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Summary of Significant Accounting Policies - Revenue Recognition (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2024	Jan. 03, 2023	Dec. 28, 2021
Revenue Recognition
Gift card breakage period	3 years
Revenue recognized	$ 7.3	$ 7.0	$ 6.8
Promotional programs
Revenue Recognition
Deferred revenue	27.5	27.3	27.5
Deferred revenue recognized	$ 23.3	$ 23.6	$ 15.2
Minimum
Revenue Recognition
Revenue recognition agreement term	5 years
Revenue recognition for development and site fees over the life of the applicable licensee agreements (in years)	8 years
Maximum
Revenue Recognition
Revenue recognition agreement term	7 years
Revenue recognition for development and site fees over the life of the applicable licensee agreements (in years)	30 years

X

- Definition

Represents the period of breakage recognized related to unredeemed gift cards.

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- Definition

Revenue recognition for development and site fees over the life of the applicable guarantee agreement, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

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Revenue recognition for development and site fees over the life of the applicable licensee agreement, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

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- Definition

Amount of obligation to transfer good or service to customer for which consideration has been received or is receivable.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479837/606-10-45-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
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-Section 50
-Paragraph 8
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479806/606-10-50-8

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
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-Section 45
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- Definition

Amount of revenue recognized arising from contract liability from change in timeframe for performance obligation to be satisfied.

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- Definition

Amount of revenue recognized that was previously included in balance of obligation to transfer good or service to customer for which consideration from customer has been received or is due.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
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