Your second requirement is not totally clear. For example, is it okay for the midpoint to have one integer value and one non-integer value, like (4,4.5)? or do both need to be non-integer? Just looking at each line you can tell that at least x OR y in every pair is non-integer. If both need to be non-integer, I'll need to keep working.
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Good question, either x, or y being non-integer is sufficient for the midpoints to be valid so (4, 4.5) would be fine.