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Share-based Payments - Narrative (Details) - USD ($) $ in Millions | 6 Months Ended
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Feb. 28, 2023 | Feb. 28, 2022
Share-Based Payment Arrangement [Abstract] |  |
Share-based payment arrangement, expense, tax benefit | $ 1.7 | $ 4.4

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- Definition Amount of tax benefit for recognition of expense of 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 (h)(1)(i) -URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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