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Share-Based Compensation (Details) - USD ($)
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
SHARE-BASED COMPENSATION      
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Available for Grant 712,092    
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost $ 180,000    
Performance-Accelerated Restricted Share Awards      
SHARE-BASED COMPENSATION      
Vesting period 5 years    
Pretax compensation expense $ 5,600,000 $ 4,300,000 $ 4,000,000.0
Compensation Plan for Non-Employee Directors      
SHARE-BASED COMPENSATION      
Pretax compensation expense 1,300,000 1,300,000 1,100,000
Total share-based compensation cost 1,400,000    
Total income tax benefit recognized   1,200,000 1,100,000
Total unrecognized compensation cost related to share-based compensation arrangements $ 7,900,000    
Remaining weighted-average period for recognition of total unrecognized compensation cost 1 year 7 months 6 days    
Compensation Plan for Non-Employee Directors | Selling, general and administrative expenses      
SHARE-BASED COMPENSATION      
Total share-based compensation cost $ 6,900,000 $ 5,600,000 $ 5,100,000
RSU      
SHARE-BASED COMPENSATION      
Vesting period 3 years 6 months