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Shareholders' Equity - Additional information (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
May 31, 2019
Stockholders Equity Note [Abstract]        
Number of shares of common stock authorized for buyback (in shares)       10,000,000
Remaining number of shares authorized to be repurchased (in shares) 6,531,394      
Treasury stock, shares, acquired (in shares) 927,934 550,853 4,866,532  
Treasury stock, value, acquired, cost method $ 107.8 $ 40.8 $ 350.1