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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, 2021
Mar. 31, 2020
Mar. 31, 2021
Mar. 31, 2020
Share-Based Compensation (Textual) [Abstract]        
Pre-tax share-based compensation expense $ 12.9 $ 10.9 $ 24.4 $ 22.4
Stock options        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     196 970
Wtd. Avg. Share Fair Value (usd per share)     $ 55.50 $ 35.78
Performance shares        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     44 37
Wtd. Avg. Share Fair Value (usd per share)     $ 298.10 $ 265.04
Restricted stock and restricted stock units        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     167 49
Wtd. Avg. Share Fair Value (usd per share)     $ 246.61 $ 192.60
Unrestricted stock        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Grants (in shares)     6 7
Wtd. Avg. Share Fair Value (usd per share)     $ 228.80 $ 171.51