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Stock-based Compensation - Narrative (Details) |  | 12 Months Ended |
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Feb. 09, 2022 member shares | Sep. 30, 2022 USD ($) $ / shares | Sep. 30, 2021 USD ($) | Sep. 30, 2020 USD ($) | Feb. 07, 2022 shares
Share-Based Payment Arrangement [Abstract] |  |  |  |  |
Number of shares authorized for issuance (in shares) | shares |  |  |  |  | 300,000
Additional shares authorized for issuance (in shares) | shares | 50,000 |  |  |  |
Number of members of management receiving approved grant of stock | member | 6 |  |  |  |
Stock-based compensation |  | $ 2,353,000 | $ 0 | $ 0 |
Stock-based compensation tax benefit |  | 569,000 |  |  |
Unrecognized stock based compensation expense, stock options |  | $ 7,100,000 |  |  |
Compensation cost not yet recognized, period for recognition |  | 4 years 4 months 24 days |  |  |
Vesting period | 4 years |  |  |  |
Vesting percentage | 20.00% |  |  |  |
Weighted average grant date fair value (in usd per share) | $ / shares |  | $ 31.37 |  |  |
Expiration period | 5 years |  |  |  |

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- Definition Amount of expense for award under share-based payment arrangement. Excludes amount capitalized. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (h)(1)(i) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Amount of cost not yet recognized for nonvested award under share-based payment arrangement. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (i) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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