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Summary of Significant Accounting Policies - Warrant Instruments (Details)	Dec. 31, 2025 shares
Summary of Significant Accounting Policies
Warrants outstanding	11,666,666
Public Warrant
Summary of Significant Accounting Policies
Warrants outstanding	7,666,666
Private placement warrants
Summary of Significant Accounting Policies
Warrants outstanding	4,000,000

X

- 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

No definition available.

+ Details

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

X

- Definition

Number of warrants or rights outstanding.

+ References

No definition available.

+ Details

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

X

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=adac_PublicWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=adac_PrivatePlacementWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: