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Stock-Based Compensation Plans - Expense Components (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 26, 2023	Aug. 27, 2022	Aug. 28, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	$ 10.9	$ 17.1	$ 15.3
Time-based
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	9.8	7.6	5.7
Performance-based
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	(0.9)	7.4	7.9
Stock options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	1.3	1.0	1.0
Other
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	$ 0.7	$ 1.1	$ 0.7

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Amount of noncash expense for share-based payment arrangement.

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