n/a

No definition available.

Name:	amch_ComponentsOfRecordedAndUnrecognizedStockBasedCompensationExpenseRollforward
Namespace Prefix:	amch_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of expense for award under share-based payment arrangement. Excludes amount capitalized.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 14.F)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479830/718-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (h)(1)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_AllocatedShareBasedCompensationExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of cost not yet recognized for nonvested award under share-based payment arrangement.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

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

- Definition

Weighted-average period over which cost not yet recognized is expected to be recognized for award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

+ Details

Name:	us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of shares authorized for issuance under share-based payment arrangement.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_GranteeStatusAxis=srt_DirectorMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_PlanNameAxis=amch_EquityIncentivePlan2024Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=amch_EquityClassifiedAwardsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=amch_PerformanceStockUnitsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=us-gaap_RestrictedStockUnitsRSUMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=amch_LiabilityClassifiedAwardsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=amch_RestrictedAndPerformanceStockUnitExpenseMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

STOCKHOLDERS' DEFICIT - Stock-based compensation (Details) - USD ($) shares in Millions, $ in Millions	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022	Jun. 05, 2024
Stock Based Compensation Expense
Stock-based compensation expense	$ 22.0	$ 42.5	$ 22.5
Total estimated unrecognized compensation cost related to nonvested stock-based compensation arrangements	$ 12.0
Weighted average period recognized	1 year 3 months 29 days
Board of director stock award expense
Stock Based Compensation Expense
Stock-based compensation expense	$ 1.0	0.9	0.8
2024 Equity Incentive Plan
Stock Based Compensation Expense
Number of shares authorized				25.0
Equity Classified Awards
Stock Based Compensation Expense
Stock-based compensation expense	21.9	42.1	22.5
Performance stock unit expense
Stock Based Compensation Expense
Stock-based compensation expense	6.5	6.7	8.4
Restricted stock unit expense
Stock Based Compensation Expense
Stock-based compensation expense	12.3	14.3	$ 13.3
Liability classified awards
Stock Based Compensation Expense
Stock-based compensation expense	0.1	0.4
Restricted and performance stock unit expense
Stock Based Compensation Expense
Stock-based compensation expense	$ 0.1	$ 0.4