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Acquisitions and Disposition - Disposition Narrative (Details) - USD ($) $ in Millions |  |  | 3 Months Ended | 12 Months Ended
--- | --- | --- | --- | ---
Jul. 20, 2022 | Aug. 18, 2020 | Oct. 02, 2022 | Jul. 03, 2022 | Jan. 01, 2023 | Jan. 02, 2022 | Jan. 03, 2021
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items] |  |  |  |  |  |  |
Cash disposed from sale of Russia, net of proceeds |  |  |  |  | $ 6.0 | $ 0.0 | $ 0.0
Loss on disposal |  |  |  |  | 18.7 | 0.0 | 0.0
Proceeds from sale of Brazil, net of cash disposed |  |  |  |  | 0.0 | 0.0 | 1.2
Brazil |  |  |  |  |  |  |
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items] |  |  |  |  |  |  |
Purchase price of disposition |  | $ 1.4 |  |  |  |  |
Proceeds from sale of Brazil, net of cash disposed |  | 1.2 |  |  |  |  |
Indemnification liabilities, range of outcomes, value, high |  | 8.8 |  |  |  |  |
Indemnification liability |  | $ 2.5 |  |  |  |  |
Russian Operations | Disposal Group, Not Discontinued Operations |  |  |  |  |  |  |
Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items] |  |  |  |  |  |  |
Proceeds from investment in PersolKelly Asia Pacific equity affiliate | $ 7.4 |  |  |  |  |  |
Cash disposed from sale of Russia, net of proceeds | $ 6.0 |  |  |  |  |  |
Disposal Group, Not Discontinued Operation, Loss (Gain) on Write-down |  |  |  | $ 18.5 |  |  |
Loss on disposal |  |  | $ 0.2 |  | 18.7 |  |
Loss on disposal, cumulative translation adjustment |  |  |  |  | 1.4 |  |
Disposal Group, Including Discontinued Operation, Revenue |  |  |  |  | 63.4 | 132.2 | 118.5
Discontinued Operation, Income (Loss) from Discontinued Operation During Phase-out Period, before Income Tax, Attributable to Parent |  |  |  |  | $ 1.4 | $ 3.2 | $ 2.4

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