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Restructuring and Integration Expense - Summary of Restructuring Expenses by Segment (Details) - USD ($) $ in Millions | 3 Months Ended | 9 Months Ended
--- | --- | ---
Mar. 02, 2024 | Mar. 04, 2023 | Mar. 02, 2024 | Mar. 04, 2023
Restructuring Cost and Reserve [Line Items] |  |  |  |
Restructuring expense | $ 1.7 | $ 4.6 | $ 8.7 | $ 19.8
Americas Contract |  |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |  |
Restructuring expense | 1.5 | 4.4 | 5.8 | 17.5
International Contract & Specialty |  |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |  |
Restructuring expense | 0.1 | 0.0 | 1.6 | 0.7
Global Retail |  |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |  |
Restructuring expense | 0.1 | 0.2 | 1.3 | 1.6
Knoll Integration |  |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |  |
Restructuring expense | 7.6 | 4.0 | 18.4 | 12.7
Knoll Integration | Corporate |  |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |  |
Restructuring expense | 0.0 | 1.3 | 0.1 | 4.3
Knoll Integration | Americas Contract | Operating Segments |  |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |  |
Restructuring expense | 5.8 | 2.2 | 15.3 | 6.2
Knoll Integration | International Contract & Specialty | Operating Segments |  |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |  |
Restructuring expense | 1.8 | 0.5 | 3.0 | 2.0
Knoll Integration | Global Retail | Operating Segments |  |  |  |
Restructuring Cost and Reserve [Line Items] |  |  |  |
Restructuring expense | $ 0.0 | $ 0.0 | $ 0.0 | $ 0.2

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