Goodwill and Intangible Assets - Amortization (Details) - USD ($) $ in Thousands	3 Months Ended
Nov. 30, 2022	Nov. 30, 2021	Aug. 31, 2022
Goodwill and Intangible Assets Disclosure [Abstract]
Amortization - Intangible assets	$ 109,069	$ 102,542
Finite-Lived Intangible Assets, Amortization Expense, Maturity Schedule [Abstract]
Remainder of 2023	333,744
2024	373,490
2025	339,358
2026	293,457
2027	232,307
Thereafter	457,658
Net Carrying Amount	$ 2,030,014		$ 1,930,808

Finite-Lived Intangible Asset, Expected Amortization, After Year Four

No definition available.

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- Definition

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. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
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-Publisher FASB
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- Definition

Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 50
-Paragraph 2
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-URI https://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275

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- Definition

Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in remainder of current fiscal year.

+ References

No definition available.

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- Definition

Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

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- Definition

Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

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- Definition

Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

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- References

No definition available.

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- Definition

Amount after amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 926
-SubTopic 20
-Section 50
-Paragraph 5
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