A Special Addition Chain

For n=375494703 holds: 34 = l(2n) < l(n) = 35.

Using the window-method on the binary representation 10110011000011001100000101111₂ of this value n, it is easy to construct a star chain of length 35 by hand for n.
But how to construct a shorter chain for the twice of this number? Finally, we must prove, that l(n)=35 is indeed minimal. This is hard! To be precise, we should also show that l(2n)=34 is smallest possible.