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 $k$ .