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Stockholders' Equity and Stock-Based Compensation Stock Option Awards (Details) - USD ($) $ in Millions		12 Months Ended
	Jan. 06, 2020	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Options outstanding, Weighted-average remaining contractual life (in years)		4 years 3 months 18 days	5 years 2 months 12 days	6 years 2 months 12 days	6 years 6 months
Granted (in shares)		0	0	550,941
Proceeds from stock options exercised		$ 0.1	$ 0.1	$ 0.1
Share-based Payment Arrangement, Exercise of Option, Tax Benefit		3.7	4.5	2.4
Exercises in period, intrinsic value		21.7	29.5	19.5
Vested in period, fair value		24.8	$ 19.9	$ 17.4
Outstanding, intrinsic value		125.0
Exercisable, intrinsic value		119.7
Total compensation cost not yet recognized		$ 10.2
Share-based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition		1 year 3 months 18 days
Options exercisable, Weighted-average remaining contractual life (in years)		4 years 1 month 6 days
Nonqualified Stock Options Under Long Term Incentive Program [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted (in shares)	550,941
Award vesting rights, percentage		33.33%
Expiration period		10 years
Incentive Stock Options [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares Issued, Shares, Share-based Payment Arrangement, before Forfeiture				0