\[ S = \{1, 7, 13, 19, 25, \ldots , 199\}. \]

Find the least value \(n\) such that for any subset \(T \subset S\) with \(n\) elements, we are guaranteed of finding two distinct elements of \(T\) that sum to 206.

Clarification: The elements of \(S\) are all integers of the form \(6k + 1\) for all integers \(k\) from \(0\) to \(33\) inclusive.

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