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Stock-Based Compensation - Schedule of Nonvested Stock Activity (Details) - Nonvested Stock Awards [Member] - $ / shares
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Number of Shares      
Nonvested, beginning of year (in shares) 346,808 411,510 332,473
Granted (in shares) 307,025 183,725 278,175
Forfeited (in shares) (36,545) (27,076) (13,610)
Vested (in shares) (222,400) (221,351) (185,528)
Nonvested, end of year (in shares) 394,888 346,808 411,510
Weighted-Average Per Share Fair Value      
Nonvested, beginning of year (in dollars per share) $ 79.44 $ 72.66 $ 69.15
Granted (in dollars per share) 82.80 87.82 69.98
Forfeited (in dollars per share) 78.81 80.57 71.17
Vested (in dollars per share) 80.39 73.64 62.47
Nonvested, end of year (in dollars per share) $ 81.58 $ 79.44 $ 72.66