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General (Details)
$ / shares in Units, $ in Thousands
 3 Months Ended 12 Months Ended
Dec. 31, 2016
USD ($)
segment
facilities
$ / shares
Oct. 01, 2016
$ / shares
Jul. 02, 2016
$ / shares
Apr. 02, 2016
$ / shares
Jan. 02, 2016
USD ($)
$ / shares
Oct. 03, 2015
$ / shares
Jul. 04, 2015
$ / shares
Apr. 04, 2015
$ / shares
Dec. 31, 2016
USD ($)
weeks
segment
facilities
$ / shares
shares
Jan. 02, 2016
USD ($)
weeks
$ / shares
shares
Jan. 03, 2015
USD ($)
weeks
$ / shares
shares
Jan. 07, 2014
USD ($)
continent
Dec. 29, 2013
segment
General [Line Items]                          
Number of Operating Segments | segment 3               3       3
Accounting Policies [Abstract]                          
Number Of Weeks Year To Date | weeks                 52 52 53    
Cash and Cash Equivalents [Abstract]                          
Investments Classified As Cash Equivalents, Original Maturity                 3 months        
Goodwill [Abstract]                          
Goodwill $ 1,225,893       $ 1,233,102       $ 1,225,893 $ 1,233,102 $ 1,320,419    
Basic:                          
Net income                 $ 102,313 $ 78,531 $ 64,215    
Shares (in shares) | shares                 164,600,000 165,031,000 164,627,000    
Basic (in dollars per share) | $ / shares $ 0.25 $ 0.17 $ 0.19 $ 0.01 $ 0.51 $ (0.06) $ 0.02 $ 0.00 $ 0.62 $ 0.48 $ 0.39    
Effect of dilutive securities: [Abstract]                          
Add: Option shares in the money and dilutive effect of nonvested stock (in shares) | shares                 1,329,000 168,000 806,000    
Less: Pro-forma treasury shares (in shares) | shares                 (717,000) (80,000) (374,000)    
Diluted:                          
Net Income                 $ 102,313 $ 78,531 $ 64,215    
Shares (in shares) | shares                 165,212,000 165,119,000 165,059,000    
Diluted (in dollars per share) | $ / shares $ 0.25 $ 0.17 $ 0.19 $ 0.01 $ 0.51 $ (0.06) $ 0.02 $ 0.00 $ 0.62 $ 0.48 $ 0.39    
Stock Based Compensation [Abstract]                          
Stock-based compensation expense                 $ 10,300 $ 9,000 $ 20,900    
Employee service share-based compensation, tax benefit from compensation expense                 3,400 3,300 5,900    
Payments related to tax withholding for share-based compensation                 (400) (400)      
Excess tax benefit from stock-based compensation                 0 0 2,420    
Foreign currency translation                 $ (3,700) $ (164,800) $ (125,900)    
Stock Options [Member]                          
Antidilutive Securities [Abstract]                          
Antidilutive securities excluded from computation of earnings per share, amount | shares                 1,148,707 790,092 319,240    
Non Vested Stock [Member]                          
Antidilutive Securities [Abstract]                          
Antidilutive securities excluded from computation of earnings per share, amount | shares                 758,557 587,961 751,444    
Vion Ingredients [Member]                          
General [Line Items]                          
Expected Business Combination, Number of Continents in which Entity Operates | continent                       5  
Goodwill [Abstract]                          
Goodwill                       $ 702,672  
Minimum [Member]                          
General [Line Items]                          
Number of Processing and Transfer Facilities | facilities 200               200        
Accounting Policies [Abstract]                          
Number Of Weeks Year To Date | weeks                 52        
Minimum [Member] | Buildings and improvements [Member]                          
Long Lived Assets [Abstract]                          
Property, Plant and Equipment, Useful Life                 15 years        
Minimum [Member] | Machinery and equipment [Member]                          
Long Lived Assets [Abstract]                          
Property, Plant and Equipment, Useful Life                 3 years        
Minimum [Member] | Vehicles [Member]                          
Long Lived Assets [Abstract]                          
Property, Plant and Equipment, Useful Life                 3 years        
Minimum [Member] | Aircraft [Member]                          
Long Lived Assets [Abstract]                          
Property, Plant and Equipment, Useful Life                 7 years        
Minimum [Member] | Routes [Member]                          
Long Lived Assets [Abstract]                          
Finite-Lived Intangible Assets, Useful Life                 5 years        
Minimum [Member] | Permits [Member]                          
Long Lived Assets [Abstract]                          
Finite-Lived Intangible Assets, Useful Life                 10 years        
Minimum [Member] | Non-compete agreements [Member]                          
Long Lived Assets [Abstract]                          
Finite-Lived Intangible Assets, Useful Life                 3 years        
Minimum [Member] | Trade Names [Member]                          
Long Lived Assets [Abstract]                          
Finite-Lived Intangible Assets, Useful Life                 4 years        
Maximum [Member]                          
Accounting Policies [Abstract]                          
Number Of Weeks Year To Date | weeks                 53        
Maximum [Member] | Buildings and improvements [Member]                          
Long Lived Assets [Abstract]                          
Property, Plant and Equipment, Useful Life                 30 years        
Maximum [Member] | Machinery and equipment [Member]                          
Long Lived Assets [Abstract]                          
Property, Plant and Equipment, Useful Life                 10 years        
Maximum [Member] | Vehicles [Member]                          
Long Lived Assets [Abstract]                          
Property, Plant and Equipment, Useful Life                 8 years        
Maximum [Member] | Aircraft [Member]                          
Long Lived Assets [Abstract]                          
Property, Plant and Equipment, Useful Life                 10 years        
Maximum [Member] | Routes [Member]                          
Long Lived Assets [Abstract]                          
Finite-Lived Intangible Assets, Useful Life                 21 years        
Maximum [Member] | Permits [Member]                          
Long Lived Assets [Abstract]                          
Finite-Lived Intangible Assets, Useful Life                 20 years        
Maximum [Member] | Non-compete agreements [Member]                          
Long Lived Assets [Abstract]                          
Finite-Lived Intangible Assets, Useful Life                 7 years        
Maximum [Member] | Trade Names [Member]                          
Long Lived Assets [Abstract]                          
Finite-Lived Intangible Assets, Useful Life                 15 years        
Best Hides GmbH [Member] | Vion Ingredients [Member]                          
General [Line Items]                          
Business Acquisition, Percentage of Voting Interests Acquired                       60.00%