Quarterly Financial Information (Unaudited) (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended								12 Months Ended
	Jan. 03, 2021	Sep. 27, 2020	Jun. 28, 2020	Mar. 29, 2020	Dec. 29, 2019	Sep. 29, 2019	Jun. 30, 2019	Mar. 31, 2019	Jan. 03, 2021	Dec. 29, 2019	Dec. 30, 2018
Quarterly Financial Data Table
Revenues	$ 474,317	$ 452,242	$ 402,306	$ 404,960	$ 427,191	$ 437,880	$ 435,348	$ 408,583	$ 1,733,825	$ 1,709,002	$ 1,589,936
Cost of sales	164,737	159,545	140,626	149,999	151,434	152,425	151,092	142,579	614,907	597,530	548,588
Operating profit	78,567	81,348	60,661	48,732	36,717	79,023	80,573	66,266	269,308	262,579	249,892
Net Income	$ 38,734	$ 39,753	$ 24,904	$ 14,441	$ 26,533	$ 46,127	$ 32,386	$ 31,894	$ 117,832	$ 136,940	$ 460,115
Basic income per share
Basic income per share	$ 0.17	$ 0.18	$ 0.11	$ 0.06	$ 0.12	$ 0.20	$ 0.14	$ 0.14	$ 0.53	$ 0.60	$ 1.93
Diluted income per share
Diluted income per share	$ 0.17	$ 0.17	$ 0.11	$ 0.06	$ 0.11	$ 0.20	$ 0.14	$ 0.14	$ 0.52	$ 0.58	$ 1.88
Advertising funds deficit		$ 7,293	$ 3,205	$ 1,387					$ (2,904)	$ (1,337)	$ (4,153)
Reorganization and realignment costs	$ 5,834	$ 3,375	$ 2,911	$ 3,910	$ 12,194				16,030	16,965	9,068
Investment income, net					24,599				(225)	25,598	450,736
Franchise support and other costs					16,400				26,464	43,686	25,203
Loss on early extinguishment of debt					$ 1,346		$ 7,150		$ 0	$ 8,496	$ 11,475