Revenue - Disaggregation of Revenues by Geographic Region (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Disaggregation of Revenue [Line Items]
Revenue from services	$ 4,909.7	$ 4,516.0	$ 5,355.6
Americas
Disaggregation of Revenue [Line Items]
Revenue from services	3,863.2	3,591.1	4,260.9
Asia Pacific
Disaggregation of Revenue [Line Items]
Revenue from services	39.5	29.6	26.8
Science, Engineering & Technology
Disaggregation of Revenue [Line Items]
Revenue from services	1,156.8	1,019.1	1,131.8
Science, Engineering & Technology | Americas
Disaggregation of Revenue [Line Items]
Revenue from services	1,149.3	1,013.7	1,122.5
Science, Engineering & Technology | Europe
Disaggregation of Revenue [Line Items]
Revenue from services	7.5	5.4	9.3
Outsourcing & Consulting
Disaggregation of Revenue [Line Items]
Revenue from services	432.1	363.5	377.7
Outsourcing & Consulting | Americas
Disaggregation of Revenue [Line Items]
Revenue from services	369.4	302.2	318.1
Outsourcing & Consulting | Europe
Disaggregation of Revenue [Line Items]
Revenue from services	23.2	31.7	32.8
Outsourcing & Consulting | Asia Pacific
Disaggregation of Revenue [Line Items]
Revenue from services	39.5	29.6	26.8
International
Disaggregation of Revenue [Line Items]
Revenue from services	1,067.8	988.6	1,182.5
International | Americas
Disaggregation of Revenue [Line Items]
Revenue from services	91.5	130.4	156.7
International | Europe
Disaggregation of Revenue [Line Items]
Revenue from services	$ 976.3	$ 858.2	$ 1,025.8