System Optimization Gains, Net Summary of Disposition Activity (Details) $ in Thousands	12 Months Ended
Dec. 31, 2023 USD ($) number_of_restaurants	Jan. 01, 2023 USD ($) number_of_restaurants	Jan. 02, 2022 USD ($) number_of_restaurants	Jan. 01, 2017
System optimization gains, net
Company-operated restaurant ownership percentage				5.00%
Proceeds from sales of restaurants	$ 2,115	$ 8,237	$ 55,118
Gain on sales-type leases	2,466	2,981	4,244
System optimization gains, net	$ 880	$ 6,779	$ 33,545
Sale of franchise-operated restaurants to franchisees
System optimization gains, net
Number of restaurants sold to franchisees \| number_of_restaurants	99	79	34
Sale of company-operated restaurants to franchisees
System optimization gains, net
Number of restaurants sold to franchisees \| number_of_restaurants	0	1	47
Proceeds from sales of restaurants	$ 0	$ 79	$ 50,518
Net assets sold	0	(141)	(16,939)
Goodwill related to sales of restaurants	0	0	(4,847)
Net unfavorable leases	0	(360)	(2,939)
Gain on sales-type leases	0	0	7,156
Other	0	6	(2,148)
Gain on sales of restaurants, net, before post-closing adjustments	0	(416)	30,801
Post-closing adjustments on sales of restaurants	858	2,877	1,218
System optimization gains, net	858	2,461	32,019
Favorable lease			3,799
Unfavorable lease			6,738
Deferred gain on sale of property			3,500
Recognition of deferred gain on sale of property	858	3,522	515
Sale of other assets
System optimization gains, net
Proceeds from sales of restaurants	2,115	7,780	4,561
System optimization gains, net	$ 22	4,318	1,526
Sale of manhattan company-operated restaurants to franchisees note receivable
System optimization gains, net
Proceeds from sales of restaurants		$ 378	39
Sale of manhattan company-operated restaurants to franchisees
System optimization gains, net
Gain on sales-type leases			1,625
Write-off of lease assets			$ 927

Amount of gain on the sale of property that does not qualify for gain recognition as of the balance sheet date.

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This element represents the identifiable intangible asset established upon acquisition based on a favorable difference between the terms of an acquired lease and the current market terms for that lease at the acquisition date.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
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Amount of gain (loss) on sale or disposal of property, plant and equipment assets, including oil and gas property and timber property.

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Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
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Amount of increase (decrease) of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

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Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
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This element represents a liability associated with the acquisition of an off-market lease when the terms of the lease are unfavorable to the market terms for the lease at the date of acquisition.

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The cash inflow from the sale of long-lived, physical assets that are used in the normal conduct of business to produce goods and services and not intended for resale.

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Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

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No definition available.

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Amount of profit (loss) for sales-type lease and (loss) for direct financing lease recognized at commencement.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
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The number of franchises sold during the period when there are significant changes in franchisor-owned outlets or franchised outlets during the period.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 952
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Approximate Company-operated restaurant ownership percentage

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Gain (loss) on disposition of restaurants to franchisees as part of the system optimization initiative, before the impact of post closing purchase price adjustments on previously completed dispositions.

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No definition available.

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Lease Assets, Write-offs

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Net Assets Sold

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Net Lease Assets (Liabilities) - Net of favorable lease assets and unfavorable lease liabilities as a result of the lease and/or sublease of land, buildings, and/or leasehold improvements to franchisees, in connection with sales of restaurants.

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Other gain (loss) on disposition, net

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Post Closing Adjustments on Sales of Restaurants

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Recognition of deferred gain on sale of property

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