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If $$N$$ is the number of real solutions of $$x$$ in the interval $$[0, \pi]$$ that satisfy the equation$$\sin^{-1} \left ( \sin (2014x) \right) = \cos^{-1} \left ( \cos (x) \right )$$

And $$N= 2^A \times 3^B \times 5^C \times 7^D$$ for non-negative integers $$A,B,C,D$$. What is the value of $$A+B+C+D$$?

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