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Share-Based Compensation (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
3 Months Ended 6 Months Ended
Mar. 31, 2023
Mar. 31, 2022
Mar. 31, 2023
Mar. 31, 2022
Share-Based Compensation (Textual) [Abstract]        
Pre-tax share-based compensation expense $ 23.2 $ 15.7 $ 41.6 $ 31.2
Stock options        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     233 164
Wtd. Avg. Share Fair Value (usd per share)     $ 77.62 $ 87.68
Performance shares        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     66 37
Wtd. Avg. Share Fair Value (usd per share)     $ 340.77 $ 481.28
Restricted stock and restricted stock units        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     228 149
Wtd. Avg. Share Fair Value (usd per share)     $ 261.59 $ 343.56
Unrestricted stock        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     7 3
Wtd. Avg. Share Fair Value (usd per share)     $ 261.72 $ 345.00