673 O(nlogn) possible?

In [673 Solution](https://github.com/lzl124631x/LeetCode/tree/master/leetcode/673.%20Number%20of%20Longest%20Increasing%20Subsequence) you have an O(n^2) solution. However in the [discussion](https://leetcode.com/problems/number-of-longest-increasing-subsequence/discuss/?currentPage=1&orderBy=most_votes&query=) there are several posts claiming to achieve O(nlogn). What are your thoughts?