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Shareholders' Deficit - Additional Information (Details) - USD ($) shares in Millions	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Approved share repurchase program	$ 600,000,000
Remaining authorized stock purchase plan	$ 348,000,000
Stock options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Antidilutive securities excluded from computation of earnings per share, amount	0.4	0.1	0.2
Stock options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Proceeds from stock options exercised	$ 1,100,000
Tax benefit from exercise of stock options	1,300,000
Stock-based compensation expense related to non-vested awards	$ 4,800,000
Weighted average period to recognize remaining expense over	1 year 9 months 18 days
Time- Based Stock Awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation expense related to non-vested awards	$ 9,700,000
Weighted average period to recognize remaining expense over	1 year 9 months 18 days
Performance- Based Stock Awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation expense related to non-vested awards	$ 7,400,000
Weighted average period to recognize remaining expense over	1 year 9 months 18 days