Acquisitions and Dispositions - Acquired Entities (Details) - USD ($) $ in Millions				3 Months Ended	12 Months Ended
	Oct. 03, 2022	Jan. 31, 2022	Apr. 01, 2021	Sep. 30, 2022	Dec. 31, 2022	Sep. 30, 2022	Dec. 31, 2021	Dec. 31, 2020	Mar. 09, 2020	Jul. 18, 2017
Business Acquisition [Line Items]
G4S intercompany payments					$ 139.2		$ 45.1	$ (114.5)
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Restricted cash					438.5		376.4
Right-of-use assets, net					314.5		299.1
Goodwill					1,450.9		1,411.7	1,219.2
Transaction Costs					5.6		$ 6.5	19.3
NoteMachine
Business Acquisition [Line Items]
Acquisition date	Oct. 03, 2022
Percentage of shares acquired	100.00%
Annual revenues						$ 150.0
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Purchase consideration - cash paid					178.9
Contingent consideration	$ 14.8
Fair value of purchase consideration	193.7
Cash	6.8
Restricted cash	15.3
Accounts receivables	38.1
Other current assets	14.5
Property and Equipment, net	39.9
Intangible assets	84.2
Goodwill	62.7
Other noncurrent assets	5.1
Current liabilities	(50.2)
Noncurrent liabilities	(22.7)
Fair value of net assets acquired	$ 193.7
NoteMachine | Europe
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Goodwill					61.0
NoteMachine | North America
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Goodwill					2.0
Touchpoint 21 LLC
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Fair value of purchase consideration		$ 15.0
PAI
Business Acquisition [Line Items]
Acquisition date			Apr. 01, 2021
Percentage of shares acquired			100.00%
Annual revenues								$ 94.0
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Purchase consideration - cash paid			$ 215.5
Fair value of purchase consideration			215.5
Cash			12.3
Accounts receivables			7.3
Other current assets			5.5
Property and Equipment, net			14.6
Intangible assets			95.0
Goodwill			126.1		$ 2.0
Other noncurrent assets			4.5
Current liabilities			(41.2)
Noncurrent liabilities			(8.6)
Fair value of net assets acquired			215.5
G4Si
Business Acquisition [Line Items]
Percentage of shares acquired									100.00%
G4S
Business Acquisition [Line Items]
Percentage of shares acquired					100.00%
Annual revenues					$ 800.0
G4S intercompany payments					114.0
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Purchase consideration - cash paid					816.9
Contingent consideration					22.0
Liabilities assumed from seller					2.9
Indemnification assets					(15.9)
Fair value of purchase consideration					825.9
Cash					244.4
Restricted cash					30.1
Accounts receivables					145.8
Other current assets					30.8
Property and Equipment, net					123.8
Right-of-use assets, net					77.5
Intangible assets					207.0
Goodwill					534.1
Other noncurrent assets					16.2
Current liabilities					(296.3)
Lease liability					(68.1)
Noncurrent liabilities					(103.9)
Fair value of net assets acquired					941.4
Fair value of noncontrolling interest					(115.5)
G4S | Europe
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Goodwill					191.0
G4S | Rest of World
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Goodwill					340.0
G4S | Latin America
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Goodwill					$ 3.0
G4S Tranche III
Business Acquisition [Line Items]
Percentage of shares acquired					100.00%
Maco
Business Acquisition [Line Items]
Percentage of shares acquired										100.00%
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Severance Costs				$ 12.5
Customer relationships | NoteMachine
Business Acquisition [Line Items]
Remaining Amortization Period					13 years
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Intangible assets			47.0
Customer relationships | PAI
Business Acquisition [Line Items]
Remaining Amortization Period					10 years
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Intangible assets			60.0
Customer relationships | G4S
Business Acquisition [Line Items]
Remaining Amortization Period					15 years
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Intangible assets					$ 207.0
Developed technology | NoteMachine
Business Acquisition [Line Items]
Remaining Amortization Period					12 years
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Intangible assets			27.0
Developed technology | PAI
Business Acquisition [Line Items]
Remaining Amortization Period					12 years
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Intangible assets			26.0
Finite-lived trade names | NoteMachine
Business Acquisition [Line Items]
Remaining Amortization Period					5 years
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Intangible assets			10.0
Finite-lived trade names | PAI
Business Acquisition [Line Items]
Remaining Amortization Period					5 years
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net [Abstract]
Intangible assets			$ 9.0