Income Taxes (Narrative) (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Income Tax Examination [Line Items]
Deferred tax liabilities, net	$ (547.9)	$ (644.0)
Deferred tax assets	157.2	164.9
Unrecognized tax benefits	5.7	8.8	$ 6.8	$ 6.9
Unrecognized tax benefits, recognized interest income (expense)	(0.1)	(1.4)	0.4
Unrecognized tax benefits, accrued interest	1.2	1.3	$ 2.7
Unrecognized tax benefits including accrued that could change in coming year	1.4
Net operating losses	$ 7.6	$ 8.8
Tax effected net operating losses, expiration period	15 years	15 years
Valuation allowance	$ 5.2	$ 5.3
Income tax holiday, amount of decrease in provision for income taxes	4.3
Undistributed earnings of foreign subsidiaries	261.1
Deferred tax liability for local withholding taxes, not recorded	25.5
Deferred Income Tax Asset, Net
Income Tax Examination [Line Items]
Deferred tax assets	44.0	35.7
Deferred Income Tax Liabilities, Net
Income Tax Examination [Line Items]
Deferred tax liabilities, net	$ (591.9)	$ (679.7)