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Basis of Presentation - Depreciation and Amortization (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 28, 2026	Feb. 28, 2025	Feb. 28, 2026	Feb. 28, 2025
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Depreciation	$ 142,686	$ 133,809	$ 286,269	$ 266,908
Amortization—Deferred transition	79,083	79,131	160,023	164,455
Amortization—Intangible assets	171,754	152,162	324,201	312,376
Operating lease cost	189,940	173,866	393,741	360,395
Other	2,037	5,902	3,057	10,076
Total depreciation, amortization and other	$ 585,500	$ 544,870	$ 1,167,291	$ 1,114,210

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The aggregate expense recognized in the current period that allocates the cost of tangible assets, intangible assets, or depleting assets to periods that benefit from use of the assets.

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The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets.

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