# More splitting

Computer Science Level pending

Consider the shape in the problem Splitting Them Up; that is, the irregular hexagon given by the points $$(0,0)$$, $$(0,6)$$, $$(6,6)$$, $$(6,2)$$, $$(12,2)$$, $$(12,0)$$. Let $$f(k)$$ be equal to the sum of the slopes of the lines through $$(0,0)$$ which divide the figure into $$k$$ equal areas ($$f(2) = \frac{2}{3}$$, $$f(4) = \frac{7}{3}$$). If $$f(1000) = \frac{m}{n}$$, where $$m$$ and $$n$$ are co-prime, and $$m ≡ q\space(mod\space n)$$, find the sum of the digits of q.

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