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Business Combinations, Asset Acquisitions, and Joint Venture Formation (Details) $ in Thousands, € in Millions		6 Months Ended
	Sep. 04, 2024 USD ($)	Feb. 28, 2026 USD ($)	Feb. 28, 2025 USD ($)	Feb. 28, 2026 EUR (€)	Aug. 31, 2025 USD ($)	Sep. 04, 2024 EUR (€)
Business Combination [Line Items]
Payments to Acquire Businesses, Net of Cash Acquired \| $		$ 0	$ 27,196
Goodwill \| $		$ 290,617			$ 289,787
Developed Technology
Business Combination [Line Items]
Weighted Average Amortization Period (Years)		7 years		7 years
Customer Relationships
Business Combination [Line Items]
Weighted Average Amortization Period (Years)		14 years		14 years
Technology-Based Intangible Assets
Business Combination [Line Items]
Weighted Average Amortization Period (Years)		7 years		7 years
DTA
Business Combination [Line Items]
Business Combination, Contingent Consideration, Liability \| €				€ 2.5
Payments to Acquire Businesses, Net of Cash Acquired \| $	$ 26,700
Business Combination, Contingent Consideration, Range of Outcomes, Maximum, Amount \| €						€ 36.0
DTA \| Maximum
Business Combination [Line Items]
Business Combination, Contingent Consideration, Liability \| €						€ 12.0