Impairment of Long-Lived Assets (Details) - USD ($) $ in Thousands	12 Months Ended
Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021
Impairment of Long-Lived Assets
Impairment of long-lived assets	$ 6,420	$ 2,251	$ 8,037
Company-operated restaurants
Impairment of Long-Lived Assets
Impairment of long-lived assets	5,485	1,862	7,586
Restaurants leased or subleased to franchisees
Impairment of Long-Lived Assets
Impairment of long-lived assets	242	189	0
Surplus properties
Impairment of Long-Lived Assets
Impairment of long-lived assets	$ 693	$ 200	$ 451

Amount of write-down of assets recognized in the income statement. Includes, but is not limited to, losses from tangible assets, intangible assets and goodwill.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3602-108585

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 45
-Paragraph 4
-URI https://asc.fasb.org/extlink&oid=126905981&loc=d3e2420-110228

Name:	us-gaap_AssetImpairmentCharges
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration