Business Combinations, Asset Acquisitions, and Joint Venture Formation (Details) - USD ($) $ in Thousands	May 31, 2025	Aug. 31, 2024
Asset Acquisition [Line Items]
Goodwill	$ 287,630	$ 269,597
DTA
Asset Acquisition [Line Items]
Business Combination, Recognized Asset Acquired, Asset, Current	5,624
Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill	14,977
Goodwill	14,846
Business Combination, Recognized Asset Acquired, Asset, Noncurrent	531
Business Combination, Recognized Asset Acquired, Asset	38,819
Business Combination, Recognized Liability Assumed, Liability, Current	(6,516)
Business Combination, Recognized Liability Assumed, Liability, Noncurrent	(5,559)
Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less)	26,744
Business Combination, Recognized Asset Acquired, Property, Plant, and Equipment	$ 2,841

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