Net Income Per Share - Computation of Net Income Per Share (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Dec. 27, 2020
Earnings Per Share [Abstract]
Net income	$ 292.4	$ 294.4	$ 194.8
Weighted average common shares outstanding:
Weighted average common shares outstanding (in shares)	133.9	134.7	134.1
Effect of dilutive stock options and restricted stock awards (in shares)	0.2	0.6	1.0
Weighted average common shares outstanding and potential common shares (in shares)	134.1	135.3	135.1
Net income per share:
Basic (in dollars per share)	$ 2.18	$ 2.18	$ 1.45
Diluted (in dollars per share)	$ 2.18	$ 2.18	$ 1.44