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Share-Based Compensation (Summary of Deferred Stock Units Activity) (Details) - $ / shares
12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Deferred Stock Units      
Shares      
Outstanding, beginning (shares) 730,000    
Granted (shares) 206,000    
Paid out (shares) (159,000)    
Forfeited (shares) (87,000)    
Adjusted (in shares) 10,000    
Outstanding, ending (shares) 700,000 730,000  
Weighted Average Grant Date Fair Value      
Outstanding, beginning (in dollars per share) $ 222.13    
Granted (in dollars per share) 389.34    
Paid out (in dollars per share) 164.08    
Forfeited (in dollars per share) 248.26    
Adjusted (in dollars per share) 315.33    
Outstanding, ending (in dollars per share) $ 282.60 $ 222.13  
Market-Based Deferred Stock Unit      
Shares      
Granted (shares) 85,612 74,364 77,251
Weighted Average Grant Date Fair Value      
Granted (in dollars per share) $ 502.03 $ 427.23 $ 235.48