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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