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Income Taxes Reconciliation of Income Tax Expense (Details) - USD ($)
$ in Thousands
12 Months Ended
Jan. 03, 2016
Dec. 28, 2014
Dec. 29, 2013
Income Tax Contingency [Line Items]      
Tax at statutory rate $ 85,405 $ 59,361 $ 57,289
Non-U.S. rate differential, net (51,814) (36,616) (36,377)
U.S. taxation of multinational operations 1,732 2,367 3,658
State income taxes, net 649 1,970 (1,762)
Prior year tax matters (7,202) (7,009) (23,534)
Federal tax credits (2,295) (3,399) (5,452)
Change in valuation allowance 2,593 (7,679) (4,675)
Other, net 2,259 (558) 270
Total $ 31,327 $ 8,437 $ (10,583)