Name:	cmiii_SignificantAccountingPoliciesDetailsLineItems
Namespace Prefix:	cmiii_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

Number of new units issued during the period.

No definition available.

Name:	cmiii_UnitsIssuedDuringPeriodSharesNewIssues
Namespace Prefix:	cmiii_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

The amount of working capital deficit.

No definition available.

Name:	cmiii_WorkingCapitalDeficit
Namespace Prefix:	cmiii_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

The amount of working capital loans.

No definition available.

Name:	cmiii_WorkingCapitalLoans
Namespace Prefix:	cmiii_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

Amount of currency on hand as well as demand deposits with banks or financial institutions. Includes other kinds of accounts that have the general characteristics of demand deposits. Excludes cash and cash equivalents within disposal group and discontinued operation.

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-4

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482913/230-10-50-8

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477657/942-210-S45-1

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478478/942-210-S50-1

Reference 6: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1

Reference 7: http://www.xbrl.org/2003/role/exampleRef
-Topic 944
-SubTopic 605
-Name Accounting Standards Codification
-Section 55
-Paragraph 14
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477548/944-605-55-14

Reference 8: http://www.xbrl.org/2003/role/exampleRef
-Topic 944
-SubTopic 605
-Name Accounting Standards Codification
-Section 55
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477548/944-605-55-11

Reference 9: http://www.xbrl.org/2003/role/exampleRef
-Topic 852
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 10
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481372/852-10-55-10

Reference 10: http://www.xbrl.org/2003/role/exampleRef
-Topic 946
-SubTopic 830
-Name Accounting Standards Codification
-Section 55
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479168/946-830-55-12

Reference 11: http://www.xbrl.org/2003/role/disclosureRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(2))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

Reference 12: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-04(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479170/946-210-S99-1

Reference 13: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section 45
-Paragraph 21
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477796/946-210-45-21

Reference 14: http://www.xbrl.org/2003/role/disclosureRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 20
-SubTopic 210
-Topic 946
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477796/946-210-45-20

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

The cash inflow associated with the amount received from entity's first offering of stock to the public.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 14
-Subparagraph (a)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-14

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

The cash inflow associated with the amount received from entity's raising of capital via private rather than public placement.

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

The number of shares issued or sold by the subsidiary or equity method investee per stock transaction.

No definition available.

Name:	us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

Per share amount received by subsidiary or equity investee for each share of common stock issued or sold in the stock transaction.

No definition available.

Name:	us-gaap_SaleOfStockPricePerShare
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

Carrying value as of the balance sheet date, including the current and noncurrent portions, of collateralized debt obligations (with maturities initially due after one year or beyond the operating cycle, if longer). Such obligations include mortgage loans, chattel loans, and any other borrowings secured by assets of the borrower.

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477657/942-210-S45-1

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478478/942-210-S50-1

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(16))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 9
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480657/210-10-S50-9

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 6: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(16)(a)(2))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

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

Number of shares (or other type of equity) forfeited during the period.

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section S45
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480100/505-10-S45-3

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section S45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480100/505-10-S45-2

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(28))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 6: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480657/210-10-S50-11

Name:	us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensationForfeited
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

Name:	us-gaap_SubsequentEventTypeAxis=us-gaap_SubsequentEventMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap_RelatedPartyTransactionsByRelatedPartyAxis=cmiii_SponsorMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_IPOMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_OverAllotmentOptionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_PrivatePlacementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: