Fair Value of Financial Instruments - Schedule of Long-Term Debt (Details) - USD ($) $ in Thousands	Jun. 30, 2025	Dec. 31, 2024
Level 2 \| Carrying Value \| Fair Value, Recurring
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	$ (5,123)	$ 0
Level 2 \| Fair Value \| Fair Value, Recurring
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	(5,123)	0
Level 2 \| Swap contracts \| Carrying Value \| Fair Value, Recurring
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	(3,283)	0
Level 2 \| Swap contracts \| Carrying Value \| Fair Value, Recurring \| Other current assets
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	9	0
Level 2 \| Swap contracts \| Carrying Value \| Fair Value, Recurring \| Non-current liability
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	(3,292)	0
Level 2 \| Swap contracts \| Fair Value \| Fair Value, Recurring
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	(3,283)	0
Level 2 \| Swap contracts \| Fair Value \| Fair Value, Recurring \| Other current assets
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	9	0
Level 2 \| Swap contracts \| Fair Value \| Fair Value, Recurring \| Non-current liability
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	(3,292)	0
Level 2 \| Collar contracts \| Carrying Value \| Fair Value, Recurring
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	(1,840)	0
Level 2 \| Collar contracts \| Carrying Value \| Fair Value, Recurring \| Non-current liability
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	(1,604)	0
Level 2 \| Collar contracts \| Carrying Value \| Fair Value, Recurring \| Current liability
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	(236)	0
Level 2 \| Collar contracts \| Fair Value \| Fair Value, Recurring
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	(1,840)	0
Level 2 \| Collar contracts \| Fair Value \| Fair Value, Recurring \| Non-current liability
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	(1,604)	0
Level 2 \| Collar contracts \| Fair Value \| Fair Value, Recurring \| Current liability
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total collar contracts	(236)	0
Senior notes \| Level 2 \| Carrying Value \| Fair Value, Recurring
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt fair value	638,859	638,075
Senior notes \| Level 2 \| Fair Value \| Fair Value, Recurring
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt fair value	$ 672,750	$ 660,972
Senior notes \| 6.875% senior notes
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Interest rate of debt (as a percent)	6.875%	6.875%
Revolving Credit Facility \| Level 2 \| Carrying Value \| Fair Value, Recurring
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt fair value	$ 85,000	$ 0
Revolving Credit Facility \| Level 2 \| Fair Value \| Fair Value, Recurring
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt fair value	83,725	0
Term Loan \| Level 2 \| Carrying Value \| Fair Value, Recurring
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt fair value	935,029	835,412
Term Loan \| Level 2 \| Fair Value \| Fair Value, Recurring
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt fair value	$ 948,810	$ 853,174

Contractual interest rate for funds borrowed, under the debt agreement.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22)(a)(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

+ Details

Name:	us-gaap_DebtInstrumentInterestRateStatedPercentage
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Fair values as of the balance sheet date of the net amount of all assets and liabilities resulting from contracts that meet the criteria of being accounted for as derivative instruments.

+ References

+ Details

Name:	us-gaap_DerivativeAssetsLiabilitiesAtFairValueNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
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

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Name Accounting Standards Codification
-Section 55
-Paragraph 10
-SubTopic 10
-Topic 825
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482881/825-10-55-10

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 11
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-11

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 11
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-11

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 10
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-10

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 13
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-13

Reference 6: http://www.xbrl.org/2003/role/exampleRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482881/825-10-55-12

+ Details

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

- Definition

The fair value amount of long-term debt whether such amount is presented as a separate caption or as a parenthetical disclosure. Additionally, this element may be used in connection with the fair value disclosures required in the footnote disclosures to the financial statements. The element may be used in both the balance sheet and disclosure in the same submission.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Name Accounting Standards Codification
-Section 55
-Paragraph 10
-SubTopic 10
-Topic 825
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482881/825-10-55-10

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 28
-Subparagraph (c)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-28

Reference 6: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 11
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-11

Reference 7: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 11
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-11

Reference 8: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 10
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-10

Reference 9: http://www.xbrl.org/2003/role/exampleRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482881/825-10-55-12

Reference 10: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

+ Details

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

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel2Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByMeasurementBasisAxis=us-gaap_CarryingReportedAmountFairValueDisclosureMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByMeasurementFrequencyAxis=us-gaap_FairValueMeasurementsRecurringMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByMeasurementBasisAxis=us-gaap_EstimateOfFairValueFairValueDisclosureMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=us-gaap_SwapMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BalanceSheetLocationAxis=us-gaap_OtherCurrentAssetsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BalanceSheetLocationAxis=us-gaap_OtherNoncurrentLiabilitiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=cghp_CollarMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BalanceSheetLocationAxis=us-gaap_OtherCurrentLiabilitiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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

- Details

Name:	us-gaap_DebtInstrumentAxis=cghp_A6.875SeniorNotesDueJuly152032Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_LineOfCreditMember
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: