Reconciliation of Total Segment Income to Consolidated Income Before Provision for Income Taxes (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2023	Jan. 01, 2023	Jan. 02, 2022
Segment Reconciliation [Abstract]
Total Segment Income	$ 939,121	$ 857,525	$ 883,699
Depreciation and amortization	(80,640)	(80,251)	(72,923)
Refranchising (loss) gain	(149)	21,173	0
Loss on sale/disposal of assets	(1,299)	(1,813)	(1,189)
Non-cash equity-based compensation expense	(37,514)	(28,709)	(28,670)
Recapitalization-related expenses	0	0	(509)
Income from operations	819,519	767,925	780,408
Other Income	17,713	0	36,758
Interest income	11,683	3,162	345
Interest expense	(196,475)	(198,254)	(191,806)
Income before provision for income taxes	$ 652,440	$ 572,833	$ 625,705