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Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Mar. 04, 2023
Dec. 03, 2022
Sep. 03, 2022
Feb. 26, 2022
Nov. 27, 2021
Aug. 28, 2021
Mar. 04, 2023
Feb. 26, 2022
Accumulated Other Comprehensive Income [Roll Forward]                
Balance at beginning of period     $ 1,427.1       $ 1,427.1  
Other comprehensive (loss) income, net of tax before reclassifications             (5.7) $ (30.4)
Reclassification from accumulated other comprehensive loss - Other, net             7.5 3.3
Tax benefit             (0.2) (0.8)
Net reclassifications             7.3 2.5
Net current period other comprehensive (loss) income $ 7.6 $ 51.8 (57.8) $ 15.1 $ (27.8) $ (15.2) 1.6 (27.9)
Balance at end of period 1,433.9           1,433.9  
Accumulated Other Comprehensive Loss                
Accumulated Other Comprehensive Income [Roll Forward]                
Balance at beginning of period     (107.1)     (65.1) (107.1) (65.1)
Net current period other comprehensive (loss) income 7.6 $ 51.8 (57.8) 15.1 $ (27.8) (15.2)    
Balance at end of period (105.5)     (93.0)     (105.5) (93.0)
Cumulative Translation Adjustments                
Accumulated Other Comprehensive Income [Roll Forward]                
Balance at beginning of period     (93.9)     (3.9) (93.9) (3.9)
Other comprehensive (loss) income, net of tax before reclassifications             (30.6) (46.7)
Reclassification from accumulated other comprehensive loss - Other, net             0.0 0.0
Tax benefit             0.0 0.0
Net reclassifications             0.0 0.0
Net current period other comprehensive (loss) income             (30.6) (46.7)
Balance at end of period (124.5)     (50.6)     (124.5) (50.6)
Pension and Other Post-retirement Benefit Plans                
Accumulated Other Comprehensive Income [Roll Forward]                
Balance at beginning of period     (36.9)     (50.4) (36.9) (50.4)
Other comprehensive (loss) income, net of tax before reclassifications             0.0 0.0
Reclassification from accumulated other comprehensive loss - Other, net             0.6 6.4
Tax benefit             (0.2) (0.8)
Net reclassifications             0.4 5.6
Net current period other comprehensive (loss) income             0.4 5.6
Balance at end of period (36.5)     (44.8)     (36.5) (44.8)
Interest Rate Swap Agreement                
Accumulated Other Comprehensive Income [Roll Forward]                
Balance at beginning of period     $ 23.7     $ (10.8) 23.7 (10.8)
Other comprehensive (loss) income, net of tax before reclassifications             24.9 16.3
Reclassification from accumulated other comprehensive loss - Other, net             6.9 (3.1)
Tax benefit             0.0 0.0
Net reclassifications             6.9 (3.1)
Net current period other comprehensive (loss) income             31.8 13.2
Balance at end of period $ 55.5     $ 2.4     $ 55.5 $ 2.4