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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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