    
AOCI Attributable to Parent, Net of Tax [Roll Forward]    
Beginning balance 7.3  
Other comprehensive loss, net of tax (6.9)  
Ending balance 0.4  
Accumulated Other Comprehensive Loss, net    
AOCI Attributable to Parent, Net of Tax [Roll Forward]    
Beginning balance (25.2) (51.8)
Other comprehensive loss, net of tax (25.2) 27.6
Ending balance $ (50.4) $ (24.2)