Other Non-Current Assets - Schedule of Other Non-Current Assets (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Mar. 31, 2020	Mar. 31, 2019	Mar. 31, 2020	Mar. 31, 2019	Jun. 30, 2019
Deferred Costs, Capitalized, Prepaid, and Other Assets Disclosure [Abstract]
Deferred client conversion and start-up costs	$ 385.7		$ 385.7		$ 254.7
ROU Assets	297.6		297.6
Long-term investments	134.3		134.3		100.4
Deferred sales commissions costs	92.3		92.3		95.5
Contract assets	77.5		77.5		47.5
Deferred data center costs	25.7		25.7		29.0
Long-term broker fees	35.5		35.5		35.3
Other	34.2		34.2		30.6
Total	1,082.6		1,082.6		$ 593.1
Amortization of deferred sales commissions and set-up costs	$ 20.0	$ 16.3	$ 56.2	$ 48.9