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Segment Disclosures - Segment Earnings from Operations (Details) - USD ($) $ in Millions | 3 Months Ended | 12 Months Ended
--- | --- | ---
Jan. 01, 2023 | Oct. 02, 2022 | Jan. 01, 2023 | Jan. 02, 2022 | Jan. 03, 2021
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |
Gross profit |  |  | $ 1,011.8 | $ 919.2 | $ 827.6
SG&A expenses |  |  | (943.5) | (870.6) | (805.6)
Goodwill impairment charge | $ 10.3 | $ 30.7 | 41.0 | 0.0 | 147.7
Earnings (loss) from operations |  |  | 14.8 | 48.6 | (93.6)
Loss on disposal |  |  | (18.7) | 0.0 | 0.0
Gain on sale of assets |  |  | 6.2 | 0.0 | 0.0
Gain (loss) on investment in Persol Holdings |  |  | (67.2) | 121.8 | (16.6)
Loss on currency translation from liquidation of subsidiary |  |  | (20.4) | 0.0 | 0.0
Other income (expense), net |  |  | 1.6 | 15.4 | 3.4
Earnings (loss) before taxes and equity in net earnings (loss) of affiliate |  |  | (71.2) | 185.8 | (106.8)
Corporate |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |
Earnings (loss) from operations |  |  | (94.0) | (88.1) | (203.8)
Professional & Industrial | Reporting Segments |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |
Gross profit |  |  | 302.5 | 310.0 | 330.2
SG&A expenses |  |  | (270.5) | (278.6) | (288.6)
Earnings (loss) from operations |  |  | 32.0 | 31.4 | 41.6
Science, Engineering & Technology |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |
Goodwill impairment charge |  |  | 0.0 | 0.0 |
Science, Engineering & Technology | Reporting Segments |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |
Gross profit |  |  | 297.0 | 253.9 | 209.4
SG&A expenses |  |  | (214.9) | (180.2) | (134.4)
Earnings (loss) from operations |  |  | 82.1 | 73.7 | 75.0
Education |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |
Goodwill impairment charge |  |  | 0.0 | 0.0 |
Education | Reporting Segments |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |
Gross profit |  |  | 100.3 | 65.1 | 42.2
SG&A expenses |  |  | (81.8) | (62.1) | (51.2)
Earnings (loss) from operations |  |  | 18.5 | 3.0 | (9.0)
Outsourcing & Consulting |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |
Goodwill impairment charge |  |  | 41.0 |  |
Outsourcing & Consulting | Reporting Segments |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |
Gross profit |  |  | 169.6 | 141.4 | 119.8
SG&A expenses |  |  | (149.8) | (122.7) | (108.3)
Goodwill impairment charge |  |  | (41.0) | 0.0 | 0.0
Earnings (loss) from operations |  |  | (21.2) | 18.7 | 11.5
International | Reporting Segments |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |
Gross profit |  |  | 142.4 | 148.8 | 126.0
SG&A expenses |  |  | (132.5) | (138.9) | (134.9)
Earnings (loss) from operations |  |  | $ 9.9 | $ 9.9 | $ (8.9)

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