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Recapitalization (As Restated) (Details) - Schedule of Common Stock Issued | Mar. 31, 2024 shares
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Schedule of Common Stock Issued [Line Items] |
PIPE subscription | 588,235
Business Combination Class A common stock | 8,001,930
Legacy Montana Shares | 45,821,482
Class A and B Common Stock immediately after the Business Combination | 53,823,412
Less: Redemption of XPDB Class A common stock | (10,381,983)
Class A common stock of XPDB | 226,195
Class A Common Stock [Member] |
Schedule of Common Stock Issued [Line Items] |
XPDB Class common stock, outstanding prior to the Business Combination | 10,608,178
Class B Common Stock [Member] |
Schedule of Common Stock Issued [Line Items] |
XPDB Class common stock, outstanding prior to the Business Combination | 7,187,500

X
- Definition Number of business combination class A common stock. + References No definition available. + Details
Name: | airj_BusinessCombinationClassACommonStock
Namespace Prefix: | airj_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | instant

X
- Definition Number of cass A common stock of XPDB. . + References No definition available. + Details
Name: | airj_ClassACommonStockOfXPDB
Namespace Prefix: | airj_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | instant

X
- Definition Number ofclass common stock, outstanding prior to the business combination. + References No definition available. + Details
Name: | airj_ClassCommonStockOutstandingPriorToTheBusinessCombination
Namespace Prefix: | airj_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | instant

X
- Definition Number of stock immediately after the business combination. + References No definition available. + Details
Name: | airj_CommonStockImmediatelyAfterTheBusinessCombination
Namespace Prefix: | airj_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | instant

X
- Definition Number of Legacy montana shares in dollars. + References No definition available. + Details
Name: | airj_LegacyMontanaSharesinDollars
Namespace Prefix: | airj_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | instant

X
- Definition Number of PIPE subscription. + References No definition available. + Details
Name: | airj_PIPESubscription
Namespace Prefix: | airj_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | instant

X
- Definition Number of Redemption of XPDB class A common stock. + References No definition available. + Details
Name: | airj_RedemptionOfXPDBClassACommonStock
Namespace Prefix: | airj_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | instant

X
- References No definition available. + Details
Name: | airj_ScheduleOfCommonStockIssuedLineItems
Namespace Prefix: | airj_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Details
Name: | us-gaap_StatementClassOfStockAxis=us-gaap_CommonClassAMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_StatementClassOfStockAxis=us-gaap_CommonClassBMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |