# Daniel's path sums

For integers $$n > 2$$, let $$G_n$$ be a complete graph on $$n$$ vertices such that each vertex is labeled by a distinct number $$1,2,3,\cdots,n$$, and each edge is labeled by the sum of its endpoint labels. Let $$f(G_n)$$ be the minimum sum of edge labels in any path that touches every vertex in $$G_n$$ exactly once.

How many values of $$n$$ satisfy $f(G_n)\equiv 2013\pmod{n}?$

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