Segment Information - Financial Information Regarding Reportable Segments (Details) $ in Millions	3 Months Ended								9 Months Ended	12 Months Ended
	Dec. 29, 2019 USD ($) segment	Sep. 29, 2019 USD ($) segment	Jun. 30, 2019 USD ($)	Mar. 31, 2019 USD ($)	Dec. 30, 2018 USD ($)	Sep. 30, 2018 USD ($)	Jul. 01, 2018 USD ($)	Apr. 01, 2018 USD ($)	Sep. 29, 2019 segment	Dec. 29, 2019 USD ($) segment	Dec. 30, 2018 USD ($)	Dec. 31, 2017 USD ($)
Segment Reporting [Abstract]
Number of operating segments | segment	2	2							1
Number of reportable segments | segment	2								1	2
Segment Reporting Information [Line Items]
Revenues	$ 355.9	$ 357.3	$ 366.4	$ 357.2	$ 335.2	$ 321.1	$ 333.2	$ 337.3		$ 1,436.8	$ 1,326.8	$ 1,219.2
Operating expenses:
Cost of services (exclusive of depreciation and amortization)	220.8	221.3	227.7	218.4	210.9	202.5	201.1	206.7		888.2	821.2	778.1
Selling, general and administrative	36.2	38.9	33.7	33.6	28.2	31.7	31.3	32.6		142.4	123.8	113.3
Depreciation and amortization	22.4	22.1	22.1	21.8	24.3	24.3	24.7	24.1		88.4	97.4	93.1
Total operating expenses	279.4	282.3	283.5	273.8	263.4	258.5	257.1	263.4		1,119.0	1,042.4	984.5
Operating profit	76.5	75.0	82.9	83.4	71.8	62.6	76.1	73.9		317.8	284.4	234.7
Interest expense, net	16.6	17.5	11.9	9.7	9.8	9.6	9.7	9.6		55.7	38.7	38.6
Other (income) expense, net	0.0	0.0	(0.2)	0.1	0.3	0.0	(0.8)	0.0		(0.1)	(0.5)	(0.9)
Income before income taxes	59.9	57.5	71.2	73.6	61.7	53.0	67.2	64.3		262.2	246.2	197.0
Income taxes	14.3	15.7	19.9	19.1	15.1	14.0	17.4	16.0		69.0	62.5	35.6
Net income	45.6	$ 41.8	$ 51.3	$ 54.5	46.6	$ 39.0	$ 49.8	$ 48.3		193.2	183.7	161.4
Total assets	2,151.2				1,488.5					2,151.2	1,488.5	1,434.4
Purchases of property, equipment and computer software										68.5	66.7	54.9
Long-lived assets	982.8				345.2					982.8	345.2
U.S.
Operating expenses:
Long-lived assets	923.3				329.7					923.3	329.7
Foreign
Operating expenses:
Long-lived assets	59.5				15.5					59.5	15.5
United States
Segment Reporting Information [Line Items]
Revenues										1,266.1	1,185.1	1,098.0
Operating expenses:
Cost of services (exclusive of depreciation and amortization)										768.4	726.9	694.6
Selling, general and administrative										131.3	111.9	103.2
Depreciation and amortization										81.8	90.5	86.9
Total operating expenses										981.5	929.3	884.7
Operating profit										284.6	255.8	213.3
Interest expense, net										55.7	38.6	38.6
Other (income) expense, net										(0.2)	(0.8)	(0.5)
Income before income taxes										229.1	218.0	175.2
Income taxes										59.7	54.7	29.8
Net income										169.4	163.3	145.4
Total assets	1,963.4				1,344.3					1,963.4	1,344.3	1,297.5
Purchases of property, equipment and computer software										64.2	63.0	48.2
International
Segment Reporting Information [Line Items]
Revenues										170.7	141.7	121.2
Operating expenses:
Cost of services (exclusive of depreciation and amortization)										119.8	94.3	83.5
Selling, general and administrative										11.1	11.9	10.1
Depreciation and amortization										6.6	6.9	6.2
Total operating expenses										137.5	113.1	99.8
Operating profit										33.2	28.6	21.4
Interest expense, net										0.0	0.1	0.0
Other (income) expense, net										0.1	0.3	(0.4)
Income before income taxes										33.1	28.2	21.8
Income taxes										9.3	7.8	5.8
Net income										23.8	20.4	16.0
Total assets	$ 187.8				$ 144.2					187.8	144.2	136.9
Purchases of property, equipment and computer software										$ 4.3	$ 3.7	$ 6.7