Brain-Flak, 96 bytes

{<<>>(({})<<>>[(([{}<<>>]))]){((<<[[]]>>))}{}{}{}{}<<>>}<<>>{{{}{}{}{}{}}((<<>>){{}{}}){{{}}}}{}

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Outputs nothing if the input is perfectly paired, and 0 otherwise.

Brain-Flak, 96 bytes

{<<>>(({})<<>>[(([{}<<>>]))]){((<<[[]]>>))}{}{}{}{}<<>>}<<>>{{{}{}{}{}{}}((<<>>){{}{}}){{{}}}}{}

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Outputs nothing if the input is perfectly paired, and 0 otherwise.

Non-perfectly paired (original) version:

{<>(({})<>[({}<>)]){((<()>))}{}{}{}<>}<>{((<>))}{}

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