# Diagonals of 2015-gon

The set $$S$$ of all diagonals of a $$2015-$$gon is partitioned into $$k$$ sets, $$S_1, S_2, \ldots, S_k$$, so that, for every pair of distinct indices $$i$$ and $$j$$, some diagonal in $$S_i$$ crosses some diagonal in $$S_j$$; that is, the two diagonals share an interior point.

Find the maximum value of $$k$$.

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