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Operating Segments (Details) - USD ($) $ in Millions | 3 Months Ended | 12 Months Ended
--- | --- | ---
Jun. 01, 2019 | Mar. 02, 2019 | Dec. 01, 2018 | Sep. 01, 2018 | Jun. 02, 2018 | Mar. 03, 2018 | Dec. 02, 2017 | Sep. 02, 2017 | Jun. 03, 2017 | Mar. 04, 2017 | Dec. 03, 2016 | Sep. 03, 2016 | Jun. 01, 2019 | Jun. 02, 2018 | Jun. 03, 2017
Segment Reporting Information |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net sales | $ 671.0 | $ 619.0 | $ 652.6 | $ 624.6 | $ 618.0 | $ 578.4 | $ 604.6 | $ 580.3 | $ 577.2 | $ 524.9 | $ 577.5 | $ 598.6 | $ 2,567.2 | $ 2,381.2 | $ 2,278.2
Distributor Concentration Risk | Sales Revenue, Net |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Segment Reporting Information |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Concentration Risk, Percentage |  |  |  |  |  |  |  |  |  |  |  |  | 5.00% |  |
Customer Concentration Risk | Sales Revenue, Net |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Segment Reporting Information |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Concentration Risk, Percentage |  |  |  |  |  |  |  |  |  |  |  |  | 5.00% | 5.00% | 5.00%
Net sales |  |  |  |  |  |  |  |  |  |  |  |  | $ 129.6 | $ 109.8 | $ 102.3
Unionized Employees Concentration Risk | Workforce Subject to Collective Bargaining Arrangements |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Segment Reporting Information |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Concentration Risk, Percentage |  |  |  |  |  |  |  |  |  |  |  |  | 5.00% |  |

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