Income Taxes - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Dec. 27, 2020
Income Tax Contingency [Line Items]
Effective income tax rate reconciliation, FDII, amount	$ 15.1
Effective income tax rate reconciliation GILTI, amount	9.4
Permanently reinvested undistributed earnings on foreign subsidiaries	144.7
Cash paid for taxes, net	84.6	$ 90.0	$ 59.7
Unrecognized tax benefits that, if recognized, would affect our effective tax rate	5.9	5.1
Reserves associated with interest and penalties, net of tax	0.2	$ 0.2
Minimum
Income Tax Contingency [Line Items]
Next tax impact on reserve balance	1.0
Maximum
Income Tax Contingency [Line Items]
Next tax impact on reserve balance	$ 1.5