Debt - Narrative (Details)	Mar. 31, 2020 USD ($)
Term Loan A \| Secured debt
Debt Instrument [Line Items]
Principal amount	$ 1,750,000,000
Term Loan B Facility \| Secured debt
Debt Instrument [Line Items]
Principal amount	491,000,000
Debt issuance costs	27,000,000
Revolving Credit Facility and Term Loans \| Secured debt
Debt Instrument [Line Items]
Debt issuance costs	7,000,000
Maximum borrowing capacity	750,000,000
Revolving Credit Facility \| Secured debt
Debt Instrument [Line Items]
Maximum borrowing capacity	$ 700,000,000
Revolving Credit Facility and Term Loan A \| Maximum \| Period 1
Debt Instrument [Line Items]
Debt covenant, ratio of indebtedness to EBITDA	4.50
Revolving Credit Facility and Term Loan A \| Maximum \| Period 2
Debt Instrument [Line Items]
Debt covenant, ratio of indebtedness to EBITDA	4.25
Revolving Credit Facility and Term Loan A \| Maximum \| Period 3
Debt Instrument [Line Items]
Debt covenant, ratio of indebtedness to EBITDA	4.50
Revolving Credit Facility and Term Loan A \| Minimum
Debt Instrument [Line Items]
Debt covenant, consideration transferred threshold amount	$ 100,000,000
Debt covenant, ratio of EBITDA to interest expense	3.00

Debt Covenant, Business Combination Consideration Transferred Threshold

No definition available.

Name:	prsp_DebtCovenantBusinessCombinationConsiderationTransferredThreshold
Namespace Prefix:	prsp_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Debt Covenant, Ratio Of Earnings Before Interest, Tax, Depreciation And Amortization To Interest Expense

+ References

No definition available.

+ Details

Name:	prsp_DebtCovenantRatioOfEarningsBeforeInterestTaxDepreciationAndAmortizationToInterestExpense
Namespace Prefix:	prsp_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	instant

- Definition

Debt Covenant, Ratio Of Indebtedness To Earnings Before Interest, Tax, Depreciation And Amortization

+ References

No definition available.

+ Details

Name:	prsp_DebtCovenantRatioOfIndebtednessToEarningsBeforeInterestTaxDepreciationAndAmortization
Namespace Prefix:	prsp_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	instant

- Definition

Face (par) amount of debt instrument at time of issuance.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=114775744&loc=d3e28551-108399

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 55
-Paragraph 8
-URI http://asc.fasb.org/extlink&oid=114775985&loc=d3e28878-108400

+ Details

Name:	us-gaap_DebtInstrumentFaceAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount, before accumulated amortization, of debt issuance costs. Includes, but is not limited to, legal, accounting, underwriting, printing, and registration costs.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 3
-URI http://asc.fasb.org/extlink&oid=114775744&loc=d3e28555-108399

+ Details

Name:	us-gaap_DeferredFinanceCostsGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(b),22(b))
-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

+ Details

Name:	us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	us-gaap_DebtInstrumentAxis=prsp_TermLoanAMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_SecuredDebtMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=prsp_TermLoanBDue2025Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=prsp_RevolvingCreditFacilityDue2023Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=us-gaap_RevolvingCreditFacilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=prsp_RevolvingCreditFacilityAndTermLoanAMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	prsp_DebtCovenantPeriodAxis=prsp_DebtCovenantPeriodOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	prsp_DebtCovenantPeriodAxis=prsp_DebtCovenantPeriodTwoMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	prsp_DebtCovenantPeriodAxis=prsp_DebtCovenantPeriodThreeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: