# Flying In The Middle Of Nowhere

Geometry Level 5

In the diagram, triangle $$ABC$$ inscribed a circle with center $$O$$.

Draw altitudes $$AD, BE, CF$$ of the triangle $$ABC$$ ($$D, E, F$$ lies on the sides). The altitudes concur at orthocenter $$H$$.

$$DE$$ intersects $$CF$$ at $$M$$. $$DF$$ intersects $$BE$$ at $$N$$.

A line passes through $$A$$ and perpendicular to $$MN$$ intersects $$OH$$ at point $$K$$.

If $$S_{ABC} = 2016^{2017}, P_{DEF} = 1344^{2016}$$, length of $$KD$$ can be written as:

$KD=\dfrac{p_1^{\alpha_1} \times p_2^{\alpha_2}}{p_3^{\alpha_3}}$

where $$p_1, p_2$$ and $$p_3$$ are 3 distinct primes.

Find $$\displaystyle \sum_{x=1}^3 (p_x\alpha_x)$$.

Clarification: $$S$$ and $$P$$ denote the area and perimeter of the figure, respectively.

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