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Long-Term Debt - Convertible Notes (Details)			3 Months Ended
	Nov. 25, 2023 USD ($) $ / shares Rate	Nov. 01, 2019 USD ($) businessDay $ / shares Rate	Nov. 25, 2023 USD ($) $ / shares	Nov. 26, 2022 USD ($)	Aug. 26, 2023 USD ($)
Debt Instrument [Line Items]
Offering-related costs	$ 6,900,000		$ 6,900,000		$ 7,600,000
Interest expense, net			4,100,000	$ 5,900,000
Call Spread Transactions
Debt Instrument [Line Items]
Offering-related costs	$ 9,800,000		$ 9,800,000
Convertible Notes
Debt Instrument [Line Items]
Debt amount		$ 300,000,000
Interest rate, stated percentage		1.50%
Proceeds from issuance of notes		$ 290,200,000
Conversion rate (in shares) | Rate	1.59923%	1.56906%
Conversion price (in dollars per share) | $ / shares	$ 62.53	$ 63.73	$ 62.53
Number of trading days | businessDay		20
Number of consecutive trading days | businessDay		30
Consecutive business days | businessDay		5
Consecutive trading days | businessDay		5
Convertible Notes | Minimum
Debt Instrument [Line Items]
Percentage of the conversion price		130.00%
Convertible Notes | Maximum
Debt Instrument [Line Items]
Percentage of the conversion price		98.00%
Convertible Notes | Call Spread Transactions
Debt Instrument [Line Items]
Debt instrument, interest rate, effective percentage	2.10%		2.10%
Interest expense, net			$ 1,600,000	$ 1,600,000
Net cost incurred transaction, amount			$ 11,200,000

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