Consolidated Statements of Cash Flows - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2023	Jan. 01, 2023	Jan. 02, 2022
Cash flows from operating activities:
Net income	$ 204,440	$ 177,370	$ 200,392
Adjustments to reconcile net income to net cash provided by operating activities:
Depreciation and amortization (exclusive of amortization of cloud computing arrangements shown separately below)	135,789	133,414	125,540
Amortization of cloud computing arrangements	12,778	2,394	0
Share-based compensation	23,747	24,538	22,019
Impairment of long-lived assets	1,401	6,420	2,251
Deferred income tax	(807)	4,305	(13,781)
Non-cash rental expense, net	40,655	33,915	40,596
Change in operating lease liabilities	(47,212)	(45,682)	(45,606)
Net receipt (recognition) of deferred vendor incentives	1,034	(1,060)	715
System optimization gains, net	(880)	(6,779)	(33,545)
Gain on sale of investments, net	(31)	0	(63)
Distributions received from TimWen joint venture	12,901	12,612	16,337
Equity in earnings in joint ventures, net	(10,819)	(9,422)	(11,203)
Long-term debt related activities, net (see Note 20)	5,320	7,762	24,758
Cloud computing arrangements expenditures	(32,902)	(30,220)	(14,086)
Other, net	22,883	(4,554)	844
Changes in operating assets and liabilities:
Accounts and notes receivable, net	430	(5,857)	(5,613)
Inventories	439	(1,203)	(872)
Prepaid expenses and other current assets	(672)	6,769	(3,396)
Advertising funds restricted assets and liabilities	(18,210)	(30,503)	11,519
Accounts payable	(8,826)	(1,533)	7,586
Accrued expenses and other current liabilities	3,958	(12,782)	21,380
Net cash provided by operating activities	345,416	259,904	345,772
Cash flows from investing activities:
Capital expenditures	(85,021)	(85,544)	(77,984)
Franchise development fund	(7,951)	(3,605)	0
Acquisitions	0	0	(123,069)
Dispositions	2,115	8,237	55,118
Proceeds from sale of investments	31	0	63
Notes receivable, net	4,280	3,136	1,203
Payments for investments	0	0	(10,000)
Net cash used in investing activities	(86,546)	(77,776)	(154,669)
Cash flows from financing activities:
Proceeds from long-term debt	0	500,000	1,100,000
Repayments of long-term debt	(94,702)	(26,750)	(970,344)
Repayments of finance lease liabilities	(21,588)	(17,312)	(13,640)
Deferred financing costs	0	(10,232)	(20,873)
Repurchases of common stock, including accelerated share repurchase	(189,554)	(51,950)	(268,531)
Dividends	(209,253)	(106,779)	(94,846)
Proceeds from stock option exercises	14,667	4,865	30,003
Payments related to tax withholding for share-based compensation	(3,873)	(3,168)	(4,511)
Net cash (used in) provided by financing activities	(504,303)	288,674	(242,742)
Net cash (used in) provided by operations before effect of exchange rate changes on cash	(245,433)	470,802	(51,639)
Effect of exchange rate changes on cash	2,448	(5,967)	364
Net (decrease) increase in cash, cash equivalents and restricted cash	(242,985)	464,835	(51,275)
Cash, cash equivalents and restricted cash at beginning of period	831,801	366,966	418,241
Cash, cash equivalents and restricted cash at end of period	$ 588,816	$ 831,801	$ 366,966