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Income Taxes (Narrative) (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 01, 2022
Jan. 02, 2021
Dec. 28, 2019
Dec. 29, 2018
Income Tax Examination [Line Items]        
Deferred tax liabilities, net $ (616.3) $ (128.1)    
Deferred tax assets 162.9 110.7    
Unrecognized tax benefits 8.8 6.8 $ 6.9 $ 6.5
Unrecognized tax benefits, recognized interest income (expense) (1.4) 0.4 0.5  
Unrecognized tax benefits, accrued interest 1.3 2.7 $ 2.3  
Unrecognized tax benefits including accrued that could change in coming year 2.2      
Net operating losses $ 8.8 $ 9.2    
Tax effected net operating losses, expiration period 15 years 15 years    
Valuation allowance $ 5.3 $ 7.4    
Change in valuation allowance 3.1      
Income tax holiday, amount of decrease in provision for income taxes 4.2      
Undistributed earnings of foreign subsidiaries 169.9      
Deferred tax liability for local withholding taxes, not recorded 17.0      
Deferred tax liability for no effective rate 5.9      
Deferred Income Tax Asset, Net        
Income Tax Examination [Line Items]        
Deferred tax assets 162.9 110.7    
Deferred Income Tax Liabilities, Net        
Income Tax Examination [Line Items]        
Deferred tax liabilities, net $ (779.2) $ (238.8)