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Long-Term Debt - Convertible Notes (Details)		3 Months Ended
	Nov. 01, 2019 USD ($) consecutiveTradingDay tradingDay $ / shares Rate	Nov. 26, 2022 USD ($)	Nov. 27, 2021 USD ($)	Aug. 27, 2022 USD ($)
Debt Instrument [Line Items]
Non-cash interest expense		$ 0	$ 3,600,000
Offering-related costs		9,600,000		$ 8,800,000
Interest expense, net		$ 5,900,000	$ 10,200,000
Call Spread Transactions
Debt Instrument [Line Items]
Equity component of issuance				85,000,000
Equity component of issuance, net of tax				64,100,000
Offering-related costs				9,800,000
Convertible Notes
Debt Instrument [Line Items]
Debt amount	$ 300,000,000			300,000,000
Interest rate, stated percentage	1.50%
Proceeds from issuance of notes	$ 290,200,000
Conversion rate (in shares) | Rate	1.56906%
Conversion price (in dollars per share) | $ / shares	$ 63.73
Number of consecutive trading days | tradingDay	30
Consecutive business days | consecutiveTradingDay	5
Consecutive trading days | consecutiveTradingDay	5
Convertible Notes | Minimum
Debt Instrument [Line Items]
Percentage of the conversion price	130.00%
Number of trading days | tradingDay	20
Convertible Notes | Maximum
Debt Instrument [Line Items]
Percentage of the conversion price	98.00%
Convertible Notes | Call Spread Transactions
Debt Instrument [Line Items]
Debt amount				$ 215,000,000
Interest rate, stated percentage				8.00%
Debt instrument, interest rate, effective percentage		2.10%
Interest expense, net		$ 1,600,000
Net cost incurred transaction, amount		$ 11,200,000

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