Stock-Based Compensation - Schedule of Stock-Based Compensation Expense (Details) - USD ($)	3 Months Ended		9 Months Ended
	Jun. 03, 2023	May 28, 2022	Jun. 03, 2023	May 28, 2022
Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Stock-based compensation	$ 4,655,000	$ 4,370,000	$ 14,624,000	$ 14,559,000
Deferred income tax benefit	(1,150,000)	(1,120,000)	(3,641,000)	(3,596,000)
Stock-based compensation expense, net	3,505,000	3,250,000	10,983,000	10,963,000
Stock options
Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Stock-based compensation	0	214,000	101,000	1,019,000
Restricted stock units (1)
Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Stock-based compensation	3,827,000	3,212,000	11,495,000	11,221,000
Performance share units (1)
Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Stock-based compensation	760,000	873,000	2,800,000	2,070,000
Associate Stock Purchase Plan
Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]
Stock-based compensation	$ 68,000	$ 71,000	$ 228,000	$ 249,000