Segment Disclosures - Segment Revenue Per Service (Details) - Service - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2023	Jan. 01, 2023	Jan. 02, 2022
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	$ 4,835.7	$ 4,965.4	$ 4,909.7
Less: Intersegment revenue
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	(19.6)	(2.6)	(0.9)
Professional & Industrial | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	1,483.1	1,666.2	1,837.4
Science, Engineering & Technology | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	1,190.8	1,265.4	1,156.8
Education | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	841.9	636.2	416.5
Outsourcing & Consulting | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	454.7	468.0	432.1
International | Reporting Segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment revenue from services	$ 884.8	$ 932.2	$ 1,067.8