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Stock-Based Compensation - Schedule of Outstanding Stock Options (Details) - USD ($) $ / shares in Units, $ in Millions | 12 Months Ended |  |  |
--- | --- | --- | --- | ---
Sep. 30, 2021 | Sep. 30, 2020 | Sep. 30, 2019 | Sep. 30, 2018
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |
Stock Option Awards Outstanding, Number Outstanding (in shares) | 471,676 | 1,083,402 | 1,328,390 | 1,268,984
Stock Option Awards Outstanding, Weighted-Average Remaining Contractual Life, (in years) | 6 years 8 months 12 days |  |  |
Weighted-Average Exercise Price of Outstanding Options (in dollars per share) | $ 77.96 | $ 74.38 | $ 62.62 | $ 57.03
Stock Option Awards Outstanding, Aggregate Intrinsic Value | $ 11.5 |  |  |
Stock Option Awards Exercisable, Number Exercisable (in shares) | 251,049 | 537,241 | 709,826 |
Stock Option Awards Exercisable, Weighted-Average Remaining Contractual Life (in years) | 5 years 8 months 12 days |  |  |
Options exercisable, end of year (in dollars per share) | $ 74.73 | $ 68.16 | $ 55.11 |
Stock Option Awards Exercisable, Aggregate Intrinsic Value | $ 6.9 |  |  |
Price Range, $40.00 - $60.00 |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |
Stock Option Awards Outstanding, Exercise Prices, Low End of Range (in dollars per share) | $ 40.00 |  |  |
Stock Option Awards Outstanding, Exercise Prices, High End of Range (in dollars per share) | $ 60.00 |  |  |
Stock Option Awards Outstanding, Number Outstanding (in shares) | 14,838 |  |  |
Stock Option Awards Outstanding, Weighted-Average Remaining Contractual Life, (in years) | 1 year 1 month 6 days |  |  |
Weighted-Average Exercise Price of Outstanding Options (in dollars per share) | $ 41.52 |  |  |
Stock Option Awards Outstanding, Aggregate Intrinsic Value | $ 0.9 |  |  |
Stock Option Awards Exercisable, Number Exercisable (in shares) | 14,838 |  |  |
Stock Option Awards Exercisable, Weighted-Average Remaining Contractual Life (in years) | 1 year 1 month 6 days |  |  |
Options exercisable, end of year (in dollars per share) | $ 41.52 |  |  |
Stock Option Awards Exercisable, Aggregate Intrinsic Value | $ 0.9 |  |  |
Price Range, $60.01 - $80.00 |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |
Stock Option Awards Outstanding, Exercise Prices, Low End of Range (in dollars per share) | $ 60.01 |  |  |
Stock Option Awards Outstanding, Exercise Prices, High End of Range (in dollars per share) | $ 80.00 |  |  |
Stock Option Awards Outstanding, Number Outstanding (in shares) | 201,069 |  |  |
Stock Option Awards Outstanding, Weighted-Average Remaining Contractual Life, (in years) | 6 years |  |  |
Weighted-Average Exercise Price of Outstanding Options (in dollars per share) | $ 66.28 |  |  |
Stock Option Awards Outstanding, Aggregate Intrinsic Value | $ 7.3 |  |  |
Stock Option Awards Exercisable, Number Exercisable (in shares) | 122,137 |  |  |
Stock Option Awards Exercisable, Weighted-Average Remaining Contractual Life (in years) | 5 years 2 months 12 days |  |  |
Options exercisable, end of year (in dollars per share) | $ 66.40 |  |  |
Stock Option Awards Exercisable, Aggregate Intrinsic Value | $ 4.4 |  |  |
Price Range, $80.01 - $100.00 |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award |  |  |  |
Stock Option Awards Outstanding, Exercise Prices, Low End of Range (in dollars per share) | $ 80.01 |  |  |
Stock Option Awards Outstanding, Exercise Prices, High End of Range (in dollars per share) | $ 100.00 |  |  |
Stock Option Awards Outstanding, Number Outstanding (in shares) | 255,769 |  |  |
Stock Option Awards Outstanding, Weighted-Average Remaining Contractual Life, (in years) | 7 years 7 months 6 days |  |  |
Weighted-Average Exercise Price of Outstanding Options (in dollars per share) | $ 89.25 |  |  |
Stock Option Awards Outstanding, Aggregate Intrinsic Value | $ 3.3 |  |  |
Stock Option Awards Exercisable, Number Exercisable (in shares) | 114,074 |  |  |
Stock Option Awards Exercisable, Weighted-Average Remaining Contractual Life (in years) | 6 years 10 months 24 days |  |  |
Options exercisable, end of year (in dollars per share) | $ 87.97 |  |  |
Stock Option Awards Exercisable, Aggregate Intrinsic Value | $ 1.6 |  |  |

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- Definition The number of shares into which fully or partially vested stock options outstanding as of the balance sheet date can be currently converted under the option plan. + 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 -Subparagraph (c)(1)(iii) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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- Definition The weighted-average price as of the balance sheet date at which grantees can acquire the shares reserved for issuance on vested portions of options outstanding and currently exercisable under the stock option plan. + 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 -Subparagraph (c)(1)(iii) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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- Definition Amount by which the current fair value of the underlying stock exceeds the exercise price of options outstanding. + 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 http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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- Definition Number of options outstanding, including both vested and non-vested options. + 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 http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (c)(1)(i)-(ii) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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- Definition Weighted average price at which grantees can acquire the shares reserved for issuance under the stock option plan. + 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 -Subparagraph (c)(1)(i) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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- Definition The floor of a customized range of exercise prices for purposes of disclosing shares potentially issuable under outstanding stock option awards on all stock option plans and other required information pertaining to awards in the customized range. + 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 -Subparagraph (g) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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- Definition Weighted average remaining contractual term for vested portions of options outstanding and currently exercisable or convertible, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days. + 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 http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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