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Stock Based Compensation - Additional Information (Detail) - USD ($) $ in Millions | 3 Months Ended | 6 Months Ended
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Feb. 28, 2023 | Feb. 28, 2022 | Feb. 28, 2023 | Feb. 28, 2022
Share-Based Payment Arrangement [Abstract] |  |  |  |
Stock based compensation expense | $ 2.7 | $ 4.9 | $ 5.9 | $ 5.9

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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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