Quarterly Financial Data (Unaudited) (Details) - USD ($) $ / shares in Units, $ in Millions	3 Months Ended								12 Months Ended
	Dec. 29, 2019	Sep. 29, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 30, 2018	Sep. 30, 2018	Jul. 01, 2018	Apr. 01, 2018	Dec. 29, 2019	Dec. 30, 2018	Dec. 31, 2017
Quarterly Financial Information Disclosure [Abstract]
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
Basic net income per share of common stock (in dollars per share)	$ 0.34	$ 0.31	$ 0.38	$ 0.41	$ 0.35	$ 0.29	$ 0.37	$ 0.36	$ 1.45	$ 1.38	$ 1.21
Diluted net income per share of common stock (in dollar per share)	$ 0.34	$ 0.31	$ 0.38	$ 0.41	$ 0.35	$ 0.29	$ 0.37	$ 0.36	$ 1.44	$ 1.37	$ 1.20