Income Taxes - Unrecognized Tax Benefits (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Unrecognized Tax Benefits [Roll Forward]
Unrecognized tax benefits at beginning of year	$ 15.6	$ 16.9	$ 15.1
Additions based on tax positions taken during a prior period	1.1	0.0	5.0
Reductions based on tax positions taken during a prior period	0.0	0.0	(1.9)
Settlement on tax positions taken during a prior period	0.0	(1.7)	0.0
Additions related to acquired entities	1.7	0.0	0.0
Lapse in statute of limitations	(2.5)	(1.0)	(2.9)
Additions based on tax positions taken during the current period	1.7	1.3	1.7
Cash payments	0.0	(0.2)	(0.2)
Foreign exchange	(0.1)	0.3	0.1
Unrecognized tax benefits at end of year	$ 17.5	$ 15.6	$ 16.9