Leases (Supplement Cash Flow Information) (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2021	Jan. 03, 2020
Leases [Abstract]
Operating cash flows from operating leases	$ 37.0	$ 37.9
Right-of-use assets obtained in exchange for Operating lease liabilities:	29.4	53.2
Operating lease right-of-use assets	128.9	140.3
Other current liabilities	33.8	28.9
Operating lease liabilities	109.2	114.1
Total operating lease liabilities	$ 143.0	$ 143.0
Weighted-average discount rate	3.86%	4.23%
Weighted-average remaining lease term	6 years	6 years
Operating Lease, Liability, Current, Statement of Financial Position [Extensible List]	us-gaap:OtherLiabilitiesCurrent	us-gaap:OtherLiabilitiesCurrent