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