Leases Properties Leased to Third Parties (Details) - USD ($) $ in Thousands	Oct. 03, 2021	Jan. 03, 2021
Property, Plant and Equipment
Properties owned by Company and leased to franchisees under operating lease, before accumulated depreciation	$ 590,061	$ 591,262
Accumulated depreciation and amortization	(179,439)	(170,722)
Properties owned by Company and leased to franchisees under operating lease, after accumulated depreciation	410,622	420,540
Land
Property, Plant and Equipment
Properties owned by Company and leased to franchisees under operating lease, before accumulated depreciation	280,767	279,956
Building and improvements
Property, Plant and Equipment
Properties owned by Company and leased to franchisees under operating lease, before accumulated depreciation	307,593	309,605
Restaurant equipment
Property, Plant and Equipment
Properties owned by Company and leased to franchisees under operating lease, before accumulated depreciation	$ 1,701	$ 1,701