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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