# Non-Splittable Subsets

Let $$S$$ be a set of three integers chosen from $$N = \{1,2,\ldots,2012\}$$. We say that $$S$$ is 4-splittable if there is an $$n \in N \setminus S$$ such that $$S \cup \{n\}$$ can be partitioned into 2 sets such that the sum of each set is the same. How many 3-element subsets of $$N$$ are not 4-splittable?

Details and assumptions

You can refer to Set Notation for the definition of $$N \setminus S$$.

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