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Business Segment Information (Details) - USD ($)
$ in Millions
 12 Months Ended
Dec. 31, 2023
Dec. 31, 2022
Dec. 31, 2021
Segment Reporting Information [Line Items]      
Total revenues $ 3,688.0 $ 3,358.8 $ 2,995.5
Operating expenses:      
Direct operating costs 2,222.8 2,018.2 1,900.2
Acquired contract cost impairment 38.6
Salaries and benefits 602.9 534.2 484.9
Selling, general and administrative 296.8 285.1 252.0
Depreciation and amortization 132.9 135.9 135.8
Total operating expenses 3,255.4 2,973.4 2,811.5
Operating income 432.6 385.4 184.0
Other income (expense)      
Interest income 15.2 2.0 0.7
Interest expense (55.6) (37.5) (38.3)
Foreign currency exchange gain (loss), net 8.0 (28.2) (10.8)
Other gains, net 0.2 0.9
Other expense, net (32.2) (62.8) (48.4)
Income before income taxes 400.4 322.6 135.6
Total Assets 5,894.4 5,403.6 4,744.3
Corporate Services, Eliminations and Other [Member]      
Segment Reporting Information [Line Items]      
Total revenues (7.9) (7.8) (8.1)
Operating expenses:      
Direct operating costs (7.9) (7.7) (8.1)
Acquired contract cost impairment    
Salaries and benefits 74.8 63.5 51.1
Selling, general and administrative 10.1 9.8 6.6
Depreciation and amortization 0.4 0.4 0.4
Total operating expenses 77.4 66.0 50.0
Operating income (85.3) (73.8) (58.1)
Other income (expense)      
Total Assets 326.3 283.8 205.8
EFT Processing [Member] | Operating Segments [Member]      
Segment Reporting Information [Line Items]      
Total revenues 1,058.3 924.2 591.2
Operating expenses:      
Direct operating costs 572.1 475.8 354.2
Acquired contract cost impairment    
Salaries and benefits 126.5 111.9 98.6
Selling, general and administrative 58.8 57.1 47.9
Depreciation and amortization 94.6 95.4 90.9
Total operating expenses 852.0 740.2 591.6
Operating income 206.3 184.0 (0.4)
Other income (expense)      
Total Assets 2,442.0 2,150.7 1,682.7
epay [Member] | Operating Segments [Member]      
Segment Reporting Information [Line Items]      
Total revenues 1,082.4 997.9 1,011.5
Operating expenses:      
Direct operating costs 819.1 753.2 760.9
Acquired contract cost impairment    
Salaries and benefits 91.1 81.8 79.5
Selling, general and administrative 39.1 36.0 39.6
Depreciation and amortization 6.9 6.2 8.5
Total operating expenses 956.2 877.2 888.5
Operating income 126.2 120.7 123.0
Other income (expense)      
Total Assets 1,204.9 1,173.3 1,234.1
Money Transfer Segment [Member] | Operating Segments [Member]      
Segment Reporting Information [Line Items]      
Total revenues 1,555.2 1,444.5 1,400.9
Operating expenses:      
Direct operating costs 839.5 796.9 793.2
Acquired contract cost impairment     38.6
Salaries and benefits 310.5 277.0 255.7
Selling, general and administrative 188.8 182.2 157.9
Depreciation and amortization 31.0 33.9 36.0
Total operating expenses 1,369.8 1,290.0 1,281.4
Operating income 185.4 154.5 119.5
Other income (expense)      
Total Assets $ 1,921.2 $ 1,795.8 $ 1,621.7