Find the smallest positive integer n that satisfies the following: We can color each positive integer with one of n colors such that the equation w + 6x = 2y + 3z has no solutions in positive integers with all of w, x, y, z the same color. w, x, y, z does not have to be distinct. For example, 5 and 7 must be different colors because (w, x, y, z) = (5, 5, 7, 7) is a solution to the equation.
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