Given n strings containing only lowercase letters, and the \(i_{th}\) string is \(s_i\). \(f(s,t)\) represent the maximum i satisfy \(s_{1...i} = t_{|t|-i+1...|t|}\), and \(f(s,t) = 0\) if such i doesn't exist. Please calculate:\(\sum_{i=1}^n\sum_{j=1}^n(i \cdot j \cdot f(s_i,s_j)) \ (\bmod 998244353)\).