A string $A = a_1 a_2 \cdots a_n$ of length $n$ is a concatenation of $n$ characters $a_1, a_2, \ldots, a_n$, and its length is denoted by $|A|$. Similarly, the concatenation of two strings $A = a_1 a_2 \cdots a_n$ and $B = b_1 b_2 \cdots b_m$ is $a_1 a_2 \cdots a_n b_1 b_2 \cdots b_m$, denoted by $A + B$.

The edit distance between two strings $A = a_1 a_2 \cdots a_n$ and $B = b_1 b_2 \cdots b_n$ of the same length $n$ is the number of indices $i$ such that $a_i \neq b_i$.

We call the string $A$ formed by the first $k$ characters of another string $B$ ($k \leq |B|$) as the $k$-th prefix of $B$, and a string $P$ as an almost prefix of another string $Q$ if $|P| \leq |Q|$ and the edit distance between $P$ and the $|P|$-th prefix of $Q$ is at most $1$.

Given two strings $S$ and $T$ consisting of lowercase English letters, you are asked to find all ways to split $S$ into many parts such that each part is a non-empty almost prefix of string $T$, and then report the sum of the squared number of parts of all ways in modulo $998244353$. More formally, let $S = P_1 + P_2 + \ldots + P_n$ be a possible way, you are asked to calculate $$\left(\sum_{\substack{S = P_1 + P_2 + \ldots + P_n \\ \forall_{i=1, 2, \ldots, n} P_i\text{ is an almost prefix of }T}}{n^2}\right) \bmod 998\,244\,353\text{.}$$