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Stock-based Compensation - Fair Value Measurement Assumptions (Details)
12 Months Ended
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Disclosure Of Compensation Related Costs Sharebased Payments [Abstract]      
Risk-free interest rate 2.88% 1.76% 1.39%
Expected dividend yield of stock 0.00% 0.00% 0.00%
Expected volatility of stock 17.00% 16.00% 16.30%
Vesting period 3 years 2 years 10 months 24 days 2 years 9 months 18 days