Inequality Satisfying Subsequences

A sequence of three positive integers $[a, b, c]$ is called a triangle if $a+b>c$ holds when reordered such that $a \leq b \leq c$.

A sequence of positive integers is triangle-free if no subsequence of length $3$ forms a triangle.

Given a sequence of positive integers $L$, count how many non-empty subsequences of $L$ are triangle-free. As the answer may be very large, you are only required to find the value modulo $998 \, 244 \, 353$.

The first line contains a single integer $n$ ($1 \leq n \leq 7\,000$) --- the size of the input sequence.

The second line contains $n$ integers $L_1, L_2, \cdots, L_n$ ($1 \leq L_i \leq 10^9$) --- the elements of the sequence $L$.

Output the number of non-empty triangle-free subsequences modulo $998 \, 244 \, 353$ on one line.