Consolidated Statements of Cash Flows - USD ($) $ in Millions		12 Months Ended
		Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Cash flows provided by (used in) operating activities:
Net income (loss)		$ (24.5)	$ (43.7)	$ 4.1
Reconciliation of net income (loss) to net cash provided by (used in) operating activities:
Depreciation and amortization		577.6	586.8	587.2
Amortization of unrecognized pension loss (gain)		(1.8)	(2.8)	(0.4)
Debt early redemption premium expense		0.0	0.0	16.3
Deferred debt issuance costs amortization and write-off		43.4	18.3	23.8
Pension settlement charge (gain)		(0.4)	0.0	2.1
Equity-based compensation expense		67.6	83.4	66.0
Restructuring charge		16.9	13.2	20.5
Restructuring payments		(15.5)	(15.2)	(16.9)
Changes in deferred income taxes		(157.7)	(131.9)	(151.0)
Changes in operating assets and liabilities:
(Increase) decrease in accounts receivable		5.5	13.7	120.9
(Increase) decrease in prepaid taxes, other prepaids and other current assets		10.1	(13.2)	(29.6)
Increase (decrease) in deferred revenue		(20.8)	25.8	8.8
Increase (decrease) in accounts payable		(5.4)	30.2	(5.2)
Increase (decrease) in accrued payroll		(2.1)	5.1	(12.4)
Increase (decrease) in other accrued and current liabilities		27.7	(35.9)	(2.1)
(Increase) decrease in other long-term assets		(36.4)	(41.6)	(53.2)
Increase (decrease) in long-term liabilities		(57.3)	(38.1)	(41.2)
Net, other non-cash adjustments		10.0	(1.9)	(0.6)
Net cash provided by (used in) operating activities		436.9	452.2	537.1
Cash flows provided by (used in) investing activities:
Acquisitions of businesses, net of cash acquired		0.0	0.0	(0.5)
Cash settlements of foreign currency contracts and net investment hedges		(1.2)	5.0	6.0
Capital expenditures		(5.7)	(4.7)	(12.6)
Additions to computer software and other intangibles		(208.2)	(194.7)	(205.3)
Other investing activities, net		(4.4)	2.6	1.9
Net cash provided by (used in) investing activities		(219.5)	(191.8)	(210.5)
Cash flows provided by (used in) financing activities:
Payment for debt early redemption premiums		0.0	0.0	(16.3)
Cash paid for repurchase of treasury shares		(9.3)	0.0	0.0
Payments of dividends		(87.5)	(86.1)	(42.9)
Payment of long term debt		0.0	0.0	(420.0)
Payment of debt issuance costs		(26.6)	0.0	(7.4)
Payment for purchase of non-controlling interests		0.0	(95.7)	(23.6)
Other financing activities, net	[1]	(26.2)	(42.6)	(14.6)
Net cash provided by (used in) financing activities		(187.9)	(282.4)	(281.1)
Effect of exchange rate changes on cash and cash equivalents		(11.3)	1.7	(14.2)
Increase (decrease) in cash, cash equivalents and restricted cash		18.2	(20.3)	31.3
Cash, Cash Equivalents and Restricted Cash, Beginning of Period		188.1	208.4	177.1
Cash, Cash Equivalents and Restricted Cash, End of Period		206.3	188.1	208.4
Reconciliation of cash, cash equivalents and restricted cash
Cash and cash equivalents reported in the condensed consolidated balance sheets		205.9	188.1	208.4
Restricted cash included within other current assets		0.4	0.0	0.0
Total cash, cash equivalents and restricted cash reported in the statements of cash flows		206.3	188.1	208.4
Cash Paid for:
Income taxes payments (refunds), net		93.9	100.2	139.8
Interest		214.5	213.3	178.5
Noncash Investing and Financing activities:
Fair value of acquired assets		0.0	0.0	1.3
Cash paid for acquired businesses		0.0	0.0	(0.5)
Assumed liabilities from acquired businesses including non-controlling interest		0.0	0.0	0.8
Noncash additions to computer software		24.8	7.2	15.0
Payments for additions to computer software reflected as financing cash flows		0.9	0.7	0.0
Predecessor Credit Facility
Cash flows provided by (used in) financing activities:
Proceeds from borrowings on lines of credit		565.0	515.1	315.1
Payments of borrowings on lines of credit		(580.0)	(540.4)	(424.8)
Successor Term Loan Facility
Cash flows provided by (used in) financing activities:
Proceeds from borrowings on lines of credit		3,103.6	0.0	460.0
Payments of borrowings on lines of credit		$ (3,126.9)	$ (32.7)	$ (106.6)

[1] Higher payments in 2024 and 2023 compared to 2022, are related to payments for finance lease liabilities and other long term obligations. See further detail in Note 12.