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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, 2022
Mar. 31, 2021
Mar. 31, 2022
Mar. 31, 2021
Share-Based Compensation (Textual) [Abstract]        
Pre-tax share-based compensation expense $ 15.7 $ 12.9 $ 31.2 $ 24.4
Stock options        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     164 196
Wtd. Avg. Share Fair Value (usd per share)     $ 87.68 $ 55.50
Performance shares        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     37 44
Wtd. Avg. Share Fair Value (usd per share)     $ 481.28 $ 298.10
Restricted stock and restricted stock units        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     149 167
Wtd. Avg. Share Fair Value (usd per share)     $ 343.56 $ 246.61
Unrestricted stock        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     3 6
Wtd. Avg. Share Fair Value (usd per share)     $ 345.00 $ 228.80