System Optimization (Losses) Gains, Net Davco and NPC Transactions (Details) $ in Thousands		3 Months Ended		9 Months Ended
	May 31, 2017 Restaurant	Oct. 01, 2017 USD ($)	Oct. 02, 2016 USD ($)	Oct. 01, 2017 USD ($)	Oct. 02, 2016 USD ($)	Jan. 01, 2017 USD ($)
Property, Plant and Equipment
Goodwill		$ 743,508		$ 743,508		$ 741,410
Proceeds from sales of restaurants				80,058	$ 173,849
System optimization (losses) gains, net		(106)	$ 37,756	(39,749)	48,106
NPC Disposition
Property, Plant and Equipment
Number of restaurants sold to franchisees | Restaurant	140
Proceeds from sales of restaurants				70,688
Net assets sold				(70,688)
Goodwill				(65,476)
Net favorable leases				24,034
Other				1,692
Favorable lease assets				30,068
Unfavorable lease liabilities				6,034
Number of sold restaurants to be remodeled by the end of 2021 | Restaurant	90
Number of new restaurants to be built by the end of 2022 | Restaurant	15
Post-closing adjustments on sales of restaurants		12
DavCo and NPC Transactions
Property, Plant and Equipment
System optimization (losses) gains, net		15	$ 0	(43,134)	$ 0
DavCo Acquisition
Property, Plant and Equipment
Restaurants acquired from franchisees | Restaurant	140
Total consideration paid				86,788
Net assets held for sale		70,688		70,688
Capital lease assets		49,360		49,360
Deferred taxes		27,639		27,639
Capital lease obligations		(97,046)		(97,046)
Net unfavorable leases		(22,330)		(22,330)
Other liabilities		(6,999)		(6,999)
Total identifiable net assets		21,312		21,312
Goodwill		65,476		65,476
Goodwill		(27)
Favorable lease assets				1,229
Unfavorable lease liabilities				23,559
Supplemental deferred purchase price				6,344
Tax deductible goodwill		$ 21,870		$ 21,870
Number of restaurants closed before acquisition | Restaurant	7