Net Income Per Common Share (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended								12 Months Ended
	Jan. 02, 2016	Oct. 03, 2015	Jul. 04, 2015	Apr. 04, 2015	Jan. 03, 2015	Sep. 27, 2014	Jun. 28, 2014	Mar. 29, 2014	Jan. 02, 2016	Jan. 03, 2015	Dec. 28, 2013
Net income per common share amounts
Income from continuing operations	$ 56.5	$ 81.3	$ 64.7	$ 71.9	$ 69.8	$ 60.9	$ 50.2	$ 66.4	$ 274.4	$ 247.3	$ 241.7
Loss from discontinued operations, net of tax									(0.1)	(2.2)	(28.5)
Net income available to common shareholders	$ 57.0	$ 81.7	$ 63.7	$ 71.9	$ 70.6	$ 60.2	$ 48.3	$ 66.0	$ 274.3	$ 245.1	$ 213.2
Weighted-average									91.0	93.8	98.4
Dilutive shares (additional common shares issuable under stock-based awards)									1.9	1.9	1.7
Weighted-average									92.9	95.7	100.1
Net income (loss) per common share:
Continuing operations (in dollars per share)	$ 0.62	$ 0.89	$ 0.71	$ 0.79	$ 0.76	$ 0.65	$ 0.53	$ 0.69	$ 3.01	$ 2.64	$ 2.46
Discontinued operations (in dollars per share)	0.01		(0.01)		0.01		(0.02)			(0.03)	(0.29)
Net income per common share (in dollars per share)	0.63	0.89	0.70	0.79	0.77	0.65	0.51	0.69	3.01	2.61	2.17
Net income (loss) per common share, assuming dilution:
Continuing operations (in dollars per share)	0.61	0.87	0.69	0.78	0.75	0.64	0.52	0.68	2.95	2.58	2.41
Discontinued operations (in dollars per share)	0.01	0.01	(0.01)		0.01	(0.01)	(0.02)	(0.01)		(0.02)	(0.28)
Net income per common share, assuming dilution (in dollars per share)	$ 0.62	$ 0.88	$ 0.68	$ 0.78	$ 0.76	$ 0.63	$ 0.50	$ 0.67	$ 2.95	$ 2.56	$ 2.13
Stock-based compensation awards excluded from the computation of net income per common share, assuming dilution									1.0	3.0	7.0