The Legendary Huron is planning the construction of $$$n$$$ skyscrapers on a major street in Huronland that runs from west to east. The final skyline will be an array of positive integers $$$A = [a_1, a_2, \dots, a_n]$$$, where $$$a_i$$$ is the height of the $$$i$$$-th skyscraper from the west. The order of construction and the heights are yet to be decided. For safety reasons, only one skyscraper can be built at a time.

After all skyscrapers are completed, the Tourism Office will promote each one using a panoramic photo. For each skyscraper $$$i$$$, the office selects the longest contiguous segment of skyscrapers that includes $$$i$$$, such that the maximum height in the segment is $$$a_i$$$, and takes a photo of such segment. A photo is considered successful if:

1. Skyscraper $$$i$$$ is the last one built among all skyscrapers in the photo.
2. Let $$$k$$$ be the number of skyscrapers in the segment and $$$d$$$ the absolute difference between the maximum and second maximum heights in it. Then $$$d$$$ must satisfy $$$l_k \leq d \leq r_k$$$, where $$$l_k$$$ and $$$r_k$$$ are input integers. If the segment contains only one skyscraper, the second maximum is considered $$$0$$$. For example, the segment $$$[4, 9, 1, 3]$$$ has $$$d = 5$$$; the segment $$$[2, 1, 2]$$$ has $$$d = 0$$$; and the segment $$$[4]$$$ has $$$d = 4$$$.

The Tourism Office asks the Legendary Huron to assign positive heights and a construction order so that all $$$n$$$ photos are successful. Two plans are different if the heights or construction order differ. Determine the number of such valid plans, modulo $$$998244353$$$.