Business Acquisitions, Goodwill and Acquired Intangible Assets (Assets Acquired and Liabilities Assumed) (Details) - USD ($) $ in Millions	Jan. 01, 2017	Jan. 03, 2016	Dec. 28, 2014
Business Acquisition [Line Items]
Goodwill	$ 1,193.5	$ 1,140.2	$ 1,150.6
Acquisitions in 2016
Business Acquisition [Line Items]
Current assets, excluding cash acquired	11.9
Property, plant and equipment	3.9
Goodwill	64.0
Acquired intangible assets	22.7
Other long-term assets	1.2
Total assets acquired	103.7
Current liabilities	(9.9)
Long-term liabilities	(0.4)
Total liabilities assumed	(10.3)
Noncontrolling interests	0.0
Cash paid, net of cash acquired	$ 93.4
Acquisitions in 2015
Business Acquisition [Line Items]
Current assets, excluding cash acquired		8.5
Property, plant and equipment		9.8
Goodwill		27.6
Acquired intangible assets		11.0
Other long-term assets		1.9
Total assets acquired		58.8
Current liabilities		(5.1)
Long-term liabilities		(9.0)
Total liabilities assumed		(14.1)
Noncontrolling interests		22.0
Cash paid, net of cash acquired		$ 66.7