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Income Taxes Income Taxes - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Mar. 03, 2018
Mar. 04, 2017
Mar. 03, 2018
Mar. 04, 2017
Income Tax Disclosure [Abstract]        
Federal income tax rate (percent)     29.10%  
Tax benefit from change in tax rate $ 3.0   $ 3.0  
Provisional benefit from change in tax rate on deferred tax liabilities 8.7   $ 8.7  
Provisional tax liability on undistributed foreign earnings $ 9.2      
Effective tax rates (percent) 19.00% 29.80% 27.30% 31.50%