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Segment Disclosures - Segment Earnings from Operations (Details) - USD ($) $ in Millions | 12 Months Ended
--- | ---
Jan. 02, 2022 | Jan. 03, 2021 | Dec. 29, 2019
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |
Gross profit | $ 919.2 | $ 827.6 | $ 968.4
SG&A expenses | (870.6) | (805.6) | (883.1)
Earnings (loss) from operations | 48.6 | (93.6) | 81.8
Gain (loss) on investment in Persol Holdings | 121.8 | (16.6) | 35.8
Other income (expense), net | 15.4 | 3.4 | (1.2)
Earnings (loss) before taxes and equity in net earnings (loss) of affiliate | 185.8 | (106.8) | 116.4
Corporate |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |
Earnings (loss) from operations | (88.1) | (203.8) | (97.6)
Professional & Industrial | Reporting Segments |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |
Gross profit | 310.0 | 330.2 | 388.4
SG&A expenses | (278.6) | (288.6) | (326.0)
Earnings (loss) from operations | 31.4 | 41.6 | 62.4
Science, Engineering & Technology | Reporting Segments |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |
Gross profit | 253.9 | 209.4 | 226.2
SG&A expenses | (180.2) | (134.4) | (146.7)
Earnings (loss) from operations | 73.7 | 75.0 | 79.5
Education | Reporting Segments |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |
Gross profit | 65.1 | 42.2 | 72.0
SG&A expenses | (62.1) | (51.2) | (56.2)
Earnings (loss) from operations | 3.0 | (9.0) | 15.8
Outsourcing & Consulting | Reporting Segments |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |
Gross profit | 141.4 | 119.8 | 122.3
SG&A expenses | (122.7) | (108.3) | (119.3)
Earnings (loss) from operations | 18.7 | 11.5 | 3.0
International | Reporting Segments |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |
Gross profit | 148.8 | 126.0 | 159.5
SG&A expenses | (138.9) | (134.9) | (140.8)
Earnings (loss) from operations | $ 9.9 | $ (8.9) | $ 18.7

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