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Stock-based Compensation - Restricted Stock and Restricted Stock Unit Activity (Details) - Restricted Stock Awards
12 Months Ended
Sep. 30, 2019
$ / shares
shares
Performance Vesting  
Shares/ Units  
Nonvested at beginning of period (in shares) | shares 266,082
Granted (in shares) | shares 99,260
Vested (in shares) | shares (45,157)
Forfeited (in shares) | shares (56,275)
Nonvested at end of period (in shares) | shares 263,910
Weighted Average Grant Date Fair Value Per Share  
Nonvested at beginning of period (in dollars per share) | $ / shares $ 66.69
Granted (in dollars per share) | $ / shares 80.72
Vested (in dollars per share) | $ / shares 62.39
Forfeited (in dollars per share) | $ / shares 64.74
Nonvested at end of period (in dollars per share) | $ / shares $ 73.11
Time Vesting  
Shares/ Units  
Nonvested at beginning of period (in shares) | shares 103,600
Granted (in shares) | shares 49,340
Vested (in shares) | shares (50,013)
Forfeited (in shares) | shares (6,650)
Nonvested at end of period (in shares) | shares 96,277
Weighted Average Grant Date Fair Value Per Share  
Nonvested at beginning of period (in dollars per share) | $ / shares $ 64.60
Granted (in dollars per share) | $ / shares 77.14
Vested (in dollars per share) | $ / shares 60.45
Forfeited (in dollars per share) | $ / shares 69.64
Nonvested at end of period (in dollars per share) | $ / shares $ 72.83