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Share-based Payments - Narrative (Details) - USD ($) $ in Millions | 9 Months Ended
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May 31, 2023 | May 31, 2022
Share-Based Payment Arrangement [Abstract] |  |
Share-based payment arrangement, expense, tax benefit | $ 1.7 | $ 4.6

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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 -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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