Segment Disclosures - Segment Revenue Per Service (Details) - Service - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	$ 4,965.4	$ 4,909.7	$ 4,516.0
Less: Intersegment revenue
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	(2.6)	(0.9)	(0.5)
Professional & Industrial | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	1,666.2	1,837.4	1,858.4
Science, Engineering & Technology | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	1,265.4	1,156.8	1,019.1
Education | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	636.2	416.5	286.9
Outsourcing & Consulting | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	468.0	432.1	363.5
International | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	$ 932.2	$ 1,067.8	$ 988.6