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Accumulated Other Comprehensive Loss (Details) - USD ($)
 12 Months Ended
Jun. 02, 2018
Jun. 03, 2017
May 28, 2016
Cumulative translation adjustments [Roll Forward]      
Cumulative translation adjustments at beginning of period $ (36,800,000) $ (29,600,000) $ (20,800,000)
Other comprehensive income (loss) before reclassifications (net of tax of $- , $- and ($0.3)) 2,700,000 (7,200,000) (8,800,000)
Balance at end of period (34,100,000) (36,800,000) (29,600,000)
Pension and other post-retirement benefit plans [Roll Forward]      
Pension and other post-retirement benefit plans at beginning of period (47,600,000) (34,900,000) (35,400,000)
Other comprehensive income (loss) before reclassifications (net of tax of ($2.9), $3.7 and ($0.7)) 5,300,000 (14,500,000) (2,000,000)
Net reclassifications 5,100,000 1,800,000 2,500,000
Net current period other comprehensive income 10,400,000 (12,700,000) 500,000
Balance at end of period (37,200,000) (47,600,000) (34,900,000)
Interest rate swap agreement [Roll Forward]      
Interest rate swap agreement at beginning of period 2,100,000 0 0
Other comprehensive income before reclassifications (net of tax of ($4.0), ($1.2) and $-) 7,500,000 2,100,000 0
Reclassification from accumulated other comprehensive income - Interest expense 300,000 0 0
Net reclassifications 300,000 0 0
Net current period other comprehensive income 7,800,000 2,100,000 0
Balance at end of period 9,900,000 2,100,000 0
Available for sale securities [Roll Forward]      
Available-for-sale Securities at beginning of period 100,000 0 0
Other comprehensive income before reclassifications (net of tax of $- , $- and $-) 0 100,000 0
Balance at end of period 100,000 100,000 0
Total accumulated other comprehensive loss (61,300,000) (82,200,000) (64,500,000)
Selling, General and Administrative Expenses      
Pension and other post-retirement benefit plans [Roll Forward]      
Reclassification from accumulated other comprehensive income 4,200,000 2,200,000 3,200,000
Operating Expense      
Pension and other post-retirement benefit plans [Roll Forward]      
Reclassification from accumulated other comprehensive income $ 900,000 $ (400,000) $ (700,000)