On the Domino Train

Probability Level 5

Consider a set of N(N+1)2 \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)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) F(2016) ?

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


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