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Share-Based Compensation (Details) - USD ($)	12 Months Ended
Share-Based Compensation (Details) - USD ($)	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
SHARE-BASED COMPENSATION
Share-Based Payment Arrangement, Expensed and Capitalized, Amount	$ 180,000
Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant	580,437
Performance-Accelerated Restricted Share (PARS) Awards
SHARE-BASED COMPENSATION
Pretax compensation expense	$ 6,100,000	$ 5,600,000	$ 4,300,000
Vesting period	5 years
Compensation Plan for Non-Employee Directors
SHARE-BASED COMPENSATION
Pretax compensation expense	$ 1,200,000	1,300,000	1,300,000
Total share-based compensation cost	1,500,000
Total income tax benefit recognized		1,400,000	1,200,000
Total unrecognized compensation cost related to share-based compensation arrangements	$ 11,200,000
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition	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	$ 7,300,000	$ 6,900,000	$ 5,600,000
RSU
SHARE-BASED COMPENSATION
Vesting period	3 years 6 months