Cloud Computing Arrangements (Details) - USD ($)	3 Months Ended		6 Months Ended
	Jul. 31, 2020	Jul. 31, 2019	Jul. 31, 2020	Jul. 31, 2019	Jan. 31, 2020
Capitalized Contract Cost [Line Items]
Capitalized contract cost	$ 88,300,000		$ 88,300,000		$ 98,800,000
Amortization expense	23,600,000	$ 25,500,000	46,400,000	$ 50,200,000
Cloud-based Software Hosting Arrangements
Capitalized Contract Cost [Line Items]
Capitalized contract cost	44,300,000		44,300,000		22,300,000
Accumulated amortization	2,900,000		2,900,000		$ 1,200,000
Amortization expense	$ 800,000	$ 0	$ 1,700,000	$ 0