Earnings Per Share Additional Information (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Earnings Per Share [Line Items]
Anti-dilutive stock options	605,774	1,179,088	133,505
Preferred stock, shares authorized	2,000,000
Preferred stock, par or stated value Per Share	$ 1
Purchase of common stock for treasury	$ (39.6)	$ (21.0)	$ (319.2)
Employee taxes paid under stock-based compensation plans	(14.1)	(24.8)	(16.9)
Common stock repurchase program, authorized amount	$ 400.0
Series A junior participating preferred stock [Member]
Earnings Per Share [Line Items]
Preferred stock, shares authorized	150,000
Series B junior participating preferred stock [Member]
Earnings Per Share [Line Items]
Preferred stock, shares authorized	500,000
Treasury Stock [Member]
Earnings Per Share [Line Items]
Purchase of common stock for treasury	$ (39.6)	$ (21.0)	$ (319.2)