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The aggregate total costs related to selling a firm's product and services, as well as all other general and administrative expenses. Direct selling expenses (for example, credit, warranty, and advertising) are expenses that can be directly linked to the sale of specific products. Indirect selling expenses are expenses that cannot be directly linked to the sale of specific products, for example telephone expenses, Internet, and postal charges. General and administrative expenses include salaries of non-sales personnel, rent, utilities, communication, etc.

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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	Dec. 31, 2023	Jan. 01, 2023	Jan. 02, 2022
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Gross profit			$ 961.4	$ 1,011.8	$ 919.2
SG&A expenses			(934.7)	(943.5)	(870.6)
Asset impairment charge			(2.4)	0.0	0.0
Goodwill impairment charge	$ 10.3	$ 30.7	0.0	41.0	0.0
Earnings (loss) from operations			24.3	14.8	48.6
Loss on disposal			0.0	(18.7)	0.0
Gain on sale of assets			0.0	6.2	0.0
Gain (loss) on investment in Persol Holdings			0.0	(67.2)	121.8
Loss on currency translation from liquidation of subsidiary			0.0	(20.4)	0.0
Other income (expense), net			0.6	1.6	15.4
Earnings (loss) before taxes and equity in net earnings of affiliate			24.9	(71.2)	185.8
Corporate
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Earnings (loss) from operations			(121.9)	(94.0)	(88.1)
Professional & Industrial \| Reporting Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Gross profit			263.9	302.5	310.0
SG&A expenses			(237.0)	(270.5)	(278.6)
Asset impairment charge			(0.3)	0.0	0.0
Earnings (loss) from operations			26.6	32.0	31.4
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			272.0	297.0	253.9
SG&A expenses			(197.6)	(214.9)	(180.2)
Asset impairment charge			(0.1)	0.0	0.0
Earnings (loss) from operations			74.3	82.1	73.7
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			128.7	100.3	65.1
SG&A expenses			(92.4)	(81.8)	(62.1)
Earnings (loss) from operations			36.3	18.5	3.0
Outsourcing & Consulting
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Goodwill impairment charge			0.0	41.0
Outsourcing & Consulting \| Reporting Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Gross profit			163.5	169.6	141.4
SG&A expenses			(154.6)	(149.8)	(122.7)
Asset impairment charge			(2.0)	0.0	0.0
Goodwill impairment charge			0.0	(41.0)	0.0
Earnings (loss) from operations			6.9	(21.2)	18.7
International \| Reporting Segments
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Gross profit			133.3	142.4	148.8
SG&A expenses			(131.2)	(132.5)	(138.9)
Earnings (loss) from operations			$ 2.1	$ 9.9	$ 9.9