Nature of Business and Significant Accounting Policies - Activity in the Allowance for Doubtful Accounts (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021
Accounts Receivable, Allowance for Credit Loss [Roll Forward]
Beginning balance	$ 13.5	$ 9.1	$ 8.3
Provision for allowance	10.9	4.3	3.0
(Write-offs) recoveries, net	(2.7)		(2.2)
(Write-offs) recoveries, net		0.1
Ending balance	$ 21.7	$ 13.5	$ 9.1