On the Domino Train

Consider a set of $$\frac{ N (N+1) } { 2 }$$ dominos which have faces of values 1 to N.
A train of dominos is a straight line of them, in which any 2 touching dominos display the same value.
Let $$F(N)$$ be the minimum numbers of trains that are needed to use up all of these dominos. What is the value of $$F(2016)$$?

As an explicit example, $$F(3) = 1$$ because we have the train listed in the above image.

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