Business Combinations, Asset Acquisitions, and Joint Venture Formation (Details) - USD ($)	Feb. 28, 2025	Aug. 31, 2024
Asset Acquisition [Line Items]
Goodwill	$ 277,241,000	$ 269,597,000
DTA
Asset Acquisition [Line Items]
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Assets	6,464,000
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Intangible Assets, Other than Goodwill	14,977,000
Goodwill	14,473,000
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Noncurrent Assets	531,000
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Assets	39,286,000
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Liabilities	(6,531,000)
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Noncurrent Liabilities	(5,559,000)
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Net	27,196,000
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Property, Plant, and Equipment	$ 2,841,000

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