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Share-Based Compensation - Narrative (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions | 12 Months Ended
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Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021
Share-Based Payment Arrangement [Abstract] |  |  |
Share-based compensation arrangement by share-based payment award, number of shares authorized (in shares) | 2.4 |  |
Stock options authorized (in shares) | 1.7 |  |
Allocated share-based compensation expense | $ 28.0 | $ 17.8 | $ 13.9
Weighted average grant date fair value, granted (in dollar per share) | $ 33.21 | $ 22.82 | $ 19.83
Employee service share-based compensation, non vested awards, total compensation cost not yet recognized, stock options | $ 9.2 |  |
Employee service share-based compensation, non vested awards, total compensation cost not yet recognized, period for recognition (in years) | 3 years 11 months 12 days |  |
Share-based compensation arrangement by share-based payment award, options, exercises in period, total intrinsic value | $ 4.2 | $ 39.0 | $ 11.7
Employee service share-based compensation, nonvested awards, total compensation cost not yet recognized | $ 40.5 |  |
Employee service share-based compensation, nonvested awards, total compensation cost not yet recognized, period for recognition, restricted stock | 1 year 2 months 26 days |  |

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- Definition Weighted average period over which unrecognized compensation is expected to be recognized for equity-based compensation plans, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days for restricted stock plan. + References No definition available. + Details
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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 -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SAB Topic 14.F) -Publisher FASB -URI https://asc.fasb.org//1943274/2147479830/718-10-S99-1 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (h)(1)(i) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2 + 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 -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (i) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2 + Details
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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 -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (i) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2 + 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 -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (i) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2 + 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 -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (a)(3) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2 + 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 -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2 + 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 -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (d)(2) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2 + 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 -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (d)(1) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2 + Details
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