Sponsor contributed amount.

No definition available.

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Namespace Prefix:	airj_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Carrying value as of the balance sheet date of liabilities incurred (and for which invoices have typically been received) and payable to vendors for goods and services received that are used in an entity's business.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(15)(5))
-Publisher FASB
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Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
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-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(15)(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

+ Details

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Balance Type:	credit
Period Type:	instant

- Definition

Description of terms and conditions of option to terminate lessor's operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479773/842-30-50-3

+ Details

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

- Definition

Amount of general and administrative expense classified as other.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(b))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-1

+ Details

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Balance Type:	debit
Period Type:	duration

- Definition

Amount of cash outflow for fees classified as other.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 25
-Subparagraph (g)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-25

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of transactions with related party during the financial reporting period.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 850
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483326/850-10-50-1

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
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-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483326/850-10-50-3

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- 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/disclosureRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 13
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481990/310-10-45-13

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(c)(2)(i))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(c)(2)(ii))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-1

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(g)(3))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-1

+ Details

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Balance Type:	na
Period Type:	duration

- Definition

Fees paid to advisors who provide certain management support and administrative oversight services including the organization and sale of stock, investment funds, limited partnerships and mutual funds.

+ References

+ Details

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

- Details

Name:	us-gaap_RelatedPartyTransactionAxis=airj_ConsultancyAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RelatedPartyTransactionAxis=airj_XPDBMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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Balance Type:
Period Type:

- Details

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Period Type:

- Details

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- Details

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Related Party Transactions (Details) - USD ($)				3 Months Ended		6 Months Ended
Related Party Transactions (Details) - USD ($)	Dec. 09, 2021	Oct. 31, 2020	Jan. 01, 2019	Jun. 30, 2024	Jun. 30, 2023	Jun. 30, 2024	Jun. 30, 2023	Dec. 31, 2023
Related Party Transactions [Line Items]
Lease agreement terminate						March 14, 2024
Accounts payable				$ 0	$ 2,500	$ 0	$ 2,500
Sponsor fee	$ 20,000
Related party agreement	$ 540,000
Consultancy Agreement [Member]
Related Party Transactions [Line Items]
Accounts payable				0		0
XPDB [Member]
Related Party Transactions [Line Items]
Sponsor contributed amount								$ 900,000
Lease Agreement [Member]
Related Party Transactions [Line Items]
Accounts payable				0		0		$ 2,000
Consultancy Agreement [Member]
Related Party Transactions [Line Items]
General and administrative expenses				20,000	60,000	80,000	120,000
Office Services Agreement [Member]
Related Party Transactions [Line Items]
Monthly payment		$ 5,000
General and administrative expenses				$ 5,000	$ 15,000	$ 30,000	$ 30,000
Chief Executive Officer [Member]
Related Party Transactions [Line Items]
Monthly payment			$ 20,000