Debt - Narrative (Details) $ in Millions		1 Months Ended		3 Months Ended		9 Months Ended
	May 15, 2026 USD ($)	Jun. 30, 2026 USD ($)	Mar. 31, 2026 USD ($)	Sep. 30, 2026 USD ($)	Sep. 30, 2025 USD ($)	Sep. 30, 2026 USD ($)	Sep. 30, 2025 USD ($)	Aug. 25, 2026 USD ($)	Dec. 31, 2025 USD ($)
Debt Instrument [Line Items]
Loss on extinguishment of debt						$ 27.7	$ 0.0
Interest expense				$ 49.1	$ 97.5	188.6	247.2
Amortization of capitalized discounts and deferred financing fees				2.8	4.9	11.0	12.0
Interest income				10.1	$ 4.2	15.3	12.9
Debt, fair value				3,087.0		3,087.0
Letter of Credit
Debt Instrument [Line Items]
Maximum borrowing capacity				13.8		13.8			$ 13.8
Senior notes
Debt Instrument [Line Items]
Long-term debt, gross				$ 1,035.0		$ 1,035.0			1,035.0
Interest rate				5.90%		5.90%
Senior secured notes
Debt Instrument [Line Items]
Long-term debt, gross				$ 700.0		$ 700.0			700.0
Interest rate				4.10%		4.10%
Mortgage payable
Debt Instrument [Line Items]
Long-term debt, gross				$ 0.0		$ 0.0			$ 0.6
Credit Agreement | Line of Credit
Debt Instrument [Line Items]
Weighted average interest rate for borrowings oustanding				5.50%		5.50%			6.70%
Unused commitment fee, percentage			0.25%
Long-term debt, gross				$ 1,345.6		$ 1,345.6			$ 3,977.7
Credit Agreement | Line of Credit | Possible Reduction After September 30, 2026
Debt Instrument [Line Items]
Unused commitment fee, percentage			0.05%
Credit Agreement | Line of Credit | Revolving Credit Facility
Debt Instrument [Line Items]
Repayment of line of credit						0.0	0.0
Proceeds from line of credit						0.0	$ 0.0
Madison IAQ LLC
Debt Instrument [Line Items]
Letters of credit outstanding				$ 6.8		$ 6.8			$ 6.8
Madison IAQ LLC | Credit Agreement | Line of Credit
Debt Instrument [Line Items]
Repayment of line of credit	$ 2,425.7
Loss on extinguishment of debt	$ 26.2
Maximum borrowing capacity								$ 1,365.0
Madison IAQ LLC | 2026 Incremental Revolving Facility | Line of Credit
Debt Instrument [Line Items]
Loss on extinguishment of debt		$ (1.5)
Maximum borrowing capacity			$ 1,300.0
Capitalization of lender fee			4.9
Total deferred costs			$ 5.7
Madison IAQ LLC | 2026 Incremental Revolving Facility | Line of Credit | Base Rate
Debt Instrument [Line Items]
Decrease in variable rate		0.0100
Basis spread on variable interest rate		0.75%
Madison IAQ LLC | 2026 Incremental Revolving Facility | Line of Credit | SOFR
Debt Instrument [Line Items]
Decrease in variable rate		0.0100
Basis spread on variable interest rate		1.75%
Madison IAQ LLC | Incremental Term Loan | Line of Credit
Debt Instrument [Line Items]
Repayment of line of credit		$ 200.0