Given an one-indexed array with $$$n$$$ pairwise distinct elements, find the number of pairs $$$(l, r)$$$ ($$$1 \leq l \leq r \leq n$$$) such that the inversion number of $$$(a[l], a[l+1], ..., a[r])$$$ is odd. $$$(a[l], a[l+1], ..., a[r])$$$ is a continuous subarray of $$$a$$$ that starts from $$$l$$$ and ends at $$$r$$$ (both inclusive).

For example, $$$a=[3, 2, 1]$$$, the answer is $$$3$$$: $$$(1, 2), (2, 3), (1, 3)$$$.