i find myself spending most of my time implementing rather than actually solving the problem, and this cuts my solving time by half if not more usually, any advice on how to improve implementation speed?

given a set of $$$n \le 10^5$$$ range $$$[x_i, 2 \times x_i]$$$ and $$$\sum x_i \le 10^5$$$ determine the number of arrays $$$a$$$ such that $$$x_i \le a_i \le 2 \times x_i$$$ and all the elements in $$$a$$$ are pairwise distinct