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Stock-Based Compensation Plans - Expense Components (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2024	Aug. 26, 2023	Aug. 27, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	$ 14.6	$ 10.9	$ 17.1
Time-based
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	11.6	9.8	7.6
Performance-based
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	0.5	(0.9)	7.4
Stock options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	1.4	1.3	1.0
Other
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total stock-based compensation expense	$ 1.1	$ 0.7	$ 1.1

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- Definition

Amount of noncash expense for share-based payment arrangement.

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