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It depends on the resolution. If the piece is in C major, you can borrow Ab from C minor or G# from A minor (which is the relative minor of C major). The Ab and G# are enharmonic equivalents of each other, but Ab generally goes down to G (dominant of C), while G# goes up to A (tonic of relative minor).
Although I've seen many scores where a sharpened note goes downwards (or flatted upwards), so you are free to renotate accidentals if you have a good reason.
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