Business and Summary of Significant Accounting Policies - Revenue Recognition and Franchise (Details) - restaurant	12 Months Ended
	Jan. 02, 2024	Jan. 03, 2023	Dec. 28, 2021
Franchisor Disclosure [Line Items]
Percent of gift cards expected to be unredeemed (percent)	14.00%
Gift card estimated redemption period	24 months
Number of restaurants closed	6	5	12
Franchise
Franchisor Disclosure [Line Items]
Number of restaurants	90	93	76
Number of restaurants opened during period	0	3	1
Number of restaurants closed	3	1	1
Number of company-owned restaurants acquired by franchisees		15