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Share-Based Compensation - Stock Option Plan (Details) - USD ($) $ / shares in Units, $ in Millions | 12 Months Ended
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Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2020
Share-Based Payment Arrangement [Abstract] |  |  |
Share-based compensation arrangement by share-based payment award, number of shares authorized (in shares) | 3,000,000 |  |
Stock options authorized (in shares) | 1,387,697 | 1,569,798 |
Weighted average grant date fair value, granted (in dollar per share) | $ 22.82 | $ 19.83 | $ 0.00
Employee service share-based compensation, non vested awards, total compensation cost not yet recognized, stock options | $ 10.6 |  |
Employee service share-based compensation, non vested awards, total compensation cost not yet recognized, period for recognition | 4 years 10 months 2 days |  |
Share-based compensation arrangement by share-based payment award, options, exercises in period, total intrinsic value | $ 39.0 | $ 11.7 | $ 4.2

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- Definition Weighted-average period over which cost not yet recognized is expected to be recognized for award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. + 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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- Definition Amount of cost to be recognized for option under share-based payment arrangement. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -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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- Definition Number of shares authorized for issuance under share-based payment arrangement. + References Reference 1: http://www.xbrl.org/2003/role/exampleRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (a)(3) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition The difference between the maximum number of shares (or other type of equity) authorized for issuance under the plan (including the effects of amendments and adjustments), and the sum of: 1) the number of shares (or other type of equity) already issued upon exercise of options or other equity-based awards under the plan; and 2) shares (or other type of equity) reserved for issuance on granting of outstanding awards, net of cancellations and forfeitures, if applicable. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Amount of accumulated difference between fair value of underlying shares on dates of exercise and exercise price on options exercised (or share units converted) into shares. + 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 (d)(2) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition The weighted average grant-date fair value of options granted during the reporting period as calculated by applying the disclosed option pricing methodology. + 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 (d)(1) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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