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Stock Based Compensation - Additional Information (Detail) - USD ($) $ in Millions | 3 Months Ended | 9 Months Ended
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May 31, 2022 | May 31, 2021 | May 31, 2022 | May 30, 2022 | May 31, 2021
Share-Based Payment Arrangement [Abstract] |  |  |  |  |
Stock based compensation expense | $ 5.0 | $ 3.5 | $ 10.9 | $ 10.9 | $ 12.5

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- Definition Amount of noncash expense for share-based payment arrangement. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 230 -SubTopic 10 -Section 45 -Paragraph 28 -Subparagraph (a) -URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3602-108585 + Details
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