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Revenue - Disaggregation of Revenues by Geographic Region (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021
Disaggregation of Revenue [Line Items]
Revenue from services	$ 4,965.4	$ 4,909.7	$ 4,516.0
Americas
Disaggregation of Revenue [Line Items]
Revenue from services	3,998.6	3,863.2	3,591.1
Asia Pacific
Disaggregation of Revenue [Line Items]
Revenue from services	42.1	39.5	29.6
Science, Engineering & Technology
Disaggregation of Revenue [Line Items]
Revenue from services	1,265.4	1,156.8	1,019.1
Science, Engineering & Technology | Americas
Disaggregation of Revenue [Line Items]
Revenue from services	1,250.3	1,149.3	1,013.7
Science, Engineering & Technology | Europe
Disaggregation of Revenue [Line Items]
Revenue from services	15.1	7.5	5.4
Outsourcing & Consulting
Disaggregation of Revenue [Line Items]
Revenue from services	468.0	432.1	363.5
Outsourcing & Consulting | Americas
Disaggregation of Revenue [Line Items]
Revenue from services	403.3	369.4	302.2
Outsourcing & Consulting | Europe
Disaggregation of Revenue [Line Items]
Revenue from services	22.6	23.2	31.7
Outsourcing & Consulting | Asia Pacific
Disaggregation of Revenue [Line Items]
Revenue from services	42.1	39.5	29.6
International
Disaggregation of Revenue [Line Items]
Revenue from services	932.2	1,067.8	988.6
International | Americas
Disaggregation of Revenue [Line Items]
Revenue from services	45.2	91.5	130.4
International | Europe
Disaggregation of Revenue [Line Items]
Revenue from services	$ 887.0	$ 976.3	$ 858.2

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Amount, excluding tax collected from customer, of revenue from satisfaction of performance obligation by transferring promised good or service to customer. Tax collected from customer is tax assessed by governmental authority that is both imposed on and concurrent with specific revenue-producing transaction, including, but not limited to, sales, use, value added and excise.

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