Long-Term Debt - Convertible Notes (Details)		3 Months Ended		9 Months Ended
	Nov. 01, 2019 USD ($) businessDay $ / shares Rate	May 27, 2023 USD ($)	May 28, 2022 USD ($)	May 27, 2023 USD ($)	May 28, 2022 USD ($)	Aug. 27, 2022 USD ($)
Debt Instrument [Line Items]
Non-cash interest expense			$ 3,900,000	$ 0	$ 11,200,000
Offering-related costs		$ 8,300,000		8,300,000		$ 8,800,000
Interest expense, net		$ 5,200,000	$ 10,500,000	$ 16,400,000	$ 31,100,000
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 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 amount						$ 215,000,000
Interest rate, stated percentage						8.00%
Debt instrument, interest rate, effective percentage		2.10%		2.10%
Interest expense, net		$ 1,600,000		$ 4,700,000
Net cost incurred transaction, amount				$ 11,200,000