Stock-Based Compensation - Expense (Details) - USD ($) $ in Thousands	3 Months Ended	6 Months Ended
Feb. 29, 2024	Feb. 28, 2023	Feb. 29, 2024	Feb. 28, 2023
Share-Based Payment Arrangement [Abstract]
Stock-based compensation expense	$ 16,652	$ 15,325	$ 30,962	$ 27,500

Amount of expense for award under share-based payment arrangement. Excludes amount capitalized.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 14.F)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479830/718-10-S99-1

Reference 2: 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

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration