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Investments and Fair Value Measurements - Fair Value of Contingent Consideration (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	May 27, 2023	May 28, 2022	May 27, 2023	May 28, 2022
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning fair value - contingent consideration	$ 41.8	$ 37.1	$ 39.8	$ 0.0
Additions	0.0	0.0	0.0	24.2
Fair value adjustments	0.0	11.8	2.0	24.7
Settlements	(22.0)	(13.2)	(22.0)	(13.2)
Other	0.0	(0.6)	0.0	(0.6)
Ending fair value - contingent consideration	$ 19.8	$ 35.1	$ 19.8	$ 35.1

X

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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- Definition

Amount of settlement of financial instrument classified as an asset measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

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- Definition

Amount of gain (loss) recognized in income from liability measured at fair value on recurring basis using unobservable input (level 3).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

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- Definition

Amount of purchases of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

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- Definition

Fair value of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)
-SubTopic 10
-Topic 820
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

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- Definition

Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Asset, Other

+ References

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