Leases Properties Leased to Third Parties (Details) - USD ($) $ in Thousands	Jan. 01, 2023	Jan. 02, 2022
Property, Plant and Equipment
Properties owned by Company and leased to franchisees under operating lease, before accumulated depreciation	$ 554,010	$ 548,996
Accumulated depreciation and amortization	(187,269)	(173,243)
Properties owned by Company and leased to franchisees under operating lease, after accumulated depreciation	366,741	375,753
Land
Property, Plant and Equipment
Properties owned by Company and leased to franchisees under operating lease, before accumulated depreciation	260,650	258,513
Buildings and improvements
Property, Plant and Equipment
Properties owned by Company and leased to franchisees under operating lease, before accumulated depreciation	291,659	288,782
Restaurant equipment
Property, Plant and Equipment
Properties owned by Company and leased to franchisees under operating lease, before accumulated depreciation	$ 1,701	$ 1,701