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Revenue - Disaggregation of Revenues by Geographic Region (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 03, 2021	Dec. 29, 2019	Dec. 30, 2018
Disaggregation of Revenue [Line Items]
Revenue from services	$ 4,516.0	$ 5,355.6	$ 5,513.9
Americas
Disaggregation of Revenue [Line Items]
Revenue from services	3,591.1	4,260.9	4,329.2
Asia Pacific
Disaggregation of Revenue [Line Items]
Revenue from services	29.6	26.8	22.2
Science, Engineering & Technology
Disaggregation of Revenue [Line Items]
Revenue from services	1,019.1	1,131.8	1,002.6
Science, Engineering & Technology | Americas
Disaggregation of Revenue [Line Items]
Revenue from services	1,013.7	1,122.5	989.9
Science, Engineering & Technology | Europe
Disaggregation of Revenue [Line Items]
Revenue from services	5.4	9.3	12.7
Outsourcing & Consulting
Disaggregation of Revenue [Line Items]
Revenue from services	363.5	377.7	377.1
Outsourcing & Consulting | Americas
Disaggregation of Revenue [Line Items]
Revenue from services	302.2	318.1	321.7
Outsourcing & Consulting | Europe
Disaggregation of Revenue [Line Items]
Revenue from services	31.7	32.8	33.2
Outsourcing & Consulting | Asia Pacific
Disaggregation of Revenue [Line Items]
Revenue from services	29.6	26.8	22.2
International
Disaggregation of Revenue [Line Items]
Revenue from services	988.6	1,182.5	1,275.2
International | Americas
Disaggregation of Revenue [Line Items]
Revenue from services	130.4	156.7	158.5
International | Europe
Disaggregation of Revenue [Line Items]
Revenue from services	$ 858.2	$ 1,025.8	$ 1,116.7

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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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