Segment Disclosures - Segment Revenue Per Service (Details) - Service - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	$ 4,909.7	$ 4,516.0	$ 5,355.6
Less: Intersegment revenue
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	(0.9)	(0.5)	(0.5)
Professional & Industrial | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	1,837.4	1,858.4	2,213.4
Science, Engineering & Technology | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	1,156.8	1,019.1	1,131.8
Education | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	416.5	286.9	450.7
Outsourcing & Consulting | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	432.1	363.5	377.7
International | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	$ 1,067.8	$ 988.6	$ 1,182.5