Lisa wrote a program to solve the Longest Common Substring problem. She then used the program to find, for some two strings $s$ and $t$ consisting of characters `\t{0}' and `\t{1}', the longest string $w$ that is a substring of both $s$ and $t$. If there were multiple such longest strings, she found an arbitrary one.

Notably, the length of $w$ Lisa found was very small~--- at most 3.

Lisa remembers $n$ (the length of $s$), $m$ (the length of $t$), and $w$, but she doesn't remember strings $s$ and $t$ themselves. Now she wonders how many pairs of strings $s$ and $t$ exist such that they have lengths $n$ and~$m$, respectively, consist of characters `\t{0}' and `\t{1}', and have $w$ as one of their longest common substrings.

Help Lisa and find this number of pairs modulo $998\,244\,353$. Note that if $n = m$ and $s \ne t$, pairs $(s, t)$ and $(t, s)$ are considered distinct.