The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

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Goodwill and Other Intangible Assets, net - Schedule of Other Intangible Assets (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Oct. 02, 2022	Oct. 03, 2021	Oct. 02, 2022	Oct. 03, 2021	Jan. 02, 2022
Intangible assets with definite lives
Gross Carrying Amount	$ 424,121		$ 424,121		$ 438,350
Accumulated Amortization	(115,663)		(115,663)		(103,730)
Net Amount	308,458		308,458		334,620
Intangible Assets, Net (Excluding Goodwill) [Abstract]
Gross Carrying Amount	1,082,021		1,082,021		1,096,250
Accumulated Amortization	(115,663)		(115,663)		(103,730)
Net Amount	966,358		966,358		992,520
Amortization of intangible assets	7,100	$ 7,500	21,300	$ 22,600
Trade name
Intangible assets with indefinite lives
Trade name	657,900		657,900		657,900
Franchise agreements
Intangible assets with definite lives
Gross Carrying Amount	30,632		30,632		32,545
Accumulated Amortization	(9,006)		(9,006)		(8,369)
Net Amount	21,626		21,626		24,176
Intangible Assets, Net (Excluding Goodwill) [Abstract]
Accumulated Amortization	(9,006)		(9,006)		(8,369)
Customer relationships
Intangible assets with definite lives
Gross Carrying Amount	15,000		15,000		15,000
Accumulated Amortization	(5,332)		(5,332)		(4,684)
Net Amount	9,668		9,668		10,316
Intangible Assets, Net (Excluding Goodwill) [Abstract]
Accumulated Amortization	(5,332)		(5,332)		(4,684)
Reacquired franchise rights
Intangible assets with definite lives
Gross Carrying Amount	371,989		371,989		384,305
Accumulated Amortization	(94,825)		(94,825)		(84,177)
Net Amount	277,164		277,164		300,128
Intangible Assets, Net (Excluding Goodwill) [Abstract]
Accumulated Amortization	(94,825)		(94,825)		(84,177)
Website development costs
Intangible assets with definite lives
Gross Carrying Amount	6,500		6,500		6,500
Accumulated Amortization	(6,500)		(6,500)		(6,500)
Net Amount	0		0		0
Intangible Assets, Net (Excluding Goodwill) [Abstract]
Accumulated Amortization	$ (6,500)		$ (6,500)		$ (6,500)