Earnings Per Share (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended		9 Months Ended
	May 27, 2023	May 28, 2022	May 27, 2023	May 28, 2022
Earnings Per Share [Abstract]
Net income	$ 59.1	$ 117.2	$ 172.1	$ 308.0
Weighted average common shares outstanding (in shares)	30.4	32.4	30.4	32.9
Basic earnings per common share (in dollars per share)	$ 1.95	$ 3.62	$ 5.66	$ 9.35
Interest expense on convertible notes, net of tax	$ 1.2	$ 0.0	$ 3.6	$ 0.0
Diluted net income	$ 60.3	$ 117.2	$ 175.7	$ 308.0
Dilutive impact of stock compensation awards (in shares)	0.3	0.5	0.4	0.5
Dilutive impact of convertible notes (in shares)	4.7	0.0	4.7	0.2
Weighted average common shares outstanding, assuming dilution (in shares)	35.4	32.9	35.5	33.6
Anti-dilutive securities excluded from weighted average common shares outstanding, assuming dilution (in shares)	0.1	0.2	0.1	0.2
Diluted earnings per common share (in dollars per share)	$ 1.71	$ 3.57	$ 4.95	$ 9.18